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A History of Science — Volume 2

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Title: A History of Science — Volume 2

Author: Henry Smith Williams
        Edward Huntington Williams


        
Release date: April 1, 1999 [eBook #1706]
                Most recently updated: November 17, 2009

Language: English

Other information and formats: www.gutenberg.org/ebooks/1706

Credits: Produced by Charles Keller, and David Widger


*** START OF THE PROJECT GUTENBERG EBOOK A HISTORY OF SCIENCE — VOLUME 2 ***




Produced by Charles Keller





A HISTORY OF SCIENCE

BY HENRY SMITH WILLIAMS, M.D., LL.D.

ASSISTED BY EDWARD H. WILLIAMS, M.D.

IN FIVE VOLUMES

VOLUME II.



CONTENTS

   BOOK II

   CHAPTER I. SCIENCE IN THE DARK AGE

   CHAPTER II. MEDIAEVAL SCIENCE AMONG THE ARABIANS

   CHAPTER III. MEDIAEVAL SCIENCE IN THE WEST

   CHAPTER IV. THE NEW COSMOLOGY--COPERNICUS TO KEPLER AND GALILEO

   CHAPTER V. GALILEO AND THE NEW PHYSICS

   CHAPTER VI. TWO PSEUDO-SCIENCES--ALCHEMY AND ASTROLOGY

   CHAPTER VII. FROM PARACELSUS TO HARVEY

   CHAPTER VIII. MEDICINE IN THE SIXTEENTH AND SEVENTEENTH CENTURIES

   CHAPTER IX. PHILOSOPHER-SCIENTISTS AND NEW INSTITUTIONS OF
   LEARNING

   CHAPTER X. THE SUCCESSORS OF GALILEO IN PHYSICAL SCIENCE

   CHAPTER XI. NEWTON AND THE COMPOSITION OF LIGHT

   CHAPTER XII. NEWTON AND THE LAW OF GRAVITATION

   CHAPTER XIII. INSTRUMENTS OF PRECISION IN THE AGE OF NEWTON

   CHAPTER XIV. PROGRESS IN ELECTRICITY FROM GILBERT AND VON
   GUERICKE TO FRANKLIN

   CHAPTER XV. NATURAL HISTORY TO THE TIME OF LINNAEUS

   APPENDIX




A HISTORY OF SCIENCE




BOOK II. THE BEGINNINGS OF MODERN SCIENCE

The studies of the present book cover the progress of science from the
close of the Roman period in the fifth century A.D. to about the middle
of the eighteenth century. In tracing the course of events through so
long a period, a difficulty becomes prominent which everywhere besets
the historian in less degree--a difficulty due to the conflict between
the strictly chronological and the topical method of treatment. We must
hold as closely as possible to the actual sequence of events, since,
as already pointed out, one discovery leads on to another. But, on the
other hand, progressive steps are taken contemporaneously in the various
fields of science, and if we were to attempt to introduce these
in strict chronological order we should lose all sense of topical
continuity.

Our method has been to adopt a compromise, following the course of a
single science in each great epoch to a convenient stopping-point, and
then turning back to bring forward the story of another science. Thus,
for example, we tell the story of Copernicus and Galileo, bringing the
record of cosmical and mechanical progress down to about the middle
of the seventeenth century, before turning back to take up the
physiological progress of the fifteenth and sixteenth centuries. Once
the latter stream is entered, however, we follow it without interruption
to the time of Harvey and his contemporaries in the middle of the
seventeenth century, where we leave it to return to the field of
mechanics as exploited by the successors of Galileo, who were also the
predecessors and contemporaries of Newton.

In general, it will aid the reader to recall that, so far as
possible, we hold always to the same sequences of topical treatment of
contemporary events; as a rule we treat first the cosmical, then the
physical, then the biological sciences. The same order of treatment will
be held to in succeeding volumes.

Several of the very greatest of scientific generalizations are developed
in the period covered by the present book: for example, the Copernican
theory of the solar system, the true doctrine of planetary motions,
the laws of motion, the theory of the circulation of the blood, and the
Newtonian theory of gravitation. The labors of the investigators of the
early decades of the eighteenth century, terminating with Franklin's
discovery of the nature of lightning and with the Linnaean
classification of plants and animals, bring us to the close of our
second great epoch; or, to put it otherwise, to the threshold of the
modern period.




I. SCIENCE IN THE DARK AGE

An obvious distinction between the classical and mediaeval epochs may be
found in the fact that the former produced, whereas the latter failed
to produce, a few great thinkers in each generation who were imbued with
that scepticism which is the foundation of the investigating spirit; who
thought for themselves and supplied more or less rational explanations
of observed phenomena. Could we eliminate the work of some score or so
of classical observers and thinkers, the classical epoch would seem as
much a dark age as does the epoch that succeeded it.

But immediately we are met with the question: Why do no great original
investigators appear during all these later centuries? We have already
offered a part explanation in the fact that the borders of civilization,
where racial mingling naturally took place, were peopled with
semi-barbarians. But we must not forget that in the centres of
civilization all along there were many men of powerful intellect.
Indeed, it would violate the principle of historical continuity to
suppose that there was any sudden change in the level of mentality of
the Roman world at the close of the classical period. We must assume,
then, that the direction in which the great minds turned was for
some reason changed. Newton is said to have alleged that he made his
discoveries by "intending" his mind in a certain direction continuously.
It is probable that the same explanation may be given of almost every
great scientific discovery. Anaxagoras could not have thought out the
theory of the moon's phases; Aristarchus could not have found out
the true mechanism of the solar system; Eratosthenes could not have
developed his plan for measuring the earth, had not each of these
investigators "intended" his mind persistently towards the problems in
question.

Nor can we doubt that men lived in every generation of the dark age
who were capable of creative thought in the field of science, bad they
chosen similarly to "intend" their minds in the right direction. The
difficulty was that they did not so choose. Their minds had a quite
different bent. They were under the spell of different ideals; all
their mental efforts were directed into different channels. What these
different channels were cannot be in doubt--they were the channels of
oriental ecclesiasticism. One all-significant fact speaks volumes here.
It is the fact that, as Professor Robinson(1) points out, from the time
of Boethius (died 524 or 525 A.D.) to that of Dante (1265-1321 A.D.)
there was not a single writer of renown in western Europe who was not a
professional churchman. All the learning of the time, then, centred in
the priesthood. We know that the same condition of things pertained in
Egypt, when science became static there. But, contrariwise, we have
seen that in Greece and early Rome the scientific workers were largely
physicians or professional teachers; there was scarcely a professional
theologian among them.

Similarly, as we shall see in the Arabic world, where alone there was
progress in the mediaeval epoch, the learned men were, for the most
part, physicians. Now the meaning of this must be self-evident. The
physician naturally "intends" his mind towards the practicalities. His
professional studies tend to make him an investigator of the operations
of nature. He is usually a sceptic, with a spontaneous interest in
practical science. But the theologian "intends" his mind away from
practicalities and towards mysticism. He is a professional believer in
the supernatural; he discounts the value of merely "natural" phenomena.
His whole attitude of mind is unscientific; the fundamental tenets
of his faith are based on alleged occurrences which inductive science
cannot admit--namely, miracles. And so the minds "intended" towards
the supernatural achieved only the hazy mysticism of mediaeval thought.
Instead of investigating natural laws, they paid heed (as, for example,
Thomas Aquinas does in his Summa Theologia) to the "acts of angels,"
the "speaking of angels," the "subordination of angels," the "deeds of
guardian angels," and the like. They disputed such important questions
as, How many angels can stand upon the point of a needle? They argued
pro and con as to whether Christ were coeval with God, or whether he had
been merely created "in the beginning," perhaps ages before the creation
of the world. How could it be expected that science should flourish when
the greatest minds of the age could concern themselves with problems
such as these?

Despite our preconceptions or prejudices, there can be but one answer to
that question. Oriental superstition cast its blight upon the fair field
of science, whatever compensation it may or may not have brought in
other fields. But we must be on our guard lest we overestimate or
incorrectly estimate this influence. Posterity, in glancing backward,
is always prone to stamp any given age of the past with one idea, and to
desire to characterize it with a single phrase; whereas in reality all
ages are diversified, and any generalization regarding an epoch is sure
to do that epoch something less or something more than justice. We
may be sure, then, that the ideal of ecclesiasticism is not solely
responsible for the scientific stasis of the dark age. Indeed, there was
another influence of a totally different character that is too patent
to be overlooked--the influence, namely, of the economic condition of
western Europe during this period. As I have elsewhere pointed
out,(2) Italy, the centre of western civilization, was at this time
impoverished, and hence could not provide the monetary stimulus so
essential to artistic and scientific no less than to material progress.
There were no patrons of science and literature such as the Ptolemies of
that elder Alexandrian day. There were no great libraries; no colleges
to supply opportunities and afford stimuli to the rising generation.
Worst of all, it became increasingly difficult to secure books.

This phase of the subject is often overlooked. Yet a moment's
consideration will show its importance. How should we fare to-day if no
new scientific books were being produced, and if the records of former
generations were destroyed? That is what actually happened in
Europe during the Middle Ages. At an earlier day books were made and
distributed much more abundantly than is sometimes supposed. Bookmaking
had, indeed, been an important profession in Rome, the actual makers of
books being slaves who worked under the direction of a publisher. It was
through the efforts of these workers that the classical works in Greek
and Latin were multiplied and disseminated. Unfortunately the climate of
Europe does not conduce to the indefinite preservation of a book;
hence very few remnants of classical works have come down to us in the
original from a remote period. The rare exceptions are certain papyrus
fragments, found in Egypt, some of which are Greek manuscripts dating
from the third century B.C. Even from these sources the output is
meagre; and the only other repository of classical books is a single
room in the buried city of Herculaneum, which contained several hundred
manuscripts, mostly in a charred condition, a considerable number of
which, however, have been unrolled and found more or less legible. This
library in the buried city was chiefly made up of philosophical works,
some of which were quite unknown to the modern world until discovered
there.

But this find, interesting as it was from an archaeological stand-point,
had no very important bearing on our knowledge of the literature of
antiquity. Our chief dependence for our knowledge of that literature
must still be placed in such copies of books as were made in the
successive generations. Comparatively few of the extant manuscripts are
older than the tenth century of our era. It requires but a momentary
consideration of the conditions under which ancient books were produced
to realize how slow and difficult the process was before the invention
of printing. The taste of the book-buying public demanded a clearly
written text, and in the Middle Ages it became customary to produce a
richly ornamented text as well. The script employed being the prototype
of the modern printed text, it will be obvious that a scribe could
produce but a few pages at best in a day. A large work would therefore
require the labor of a scribe for many months or even for several years.
We may assume, then, that it would be a very flourishing publisher who
could produce a hundred volumes all told per annum; and probably there
were not many publishers at any given time, even in the period of Rome's
greatest glory, who had anything like this output.

As there was a large number of authors in every generation of the
classical period, it follows that most of these authors must have been
obliged to content themselves with editions numbering very few copies;
and it goes without saying that the greater number of books were never
reproduced in what might be called a second edition. Even books that
retained their popularity for several generations would presently fail
to arouse sufficient interest to be copied; and in due course such works
would pass out of existence altogether. Doubtless many hundreds of books
were thus lost before the close of the classical period, the names of
their authors being quite forgotten, or preserved only through a chance
reference; and of course the work of elimination went on much more
rapidly during the Middle Ages, when the interest in classical
literature sank to so low an ebb in the West. Such collections of
references and quotations as the Greek Anthology and the famous
anthologies of Stobaeus and Athanasius and Eusebius give us glimpses
of a host of writers--more than seven hundred are quoted by Stobaeus--a
very large proportion of whom are quite unknown except through these
brief excerpts from their lost works.

Quite naturally the scientific works suffered at least as largely as
any others in an age given over to ecclesiastical dreamings. Yet in some
regards there is matter for surprise as to the works preserved. Thus, as
we have seen, the very extensive works of Aristotle on natural history,
and the equally extensive natural history of Pliny, which were preserved
throughout this period, and are still extant, make up relatively bulky
volumes. These works seem to have interested the monks of the Middle
Ages, while many much more important scientific books were allowed to
perish. A considerable bulk of scientific literature was also preserved
through the curious channels of Arabic and Armenian translations.
Reference has already been made to the Almagest of Ptolemy, which, as
we have seen, was translated into Arabic, and which was at a later
day brought by the Arabs into western Europe and (at the instance of
Frederick II of Sicily) translated out of their language into mediaeval
Latin.

It remains to inquire, however, through what channels the Greek works
reached the Arabs themselves. To gain an answer to this question we must
follow the stream of history from its Roman course eastward to the new
seat of the Roman empire in Byzantium. Here civilization centred from
about the fifth century A.D., and here the European came in contact
with the civilization of the Syrians, the Persians, the Armenians, and
finally of the Arabs. The Byzantines themselves, unlike the inhabitants
of western Europe, did not ignore the literature of old Greece; the
Greek language became the regular speech of the Byzantine people, and
their writers made a strenuous effort to perpetuate the idiom and style
of the classical period. Naturally they also made transcriptions of the
classical authors, and thus a great mass of literature was preserved,
while the corresponding works were quite forgotten in western Europe.

Meantime many of these works were translated into Syriac, Armenian, and
Persian, and when later on the Byzantine civilization degenerated, many
works that were no longer to be had in the Greek originals continued to
be widely circulated in Syriac, Persian, Armenian, and, ultimately,
in Arabic translations. When the Arabs started out in their conquests,
which carried them through Egypt and along the southern coast of the
Mediterranean, until they finally invaded Europe from the west by way
of Gibraltar, they carried with them their translations of many a Greek
classical author, who was introduced anew to the western world through
this strange channel.

We are told, for example, that Averrhoes, the famous commentator of
Aristotle, who lived in Spain in the twelfth century, did not know
a word of Greek and was obliged to gain his knowledge of the master
through a Syriac translation; or, as others alleged (denying that he
knew even Syriac), through an Arabic version translated from the Syriac.
We know, too, that the famous chronology of Eusebius was preserved
through an Armenian translation; and reference has more than once been
made to the Arabic translation of Ptolemy's great work, to which we
still apply its Arabic title of Almagest.

The familiar story that when the Arabs invaded Egypt they burned the
Alexandrian library is now regarded as an invention of later times. It
seems much more probable that the library bad been largely scattered
before the coming of the Moslems. Indeed, it has even been suggested
that the Christians of an earlier day removed the records of pagan
thought. Be that as it may, the famous Alexandrian library had
disappeared long before the revival of interest in classical learning.
Meanwhile, as we have said, the Arabs, far from destroying the western
literature, were its chief preservers. Partly at least because of their
regard for the records of the creative work of earlier generations of
alien peoples, the Arabs were enabled to outstrip their contemporaries.
For it cannot be in doubt that, during that long stretch of time when
the western world was ignoring science altogether or at most contenting
itself with the casual reading of Aristotle and Pliny, the Arabs had the
unique distinction of attempting original investigations in science.
To them were due all important progressive steps which were made in any
scientific field whatever for about a thousand years after the time of
Ptolemy and Galen. The progress made even by the Arabs during this long
period seems meagre enough, yet it has some significant features. These
will now demand our attention.




II. MEDIAEVAL SCIENCE AMONG THE ARABIANS

The successors of Mohammed showed themselves curiously receptive of the
ideas of the western people whom they conquered. They came in contact
with the Greeks in western Asia and in Egypt, and, as has been said,
became their virtual successors in carrying forward the torch of
learning. It must not be inferred, however, that the Arabian scholars,
as a class, were comparable to their predecessors in creative genius.
On the contrary, they retained much of the conservative oriental spirit.
They were under the spell of tradition, and, in the main, what they
accepted from the Greeks they regarded as almost final in its teaching.
There were, however, a few notable exceptions among their men of
science, and to these must be ascribed several discoveries of some
importance.

The chief subjects that excited the interest and exercised the ingenuity
of the Arabian scholars were astronomy, mathematics, and medicine. The
practical phases of all these subjects were given particular attention.
Thus it is well known that our so-called Arabian numerals date from
this period. The revolutionary effect of these characters, as applied to
practical mathematics, can hardly be overestimated; but it is generally
considered, and in fact was admitted by the Arabs themselves, that these
numerals were really borrowed from the Hindoos, with whom the Arabs came
in contact on the east. Certain of the Hindoo alphabets, notably that of
the Battaks of Sumatra, give us clews to the originals of the numerals.
It does not seem certain, however, that the Hindoos employed these
characters according to the decimal system, which is the prime element
of their importance. Knowledge is not forthcoming as to just when or by
whom such application was made. If this was an Arabic innovation, it was
perhaps the most important one with which that nation is to be credited.
Another mathematical improvement was the introduction into trigonometry
of the sine--the half-chord of the double arc--instead of the chord
of the arc itself which the Greek astronomers had employed. This
improvement was due to the famous Albategnius, whose work in other
fields we shall examine in a moment.

Another evidence of practicality was shown in the Arabian method of
attempting to advance upon Eratosthenes' measurement of the earth.
Instead of trusting to the measurement of angles, the Arabs decided to
measure directly a degree of the earth's surface--or rather two degrees.
Selecting a level plain in Mesopotamia for the experiment, one party
of the surveyors progressed northward, another party southward, from
a given point to the distance of one degree of arc, as determined by
astronomical observations. The result found was fifty-six miles for the
northern degree, and fifty-six and two-third miles for the southern.
Unfortunately, we do not know the precise length of the mile in
question, and therefore cannot be assured as to the accuracy of the
measurement. It is interesting to note, however, that the two degrees
were found of unequal lengths, suggesting that the earth is not a
perfect sphere--a suggestion the validity of which was not to be put
to the test of conclusive measurements until about the close of the
eighteenth century. The Arab measurement was made in the time of Caliph
Abdallah al-Mamun, the son of the famous Harun-al-Rashid. Both father
and son were famous for their interest in science. Harun-al-Rashid was,
it will be recalled, the friend of Charlemagne. It is said that he sent
that ruler, as a token of friendship, a marvellous clock which let fall
a metal ball to mark the hours. This mechanism, which is alleged to
have excited great wonder in the West, furnishes yet another instance of
Arabian practicality.

Perhaps the greatest of the Arabian astronomers was Mohammed ben Jabir
Albategnius, or El-batani, who was born at Batan, in Mesopotamia, about
the year 850 A.D., and died in 929. Albategnius was a student of the
Ptolemaic astronomy, but he was also a practical observer. He made the
important discovery of the motion of the solar apogee. That is to say,
he found that the position of the sun among the stars, at the time of
its greatest distance from the earth, was not what it had been in the
time of Ptolemy. The Greek astronomer placed the sun in longitude 65
degrees, but Albategnius found it in longitude 82 degrees, a distance
too great to be accounted for by inaccuracy of measurement. The modern
inference from this observation is that the solar system is moving
through space; but of course this inference could not well be drawn
while the earth was regarded as the fixed centre of the universe.

In the eleventh century another Arabian discoverer, Arzachel, observing
the sun to be less advanced than Albategnius had found it, inferred
incorrectly that the sun had receded in the mean time. The modern
explanation of this observation is that the measurement of Albategnius
was somewhat in error, since we know that the sun's motion is steadily
progressive. Arzachel, however, accepting the measurement of his
predecessor, drew the false inference of an oscillatory motion of the
stars, the idea of the motion of the solar system not being permissible.
This assumed phenomenon, which really has no existence in point of fact,
was named the "trepidation of the fixed stars," and was for centuries
accepted as an actual phenomenon. Arzachel explained this supposed
phenomenon by assuming that the equinoctial points, or the points of
intersection of the equator and the ecliptic, revolve in circles of
eight degrees' radius. The first points of Aries and Libra were supposed
to describe the circumference of these circles in about eight hundred
years. All of which illustrates how a difficult and false explanation
may take the place of a simple and correct one. The observations of
later generations have shown conclusively that the sun's shift of
position is regularly progressive, hence that there is no "trepidation"
of the stars and no revolution of the equinoctial points.

If the Arabs were wrong as regards this supposed motion of the fixed
stars, they made at least one correct observation as to the inequality
of motion of the moon. Two inequalities of the motion of this body were
already known. A third, called the moon's variation, was discovered by
an Arabian astronomer who lived at Cairo and observed at Bagdad in 975,
and who bore the formidable name of Mohammed Aboul Wefaal-Bouzdjani.
The inequality of motion in question, in virtue of which the moon moves
quickest when she is at new or full, and slowest at the first and third
quarter, was rediscovered by Tycho Brahe six centuries later; a fact
which in itself evidences the neglect of the Arabian astronomer's
discovery by his immediate successors.

In the ninth and tenth centuries the Arabian city of Cordova, in Spain,
was another important centre of scientific influence. There was a
library of several hundred thousand volumes here, and a college where
mathematics and astronomy were taught. Granada, Toledo, and Salamanca
were also important centres, to which students flocked from western
Europe. It was the proximity of these Arabian centres that stimulated
the scientific interests of Alfonso X. of Castile, at whose instance the
celebrated Alfonsine tables were constructed. A familiar story records
that Alfonso, pondering the complications of the Ptolemaic cycles and
epicycles, was led to remark that, had he been consulted at the time of
creation, he could have suggested a much better and simpler plan for the
universe. Some centuries were to elapse before Copernicus was to show
that it was not the plan of the universe, but man's interpretation of
it, that was at fault.

Another royal personage who came under Arabian influence was Frederick
II. of Sicily--the "Wonder of the World," as he was called by his
contemporaries. The Almagest of Ptolemy was translated into Latin at
his instance, being introduced to the Western world through this curious
channel. At this time it became quite usual for the Italian and Spanish
scholars to understand Arabic although they were totally ignorant of
Greek.

In the field of physical science one of the most important of the
Arabian scientists was Alhazen. His work, published about the year 1100
A.D., had great celebrity throughout the mediaeval period. The original
investigations of Alhazen had to do largely with optics. He made
particular studies of the eye itself, and the names given by him to
various parts of the eye, as the vitreous humor, the cornea, and the
retina, are still retained by anatomists. It is known that Ptolemy
had studied the refraction of light, and that he, in common with his
immediate predecessors, was aware that atmospheric refraction affects
the apparent position of stars near the horizon. Alhazen carried forward
these studies, and was led through them to make the first recorded
scientific estimate of the phenomena of twilight and of the height of
the atmosphere. The persistence of a glow in the atmosphere after the
sun has disappeared beneath the horizon is so familiar a phenomenon that
the ancient philosophers seem not to have thought of it as requiring an
explanation. Yet a moment's consideration makes it clear that, if
light travels in straight lines and the rays of the sun were in no wise
deflected, the complete darkness of night should instantly succeed to
day when the sun passes below the horizon. That this sudden change does
not occur, Alhazen explained as due to the reflection of light by the
earth's atmosphere.

Alhazen appears to have conceived the atmosphere as a sharply defined
layer, and, assuming that twilight continues only so long as rays of
the sun reflected from the outer surface of this layer can reach the
spectator at any given point, he hit upon a means of measurement that
seemed to solve the hitherto inscrutable problem as to the atmospheric
depth. Like the measurements of Aristarchus and Eratosthenes, this
calculation of Alhazen is simple enough in theory. Its defect consists
largely in the difficulty of fixing its terms with precision, combined
with the further fact that the rays of the sun, in taking the slanting
course through the earth's atmosphere, are really deflected from a
straight line in virtue of the constantly increasing density of the air
near the earth's surface. Alhazen must have been aware of this latter
fact, since it was known to the later Alexandrian astronomers, but he
takes no account of it in the present measurement. The diagram will make
the method of Alhazen clear.

His important premises are two: first, the well-recognized fact that,
when light is reflected from any surface, the angle of incidence is
equal to the angle of reflection; and, second, the much more doubtful
observation that twilight continues until such time as the sun,
according to a simple calculation, is nineteen degrees below the
horizon. Referring to the diagram, let the inner circle represent the
earth's surface, the outer circle the limits of the atmosphere, C being
the earth's centre, and RR radii of the earth. Then the observer at the
point A will continue to receive the reflected rays of the sun until
that body reaches the point S, which is, according to the hypothesis,
nineteen degrees below the horizon line of the observer at A. This
horizon line, being represented by AH, and the sun's ray by SM, the
angle HMS is an angle of nineteen degrees. The complementary angle SMA
is, obviously, an angle of (180-19) one hundred and sixty-one degrees.
But since M is the reflecting surface and the angle of incidence equals
the angle of reflection, the angle AMC is an angle of one-half of one
hundred and sixty-one degrees, or eighty degrees and thirty minutes.
Now this angle AMC, being known, the right-angled triangle MAC is easily
resolved, since the side AC of that triangle, being the radius of the
earth, is a known dimension. Resolution of this triangle gives us the
length of the hypotenuse MC, and the difference between this and the
radius (AC), or CD, is obviously the height of the atmosphere (h), which
was the measurement desired. According to the calculation of Alhazen,
this h, or the height of the atmosphere, represents from twenty to
thirty miles. The modern computation extends this to about fifty miles.
But, considering the various ambiguities that necessarily attended
the experiment, the result was a remarkably close approximation to the
truth.

Turning from physics to chemistry, we find as perhaps the greatest
Arabian name that of Geber, who taught in the College of Seville in the
first half of the eighth century. The most important researches of this
really remarkable experimenter had to do with the acids. The ancient
world had had no knowledge of any acid more powerful than acetic. Geber,
however, vastly increased the possibilities of chemical experiment by
the discovery of sulphuric, nitric, and nitromuriatic acids. He made
use also of the processes of sublimation and filtration, and his works
describe the water bath and the chemical oven. Among the important
chemicals which he first differentiated is oxide of mercury, and his
studies of sulphur in its various compounds have peculiar interest.
In particular is this true of his observation that, tinder certain
conditions of oxidation, the weight of a metal was lessened.

From the record of these studies in the fields of astronomy, physics,
and chemistry, we turn to a somewhat extended survey of the Arabian
advances in the field of medicine.


ARABIAN MEDICINE

The influence of Arabian physicians rested chiefly upon their use
of drugs rather than upon anatomical knowledge. Like the mediaeval
Christians, they looked with horror on dissection of the human body;
yet there were always among them investigators who turned constantly
to nature herself for hidden truths, and were ready to uphold the
superiority of actual observation to mere reading. Thus the physician
Abd el-Letif, while in Egypt, made careful studies of a mound of bones
containing more than twenty thousand skeletons. While examining these
bones he discovered that the lower jaw consists of a single bone, not
of two, as had been taught by Galen. He also discovered several other
important mistakes in Galenic anatomy, and was so impressed with his
discoveries that he contemplated writing a work on anatomy which should
correct the great classical authority's mistakes.

It was the Arabs who invented the apothecary, and their pharmacopoeia,
issued from the hospital at Gondisapor, and elaborated from time to
time, formed the basis for Western pharmacopoeias. Just how many drugs
originated with them, and how many were borrowed from the Hindoos, Jews,
Syrians, and Persians, cannot be determined. It is certain, however,
that through them various new and useful drugs, such as senna, aconite,
rhubarb, camphor, and mercury, were handed down through the Middle Ages,
and that they are responsible for the introduction of alcohol in the
field of therapeutics.

In mediaeval Europe, Arabian science came to be regarded with
superstitious awe, and the works of certain Arabian physicians were
exalted to a position above all the ancient writers. In modern times,
however, there has been a reaction and a tendency to depreciation of
their work. By some they are held to be mere copyists or translators
of Greek books, and in no sense original investigators in medicine. Yet
there can be little doubt that while the Arabians did copy and
translate freely, they also originated and added considerably to medical
knowledge. It is certain that in the time when Christian monarchs in
western Europe were paying little attention to science or education,
the caliphs and vizirs were encouraging physicians and philosophers,
building schools, and erecting libraries and hospitals. They made at
least a creditable effort to uphold and advance upon the scientific
standards of an earlier age.

The first distinguished Arabian physician was Harets ben Kaladah, who
received his education in the Nestonian school at Gondisapor, about the
beginning of the seventh century. Notwithstanding the fact that Harets
was a Christian, he was chosen by Mohammed as his chief medical adviser,
and recommended as such to his successor, the Caliph Abu Bekr. Thus,
at the very outset, the science of medicine was divorced from religion
among the Arabians; for if the prophet himself could employ the services
of an unbeliever, surely others might follow his example. And that this
example was followed is shown in the fact that many Christian physicians
were raised to honorable positions by succeeding generations of
Arabian monarchs. This broad-minded view of medicine taken by the Arabs
undoubtedly assisted as much as any one single factor in upbuilding
the science, just as the narrow and superstitious view taken by Western
nations helped to destroy it.

The education of the Arabians made it natural for them to associate
medicine with the natural sciences, rather than with religion. An
Arabian savant was supposed to be equally well educated in philosophy,
jurisprudence, theology, mathematics, and medicine, and to practise law,
theology, and medicine with equal skill upon occasion. It is easy to
understand, therefore, why these religious fanatics were willing to
employ unbelieving physicians, and their physicians themselves to
turn to the scientific works of Hippocrates and Galen for medical
instruction, rather than to religious works. Even Mohammed himself
professed some knowledge of medicine, and often relied upon this
knowledge in treating ailments rather than upon prayers or incantations.
He is said, for example, to have recommended and applied the cautery
in the case of a friend who, when suffering from angina, had sought his
aid.

The list of eminent Arabian physicians is too long to be given here,
but some of them are of such importance in their influence upon later
medicine that they cannot be entirely ignored. One of the first of these
was Honain ben Isaac (809-873 A.D.), a Christian Arab of Bagdad. He made
translations of the works of Hippocrates, and practised the art
along the lines indicated by his teachings and those of Galen. He is
considered the greatest translator of the ninth century and one of the
greatest philosophers of that period.

Another great Arabian physician, whose work was just beginning as
Honain's was drawing to a close, was Rhazes (850-923 A.D.), who during
his life was no less noted as a philosopher and musician than as a
physician. He continued the work of Honain, and advanced therapeutics by
introducing more extensive use of chemical remedies, such as mercurial
ointments, sulphuric acid, and aqua vitae. He is also credited with
being the first physician to describe small-pox and measles accurately.

While Rhazes was still alive another Arabian, Haly Abbas (died about
994), was writing his famous encyclopaedia of medicine, called The Royal
Book. But the names of all these great physicians have been considerably
obscured by the reputation of Avicenna (980-1037), the Arabian "Prince
of Physicians," the greatest name in Arabic medicine, and one of the
most remarkable men in history. Leclerc says that "he was perhaps
never surpassed by any man in brilliancy of intellect and indefatigable
activity." His career was a most varied one. He was at all times a
boisterous reveller, but whether flaunting gayly among the guests of
an emir or biding in some obscure apothecary cellar, his work of
philosophical writing was carried on steadily. When a friendly emir was
in power, he taught and wrote and caroused at court; but between times,
when some unfriendly ruler was supreme, he was hiding away obscurely,
still pouring out his great mass of manuscripts. In this way his entire
life was spent.

By his extensive writings he revived and kept alive the best of the
teachings of the Greek physicians, adding to them such observations
as he had made in anatomy, physiology, and materia medica. Among his
discoveries is that of the contagiousness of pulmonary tuberculosis. His
works for several centuries continued to be looked upon as the highest
standard by physicians, and he should undoubtedly be credited with
having at least retarded the decline of mediaeval medicine.

But it was not the Eastern Arabs alone who were active in the field of
medicine. Cordova, the capital of the western caliphate, became also a
great centre of learning and produced several great physicians. One of
these, Albucasis (died in 1013 A.D.), is credited with having published
the first illustrated work on surgery, this book being remarkable in
still another way, in that it was also the first book, since classical
times, written from the practical experience of the physician, and not a
mere compilation of ancient authors. A century after Albucasis came the
great physician Avenzoar (1113-1196), with whom he divides about
equally the medical honors of the western caliphate. Among Avenzoar's
discoveries was that of the cause of "itch"--a little parasite, "so
small that he is hardly visible." The discovery of the cause of this
common disease seems of minor importance now, but it is of interest
in medical history because, had Avenzoar's discovery been remembered a
hundred years ago, "itch struck in" could hardly have been considered
the cause of three-fourths of all diseases, as it was by the famous
Hahnemann.

The illustrious pupil of Avenzoar, Averrhoes, who died in 1198 A.D., was
the last of the great Arabian physicians who, by rational conception
of medicine, attempted to stem the flood of superstition that was
overwhelming medicine. For a time he succeeded; but at last the Moslem
theologians prevailed, and he was degraded and banished to a town
inhabited only by the despised Jews.


ARABIAN HOSPITALS

To early Christians belong the credit of having established the first
charitable institutions for caring for the sick; but their efforts were
soon eclipsed by both Eastern and Western Mohammedans. As early as
the eighth century the Arabs had begun building hospitals, but the
flourishing time of hospital building seems to have begun early in the
tenth century. Lady Seidel, in 918 A.D., opened a hospital at Bagdad,
endowed with an amount corresponding to about three hundred pounds
sterling a month. Other similar hospitals were erected in the years
immediately following, and in 977 the Emir Adad-adaula established an
enormous institution with a staff of twenty-four medical officers. The
great physician Rhazes is said to have selected the site for one of
these hospitals by hanging pieces of meat in various places about
the city, selecting the site near the place at which putrefaction was
slowest in making its appearance. By the middle of the twelfth century
there were something like sixty medical institutions in Bagdad alone,
and these institutions were free to all patients and supported by
official charity.

The Emir Nureddin, about the year 1160, founded a great hospital at
Damascus, as a thank-offering for his victories over the Crusaders.
This great institution completely overshadowed all the earlier Moslem
hospitals in size and in the completeness of its equipment. It was
furnished with facilities for teaching, and was conducted for several
centuries in a lavish manner, regardless of expense. But little over a
century after its foundation the fame of its methods of treatment led to
the establishment of a larger and still more luxurious institution--the
Mansuri hospital at Cairo. It seems that a certain sultan, having been
cured by medicines from the Damascene hospital, determined to build
one of his own at Cairo which should eclipse even the great Damascene
institution.

In a single year (1283-1284) this hospital was begun and completed. No
efforts were spared in hurrying on the good work, and no one was exempt
from performing labor on the building if he chanced to pass one of
the adjoining streets. It was the order of the sultan that any person
passing near could be impressed into the work, and this order was
carried out to the letter, noblemen and beggars alike being forced to
lend a hand. Very naturally, the adjacent thoroughfares became unpopular
and practically deserted, but still the holy work progressed rapidly and
was shortly completed.

This immense structure is said to have contained four courts, each
having a fountain in the centre; lecture-halls, wards for isolating
certain diseases, and a department that corresponded to the modern
hospital's "out-patient" department. The yearly endowment amounted to
something like the equivalent of one hundred and twenty-five thousand
dollars. A novel feature was a hall where musicians played day and
night, and another where story-tellers were employed, so that persons
troubled with insomnia were amused and melancholiacs cheered. Those of a
religious turn of mind could listen to readings of the Koran, conducted
continuously by a staff of some fifty chaplains. Each patient on leaving
the hospital received some gold pieces, that he need not be obliged to
attempt hard labor at once.

In considering the astonishing tales of these sumptuous Arabian
institutions, it should be borne in mind that our accounts of them are,
for the most part, from Mohammedan sources. Nevertheless, there can be
little question that they were enormous institutions, far surpassing any
similar institutions in western Europe. The so-called hospitals in the
West were, at this time, branches of monasteries under supervision of
the monks, and did not compare favorably with the Arabian hospitals.

But while the medical science of the Mohammedans greatly overshadowed
that of the Christians during this period, it did not completely
obliterate it. About the year 1000 A.D. came into prominence the
Christian medical school at Salerno, situated on the Italian coast, some
thirty miles southeast of Naples. Just how long this school had been
in existence, or by whom it was founded, cannot be determined, but its
period of greatest influence was the eleventh, twelfth, and thirteenth
centuries. The members of this school gradually adopted Arabic medicine,
making use of many drugs from the Arabic pharmacopoeia, and this formed
one of the stepping-stones to the introduction of Arabian medicine all
through western Europe.

It was not the adoption of Arabian medicines, however, that has made the
school at Salerno famous both in rhyme and prose, but rather the fact
that women there practised the healing art. Greatest among them was
Trotula, who lived in the eleventh century, and whose learning is
reputed to have equalled that of the greatest physicians of the day. She
is accredited with a work on Diseases of Women, still extant, and many
of her writings on general medical subjects were quoted through two
succeeding centuries. If we may judge from these writings, she seemed
to have had many excellent ideas as to the proper methods of treating
diseases, but it is difficult to determine just which of the writings
credited to her are in reality hers. Indeed, the uncertainty is even
greater than this implies, for, according to some writers, "Trotula"
is merely the title of a book. Such an authority as Malgaigne, however,
believed that such a woman existed, and that the works accredited to
her are authentic. The truth of the matter may perhaps never be fully
established, but this at least is certain--the tradition in regard
to Trotula could never have arisen had not women held a far different
position among the Arabians of this period from that accorded them in
contemporary Christendom.




III. MEDIAEVAL SCIENCE IN THE WEST

We have previously referred to the influence of the Byzantine
civilization in transmitting the learning of antiquity across the abysm
of the dark age. It must be admitted, however, that the importance of
that civilization did not extend much beyond the task of the common
carrier. There were no great creative scientists in the later Roman
empire of the East any more than in the corresponding empire of
the West. There was, however, one field in which the Byzantine made
respectable progress and regarding which their efforts require a few
words of special comment. This was the field of medicine.

The Byzantines of this time could boast of two great medical men, Aetius
of Amida (about 502-575 A.D.) and Paul of Aegina (about 620-690).
The works of Aetius were of value largely because they recorded the
teachings of many of his eminent predecessors, but he was not entirely
lacking in originality, and was perhaps the first physician to mention
diphtheria, with an allusion to some observations of the paralysis of
the palate which sometimes follows this disease.

Paul of Aegina, who came from the Alexandrian school about a century
later, was one of those remarkable men whose ideas are centuries ahead
of their time. This was particularly true of Paul in regard to surgery,
and his attitude towards the supernatural in the causation and treatment
of diseases. He was essentially a surgeon, being particularly familiar
with military surgery, and some of his descriptions of complicated
and difficult operations have been little improved upon even in modern
times. In his books he describes such operations as the removal of
foreign bodies from the nose, ear, and esophagus; and he recognizes
foreign growths such as polypi in the air-passages, and gives the
method of their removal. Such operations as tracheotomy, tonsillotomy,
bronchotomy, staphylotomy, etc., were performed by him, and he even
advocated and described puncture of the abdominal cavity, giving careful
directions as to the location in which such punctures should be made. He
advocated amputation of the breast for the cure of cancer, and described
extirpation of the uterus. Just how successful this last operation may
have been as performed by him does not appear; but he would hardly have
recommended it if it had not been sometimes, at least, successful.
That he mentions it at all, however, is significant, as this difficult
operation is considered one of the great triumphs of modern surgery.

But Paul of Aegina is a striking exception to the rule among Byzantine
surgeons, and as he was their greatest, so he was also their last
important surgeon. The energies of all Byzantium were so expended in
religious controversies that medicine, like the other sciences, was soon
relegated to a place among the other superstitions, and the influence
of the Byzantine school was presently replaced by that of the conquering
Arabians.


THIRTEENTH-CENTURY MEDICINE

The thirteenth century marks the beginning of a gradual change in
medicine, and a tendency to leave the time-worn rut of superstitious
dogmas that so long retarded the progress of science. It is thought that
the great epidemics which raged during the Middle Ages acted powerfully
in diverting the medical thought of the times into new and entirely
different channels. It will be remembered that the teachings of Galen
were handed through mediaeval times as the highest and best authority
on the subject of all diseases. When, however, the great epidemics made
their appearance, the medical men appealed to the works of Galen in vain
for enlightenment, as these works, having been written several centuries
before the time of the plagues, naturally contained no information
concerning them. It was evident, therefore, that on this subject, at
least, Galen was not infallible; and it would naturally follow that,
one fallible point having been revealed, others would be sought for. In
other words, scepticism in regard to accepted methods would be aroused,
and would lead naturally, as such scepticism usually does, to
progress. The devastating effects of these plagues, despite prayers and
incantations, would arouse doubt in the minds of many as to the efficacy
of superstitious rites and ceremonies in curing diseases. They had seen
thousands and tens of thousands of their fellow-beings swept away by
these awful scourges. They had seen the ravages of these epidemics
continue for months or even years, notwithstanding the fact that
multitudes of God-fearing people prayed hourly that such ravages might
be checked. And they must have observed also that when even very simple
rules of cleanliness and hygiene were followed there was a diminution
in the ravages of the plague, even without the aid of incantations. Such
observations as these would have a tendency to awaken a suspicion in the
minds of many of the physicians that disease was not a manifestation
of the supernatural, but a natural phenomenon, to be treated by natural
methods.

But, be the causes what they may, it is a fact that the thirteenth
century marks a turning-point, or the beginning of an attitude of mind
which resulted in bringing medicine to a much more rational position.
Among the thirteenth-century physicians, two men are deserving of
special mention. These are Arnald of Villanova (1235-1312) and Peter of
Abano (1250-1315). Both these men suffered persecution for expressing
their belief in natural, as against the supernatural, causes of disease,
and at one time Arnald was obliged to flee from Barcelona for declaring
that the "bulls" of popes were human works, and that "acts of charity
were dearer to God than hecatombs." He was also accused of alchemy.
Fleeing from persecution, he finally perished by shipwreck.

Arnald was the first great representative of the school of Montpellier.
He devoted much time to the study of chemicals, and was active in
attempting to re-establish the teachings of Hippocrates and Galen.
He was one of the first of a long line of alchemists who, for several
succeeding centuries, expended so much time and energy in attempting to
find the "elixir of life." The Arab discovery of alcohol first deluded
him into the belief that the "elixir" had at last been found; but later
he discarded it and made extensive experiments with brandy, employing
it in the treatment of certain diseases--the first record of the
administration of this liquor as a medicine. Arnald also revived the
search for some anaesthetic that would produce insensibility to pain in
surgical operations. This idea was not original with him, for since very
early times physicians had attempted to discover such an anaesthetic,
and even so early a writer as Herodotus tells how the Scythians,
by inhalation of the vapors of some kind of hemp, produced complete
insensibility. It may have been these writings that stimulated Arnald
to search for such an anaesthetic. In a book usually credited to him,
medicines are named and methods of administration described which will
make the patient insensible to pain, so that "he may be cut and feel
nothing, as though he were dead." For this purpose a mixture of opium,
mandragora, and henbane is to be used. This mixture was held at the
patient's nostrils much as ether and chloroform are administered by the
modern surgeon. The method was modified by Hugo of Lucca (died in 1252
or 1268), who added certain other narcotics, such as hemlock, to the
mixture, and boiled a new sponge in this decoction. After boiling for a
certain time, this sponge was dried, and when wanted for use was dipped
in hot water and applied to the nostrils.

Just how frequently patients recovered from the administration of such
a combination of powerful poisons does not appear, but the percentage
of deaths must have been very high, as the practice was generally
condemned. Insensibility could have been produced only by swallowing
large quantities of the liquid, which dripped into the nose and mouth
when the sponge was applied, and a lethal quantity might thus be
swallowed. The method was revived, with various modifications, from time
to time, but as often fell into disuse. As late as 1782 it was sometimes
attempted, and in that year the King of Poland is said to have been
completely anaesthetized and to have recovered, after a painless
amputation had been performed by the surgeons.

Peter of Abano was one of the first great men produced by the University
of Padua. His fate would have been even more tragic than that of the
shipwrecked Arnald had he not cheated the purifying fagots of the church
by dying opportunely on the eve of his execution for heresy. But if his
spirit had cheated the fanatics, his body could not, and his bones were
burned for his heresy. He had dared to deny the existence of a devil,
and had suggested that the case of a patient who lay in a trance for
three days might help to explain some miracles, like the raising of
Lazarus.

His great work was Conciliator Differentiarum, an attempt to reconcile
physicians and philosophers. But his researches were not confined to
medicine, for he seems to have had an inkling of the hitherto unknown
fact that air possesses weight, and his calculation of the length of the
year at three hundred and sixty-five days, six hours, and four minutes,
is exceptionally accurate for the age in which he lived. He was probably
the first of the Western writers to teach that the brain is the source
of the nerves, and the heart the source of the vessels. From this it
is seen that he was groping in the direction of an explanation of the
circulation of the blood, as demonstrated by Harvey three centuries
later.

The work of Arnald and Peter of Abano in "reviving" medicine was
continued actively by Mondino (1276-1326) of Bologna, the "restorer of
anatomy," and by Guy of Chauliac: (born about 1300), the "restorer of
surgery." All through the early Middle Ages dissections of human bodies
had been forbidden, and even dissection of the lower animals gradually
fell into disrepute because physicians detected in such practices
were sometimes accused of sorcery. Before the close of the thirteenth
century, however, a reaction had begun, physicians were protected, and
dissections were occasionally sanctioned by the ruling monarch. Thus
Emperor Frederick H. (1194-1250 A.D.)--whose services to science we have
already had occasion to mention--ordered that at least one human body
should be dissected by physicians in his kingdom every five years. By
the time of Mondino dissections were becoming more frequent, and he
himself is known to have dissected and demonstrated several bodies. His
writings on anatomy have been called merely plagiarisms of Galen, but
in all probability be made many discoveries independently, and on
the whole, his work may be taken as more advanced than Galen's. His
description of the heart is particularly accurate, and he seems to have
come nearer to determining the course of the blood in its circulation
than any of his predecessors. In this quest he was greatly handicapped
by the prevailing belief in the idea that blood-vessels must contain air
as well as blood, and this led him to assume that one of the cavities of
the heart contained "spirits," or air. It is probable, however, that his
accurate observations, so far as they went, were helpful stepping-stones
to Harvey in his discovery of the circulation.

Guy of Chauliac, whose innovations in surgery reestablished that science
on a firm basis, was not only one of the most cultured, but also the
most practical surgeon of his time. He had great reverence for the works
of Galen, Albucasis, and others of his noted predecessors; but this
reverence did not blind him to their mistakes nor prevent him from using
rational methods of treatment far in advance of theirs. His practicality
is shown in some of his simple but useful inventions for the sick-room,
such as the device of a rope, suspended from the ceiling over the bed,
by which a patient may move himself about more easily; and in some of
his improvements in surgical dressings, such as stiffening bandages by
dipping them in the white of an egg so that they are held firmly.
He treated broken limbs in the suspended cradle still in use, and
introduced the method of making "traction" on a broken limb by means
of a weight and pulley, to prevent deformity through shortening of the
member. He was one of the first physicians to recognize the utility of
spectacles, and recommended them in cases not amenable to treatment
with lotions and eye-waters. In some of his surgical operations, such
as trephining for fracture of the skull, his technique has been little
improved upon even in modern times. In one of these operations he
successfully removed a portion of a man's brain.


Surgery was undoubtedly stimulated greatly at this period by the
constant wars. Lay physicians, as a class, had been looked down
upon during the Dark Ages; but with the beginning of the return to
rationalism, the services of surgeons on the battle-field, to remove
missiles from wounds, and to care for wounds and apply dressings, came
to be more fully appreciated. In return for his labors the surgeon was
thus afforded better opportunities for observing wounds and diseases,
which led naturally to a gradual improvement in surgical methods.


FIFTEENTH-CENTURY MEDICINE

The thirteenth and fourteenth centuries had seen some slight advancement
in the science of medicine; at least, certain surgeons and physicians,
if not the generality, had made advances; but it was not until the
fifteenth century that the general revival of medical learning became
assured. In this movement, naturally, the printing-press played an
all-important part. Medical books, hitherto practically inaccessible
to the great mass of physicians, now became common, and this output of
reprints of Greek and Arabic treatises revealed the fact that many of
the supposed true copies were spurious. These discoveries very naturally
aroused all manner of doubt and criticism, which in turn helped in the
development of independent thought.

A certain manuscript of the great Cornelius Celsus, the De Medicine,
which had been lost for many centuries, was found in the church of St.
Ambrose, at Milan, in 1443, and was at once put into print. The effect
of the publication of this book, which had lain in hiding for so many
centuries, was a revelation, showing the medical profession how far
most of their supposed true copies of Celsus had drifted away from the
original. The indisputable authenticity of this manuscript, discovered
and vouched for by the man who shortly after became Pope Nicholas V.,
made its publication the more impressive. The output in book form of
other authorities followed rapidly, and the manifest discrepancies
between such teachers as Celsus, Hippocrates, Galen, and Pliny
heightened still more the growing spirit of criticism.

These doubts resulted in great controversies as to the proper treatment
of certain diseases, some physicians following Hippocrates, others Galen
or Celsus, still others the Arabian masters. One of the most bitter
of these contests was over the question of "revulsion," and
"derivation"--that is, whether in cases of pleurisy treated by bleeding,
the venesection should be made at a point distant from the seat of the
disease, as held by the "revulsionists," or at a point nearer and on the
same side of the body, as practised by the "derivationists." That any
great point for discussion could be raised in the fifteenth or sixteenth
centuries on so simple a matter as it seems to-day shows how necessary
to the progress of medicine was the discovery of the circulation of the
blood made by Harvey two centuries later. After Harvey's discovery no
such discussion could have been possible, because this discovery made
it evident that as far as the general effect upon the circulation is
concerned, it made little difference whether the bleeding was done near
a diseased part or remote from it. But in the sixteenth century this
question was the all-absorbing one among the doctors. At one time the
faculty of Paris condemned "derivation"; but the supporters of this
method carried the war still higher, and Emperor Charles V. himself was
appealed to. He reversed the decision of the Paris faculty, and decided
in favor of "derivation." His decision was further supported by Pope
Clement VII., although the discussion dragged on until cut short by
Harvey's discovery.

But a new form of injury now claimed the attention of the surgeons,
something that could be decided by neither Greek nor Arabian authors, as
the treatment of gun-shot wounds was, for obvious reasons, not given in
their writings. About this time, also, came the great epidemics, "the
sweating sickness" and scurvy; and upon these subjects, also, the
Greeks and Arabians were silent. John of Vigo, in his book, the Practica
Copiosa, published in 1514, and repeated in many editions, became the
standard authority on all these subjects, and thus supplanted the works
of the ancient writers.

According to Vigo, gun-shot wounds differed from the wounds made by
ordinary weapons--that is, spear, arrow, sword, or axe--in that the
bullet, being round, bruised rather than cut its way through the
tissues; it burned the flesh; and, worst of all, it poisoned it. Vigo
laid especial stress upon treating this last condition, recommending the
use of the cautery or the oil of elder, boiling hot. It is little wonder
that gun-shot wounds were so likely to prove fatal. Yet, after all, here
was the germ of the idea of antisepsis.


NEW BEGINNINGS IN GENERAL SCIENCE

We have dwelt thus at length on the subject of medical science, because
it was chiefly in this field that progress was made in the Western world
during the mediaeval period, and because these studies furnished the
point of departure for the revival all along the line. It will be
understood, however, from what was stated in the preceding chapter,
that the Arabian influences in particular were to some extent making
themselves felt along other lines. The opportunity afforded a portion
of the Western world--notably Spain and Sicily--to gain access to the
scientific ideas of antiquity through Arabic translations could not fail
of influence. Of like character, and perhaps even more pronounced in
degree, was the influence wrought by the Byzantine refugees, who, when
Constantinople began to be threatened by the Turks, migrated to the
West in considerable numbers, bringing with them a knowledge of Greek
literature and a large number of precious works which for centuries
had been quite forgotten or absolutely ignored in Italy. Now Western
scholars began to take an interest in the Greek language, which had been
utterly neglected since the beginning of the Middle Ages. Interesting
stories are told of the efforts made by such men as Cosmo de' Medici to
gain possession of classical manuscripts. The revival of learning
thus brought about had its first permanent influence in the fields of
literature and art, but its effect on science could not be long delayed.
Quite independently of the Byzantine influence, however, the striving
for better intellectual things had manifested itself in many ways before
the close of the thirteenth century. An illustration of this is found
in the almost simultaneous development of centres of teaching, which
developed into the universities of Italy, France, England, and, a little
later, of Germany.

The regular list of studies that came to be adopted everywhere
comprised seven nominal branches, divided into two groups--the so-called
quadrivium, comprising music, arithmetic, geometry, and astronomy; and
the trivium comprising grammar, rhetoric, and logic. The vagueness of
implication of some of these branches gave opportunity to the teacher
for the promulgation of almost any knowledge of which he might be
possessed, but there can be no doubt that, in general, science had
but meagre share in the curriculum. In so far as it was given
representation, its chief field must have been Ptolemaic astronomy. The
utter lack of scientific thought and scientific method is illustrated
most vividly in the works of the greatest men of that period--such men
as Albertus Magnus, Thomas Aquinas, Bonaventura, and the hosts of other
scholastics of lesser rank. Yet the mental awakening implied in their
efforts was sure to extend to other fields, and in point of fact there
was at least one contemporary of these great scholastics whose mind
was intended towards scientific subjects, and who produced writings
strangely at variance in tone and in content with the others. This
anachronistic thinker was the English monk, Roger Bacon.


ROGER BACON

Bacon was born in 1214 and died in 1292. By some it is held that he was
not appreciated in his own time because he was really a modern scientist
living in an age two centuries before modern science or methods of
modern scientific thinking were known. Such an estimate, however, is a
manifest exaggeration of the facts, although there is probably a grain
of truth in it withal. His learning certainly brought him into contact
with the great thinkers of the time, and his writings caused him to
be imprisoned by his fellow-churchmen at different times, from which
circumstances we may gather that he was advanced thinker, even if not a
modern scientist.

Although Bacon was at various times in durance, or under surveillance,
and forbidden to write, he was nevertheless a marvellously prolific
writer, as is shown by the numerous books and unpublished manuscripts of
his still extant. His master-production was the Opus Majus. In Part IV.
of this work he attempts to show that all sciences rest ultimately on
mathematics; but Part V., which treats of perspective, is of particular
interest to modern scientists, because in this he discusses reflection
and refraction, and the properties of mirrors and lenses. In this part,
also, it is evident that he is making use of such Arabian writers as
Alkindi and Alhazen, and this is of especial interest, since it has been
used by his detractors, who accuse him of lack of originality, to prove
that his seeming inventions and discoveries were in reality adaptations
of the Arab scientists. It is difficult to determine just how fully such
criticisms are justified. It is certain, however, that in this part
he describes the anatomy of the eye with great accuracy, and discusses
mirrors and lenses.

The magnifying power of the segment of a glass sphere had been noted by
Alhazen, who had observed also that the magnification was increased by
increasing the size of the segment used. Bacon took up the discussion of
the comparative advantages of segments, and in this discussion seems to
show that he understood how to trace the progress of the rays of light
through a spherical transparent body, and how to determine the place of
the image. He also described a method of constructing a telescope, but
it is by no means clear that he had ever actually constructed such an
instrument. It is also a mooted question as to whether his instructions
as to the construction of such an instrument would have enabled any one
to construct one. The vagaries of the names of terms as he uses them
allow such latitude in interpretation that modern scientists are not
agreed as to the practicability of Bacon's suggestions. For example, he
constantly refers to force under such names as virtus, species, imago,
agentis, and a score of other names, and this naturally gives rise
to the great differences in the interpretations of his writings, with
corresponding differences in estimates of them.

The claim that Bacon originated the use of lenses, in the form of
spectacles, cannot be proven. Smith has determined that as early as the
opening years of the fourteenth century such lenses were in use, but
this proves nothing as regards Bacon's connection with their invention.
The knowledge of lenses seems to be very ancient, if we may judge from
the convex lens of rock crystal found by Layard in his excavations
at Nimrud. There is nothing to show, however, that the ancients ever
thought of using them to correct defects of vision. Neither, apparently,
is it feasible to determine whether the idea of such an application
originated with Bacon.

Another mechanical discovery about which there has been a great deal of
discussion is Bacon's supposed invention of gunpowder. It appears that
in a certain passage of his work he describes the process of making a
substance that is, in effect, ordinary gunpowder; but it is more than
doubtful whether he understood the properties of the substance he
describes. It is fairly well established, however, that in Bacon's time
gunpowder was known to the Arabs, so that it should not be surprising
to find references made to it in Bacon's work, since there is reason to
believe that he constantly consulted Arabian writings.

The great merit of Bacon's work, however, depends on the principles
taught as regards experiment and the observation of nature, rather than
on any single invention. He had the all-important idea of breaking with
tradition. He championed unfettered inquiry in every field of thought.
He had the instinct of a scientific worker--a rare instinct indeed in
that age. Nor need we doubt that to the best of his opportunities he was
himself an original investigator.


LEONARDO DA VINCI

The relative infertility of Bacon's thought is shown by the fact that he
founded no school and left no trace of discipleship. The entire century
after his death shows no single European name that need claim the
attention of the historian of science. In the latter part of the
fifteenth century, however, there is evidence of a renaissance of
science no less than of art. The German Muller became famous under
the latinized named of Regio Montanus (1437-1472), although his actual
scientific attainments would appear to have been important only in
comparison with the utter ignorance of his contemporaries. The most
distinguished worker of the new era was the famous Italian Leonardo da
Vinci--a man who has been called by Hamerton the most universal genius
that ever lived. Leonardo's position in the history of art is known to
every one. With that, of course, we have no present concern; but it is
worth our while to inquire at some length as to the famous painter's
accomplishments as a scientist.

From a passage in the works of Leonardo, first brought to light by
Venturi,(1) it would seem that the great painter anticipated Copernicus
in determining the movement of the earth. He made mathematical
calculations to prove this, and appears to have reached the definite
conclusion that the earth does move--or what amounts to the same thing,
that the sun does not move. Muntz is authority for the statement that
in one of his writings he declares, "Il sole non si mouve"--the sun does
not move.(2)

Among his inventions is a dynamometer for determining the traction power
of machines and animals, and his experiments with steam have led some
of his enthusiastic partisans to claim for him priority to Watt in the
invention of the steam-engine. In these experiments, however, Leonardo
seems to have advanced little beyond Hero of Alexandria and his steam
toy. Hero's steam-engine did nothing but rotate itself by virtue of
escaping jets of steam forced from the bent tubes, while Leonardo's
"steam-engine" "drove a ball weighing one talent over a distance of six
stadia." In a manuscript now in the library of the Institut de France,
Da Vinci describes this engine minutely. The action of this machine was
due to the sudden conversion of small quantities of water into steam
("smoke," as he called it) by coming suddenly in contact with a heated
surface in a proper receptacle, the rapidly formed steam acting as
a propulsive force after the manner of an explosive. It is really a
steam-gun, rather than a steam-engine, and it is not unlikely that the
study of the action of gunpowder may have suggested it to Leonardo.

It is believed that Leonardo is the true discoverer of the
camera-obscura, although the Neapolitan philosopher, Giambattista Porta,
who was not born until some twenty years after the death of Leonardo,
is usually credited with first describing this device. There is
little doubt, however, that Da Vinci understood the principle of this
mechanism, for he describes how such a camera can be made by cutting a
small, round hole through the shutter of a darkened room, the reversed
image of objects outside being shown on the opposite wall.

Like other philosophers in all ages, he had observed a great number of
facts which he was unable to explain correctly. But such accumulations
of scientific observations are always interesting, as showing how many
centuries of observation frequently precede correct explanation. He
observed many facts about sounds, among others that blows struck upon
a bell produced sympathetic sounds in a bell of the same kind; and
that striking the string of a lute produced vibration in corresponding
strings of lutes strung to the same pitch. He knew, also, that sounds
could be heard at a distance at sea by listening at one end of a tube,
the other end of which was placed in the water; and that the same
expedient worked successfully on land, the end of the tube being placed
against the ground.

The knowledge of this great number of unexplained facts is often
interpreted by the admirers of Da Vinci, as showing an almost occult
insight into science many centuries in advance of his time. Such
interpretations, however, are illusive. The observation, for example,
that a tube placed against the ground enables one to hear movements on
the earth at a distance, is not in itself evidence of anything more than
acute scientific observation, as a similar method is in use among almost
every race of savages, notably the American Indians. On the other hand,
one is inclined to give credence to almost any story of the breadth of
knowledge of the man who came so near anticipating Hutton, Lyell, and
Darwin in his interpretation of the geological records as he found them
written on the rocks.

It is in this field of geology that Leonardo is entitled to the greatest
admiration by modern scientists. He had observed the deposit of fossil
shells in various strata of rocks, even on the tops of mountains, and he
rejected once for all the theory that they had been deposited there by
the Deluge. He rightly interpreted their presence as evidence that
they had once been deposited at the bottom of the sea. This process
he assumed bad taken hundreds and thousands of centuries, thus tacitly
rejecting the biblical tradition as to the date of the creation.

Notwithstanding the obvious interest that attaches to the investigations
of Leonardo, it must be admitted that his work in science remained
almost as infertile as that of his great precursor, Bacon. The really
stimulative work of this generation was done by a man of affairs, who
knew little of theoretical science except in one line, but who pursued
that one practical line until he achieved a wonderful result. This man
was Christopher Columbus. It is not necessary here to tell the trite
story of his accomplishment. Suffice it that his practical demonstration
of the rotundity of the earth is regarded by most modern writers as
marking an epoch in history. With the year of his voyage the epoch of
the Middle Ages is usually regarded as coming to an end. It must not be
supposed that any very sudden change came over the aspect of scholarship
of the time, but the preliminaries of great things had been achieved,
and when Columbus made his famous voyage in 1492, the man was already
alive who was to bring forward the first great vitalizing thought in
the field of pure science that the Western world had originated for more
than a thousand years. This man bore the name of Kopernik, or in its
familiar Anglicized form, Copernicus. His life work and that of his
disciples will claim our attention in the succeeding chapter.




IV. THE NEW COSMOLOGY--COPERNICUS TO KEPLER AND GALILEO

We have seen that the Ptolemaic astronomy, which was the accepted
doctrine throughout the Middle Ages, taught that the earth is round.
Doubtless there was a popular opinion current which regarded the earth
as flat, but it must be understood that this opinion had no champions
among men of science during the Middle Ages. When, in the year 1492,
Columbus sailed out to the west on his memorable voyage, his expectation
of reaching India had full scientific warrant, however much it may have
been scouted by certain ecclesiastics and by the average man of the
period. Nevertheless, we may well suppose that the successful voyage of
Columbus, and the still more demonstrative one made about thirty years
later by Magellan, gave the theory of the earth's rotundity a certainty
it could never previously have had. Alexandrian geographers had measured
the size of the earth, and had not hesitated to assert that by sailing
westward one might reach India. But there is a wide gap between theory
and practice, and it required the voyages of Columbus and his successors
to bridge that gap.

After the companions of Magellan completed the circumnavigation of the
globe, the general shape of our earth would, obviously, never again be
called in question. But demonstration of the sphericity of the earth
had, of course, no direct bearing upon the question of the earth's
position in the universe. Therefore the voyage of Magellan served to
fortify, rather than to dispute, the Ptolemaic theory. According to that
theory, as we have seen, the earth was supposed to lie immovable at the
centre of the universe; the various heavenly bodies, including the sun,
revolving about it in eccentric circles. We have seen that several
of the ancient Greeks, notably Aristarchus, disputed this conception,
declaring for the central position of the sun in the universe, and
the motion of the earth and other planets about that body. But this
revolutionary theory seemed so opposed to the ordinary observation that,
having been discountenanced by Hipparchus and Ptolemy, it did not find a
single important champion for more than a thousand years after the time
of the last great Alexandrian astronomer.

The first man, seemingly, to hark back to the Aristarchian conception
in the new scientific era that was now dawning was the noted cardinal,
Nikolaus of Cusa, who lived in the first half of the fifteenth century,
and was distinguished as a philosophical writer and mathematician. His
De Docta Ignorantia expressly propounds the doctrine of the earth's
motion. No one, however, paid the slightest attention to his suggestion,
which, therefore, merely serves to furnish us with another interesting
illustration of the futility of propounding even a correct hypothesis
before the time is ripe to receive it--particularly if the hypothesis is
not fully fortified by reasoning based on experiment or observation.

The man who was destined to put forward the theory of the earth's motion
in a way to command attention was born in 1473, at the village of Thorn,
in eastern Prussia. His name was Nicholas Copernicus. There is no more
famous name in the entire annals of science than this, yet posterity has
never been able fully to establish the lineage of the famous expositor
of the true doctrine of the solar system. The city of Thorn lies in
a province of that border territory which was then under control of
Poland, but which subsequently became a part of Prussia. It is claimed
that the aspects of the city were essentially German, and it is admitted
that the mother of Copernicus belonged to that race. The nationality of
the father is more in doubt, but it is urged that Copernicus used German
as his mother-tongue. His great work was, of course, written in Latin,
according to the custom of the time; but it is said that, when not
employing that language, he always wrote in German. The disputed
nationality of Copernicus strongly suggests that he came of a mixed
racial lineage, and we are reminded again of the influences of those
ethnical minglings to which we have previously more than once referred.
The acknowledged centres of civilization towards the close of the
fifteenth century were Italy and Spain. Therefore, the birthplace of
Copernicus lay almost at the confines of civilization, reminding us of
that earlier period when Greece was the centre of culture, but when the
great Greek thinkers were born in Asia Minor and in Italy.

As a young man, Copernicus made his way to Vienna to study medicine,
and subsequently he journeyed into Italy and remained there many years,
About the year 1500 he held the chair of mathematics in a college
at Rome. Subsequently he returned to his native land and passed his
remaining years there, dying at Domkerr, in Frauenburg, East Prussia, in
the year 1543.

It would appear that Copernicus conceived the idea of the heliocentric
system of the universe while he was a comparatively young man, since
in the introduction to his great work, which he addressed to Pope Paul
III., he states that he has pondered his system not merely nine years,
in accordance with the maxim of Horace, but well into the fourth period
of nine years. Throughout a considerable portion of this period the
great work of Copernicus was in manuscript, but it was not published
until the year of his death. The reasons for the delay are not very
fully established. Copernicus undoubtedly taught his system throughout
the later decades of his life. He himself tells us that he had even
questioned whether it were not better for him to confine himself to such
verbal teaching, following thus the example of Pythagoras. Just as his
life was drawing to a close, he decided to pursue the opposite course,
and the first copy of his work is said to have been placed in his hands
as he lay on his deathbed.

The violent opposition which the new system met from ecclesiastical
sources led subsequent commentators to suppose that Copernicus had
delayed publication of his work through fear of the church authorities.
There seems, however, to be no direct evidence for this opinion. It has
been thought significant that Copernicus addressed his work to the pope.
It is, of course, quite conceivable that the aged astronomer might wish
by this means to demonstrate that he wrote in no spirit of hostility
to the church. His address to the pope might have been considered as a
desirable shield precisely because the author recognized that his
work must needs meet with ecclesiastical criticism. Be that as it
may, Copernicus was removed by death from the danger of attack, and it
remained for his disciples of a later generation to run the gauntlet of
criticism and suffer the charges of heresy.

The work of Copernicus, published thus in the year 1543 at Nuremberg,
bears the title De Orbium Coelestium Revolutionibus.

It is not necessary to go into details as to the cosmological system
which Copernicus advocated, since it is familiar to every one. In a
word, he supposed the sun to be the centre of all the planetary motions,
the earth taking its place among the other planets, the list of which,
as known at that time, comprised Mercury, Venus, the Earth, Mars,
Jupiter, and Saturn. The fixed stars were alleged to be stationary, and
it was necessary to suppose that they are almost infinitely distant,
inasmuch as they showed to the observers of that time no parallax; that
is to say, they preserved the same apparent position when viewed from
the opposite points of the earth's orbit.

But let us allow Copernicus to speak for himself regarding his system,
His exposition is full of interest. We quote first the introduction just
referred to, in which appeal is made directly to the pope.

"I can well believe, most holy father, that certain people, when they
hear of my attributing motion to the earth in these books of mine, will
at once declare that such an opinion ought to be rejected. Now, my own
theories do not please me so much as not to consider what others may
judge of them. Accordingly, when I began to reflect upon what those
persons who accept the stability of the earth, as confirmed by the
opinion of many centuries, would say when I claimed that the earth
moves, I hesitated for a long time as to whether I should publish that
which I have written to demonstrate its motion, or whether it would not
be better to follow the example of the Pythagoreans, who used to hand
down the secrets of philosophy to their relatives and friends only in
oral form. As I well considered all this, I was almost impelled to
put the finished work wholly aside, through the scorn I had reason to
anticipate on account of the newness and apparent contrariness to reason
of my theory.

"My friends, however, dissuaded me from such a course and admonished
me that I ought to publish my book, which had lain concealed in my
possession not only nine years, but already into four times the ninth
year. Not a few other distinguished and very learned men asked me to do
the same thing, and told me that I ought not, on account of my anxiety,
to delay any longer in consecrating my work to the general service of
mathematicians.

"But your holiness will perhaps not so much wonder that I have dared to
bring the results of my night labors to the light of day, after having
taken so much care in elaborating them, but is waiting instead to hear
how it entered my mind to imagine that the earth moved, contrary to the
accepted opinion of mathematicians--nay, almost contrary to ordinary
human understanding. Therefore I will not conceal from your holiness
that what moved me to consider another way of reckoning the motions
of the heavenly bodies was nothing else than the fact that the
mathematicians do not agree with one another in their investigations. In
the first place, they are so uncertain about the motions of the sun and
moon that they cannot find out the length of a full year. In the
second place, they apply neither the same laws of cause and effect, in
determining the motions of the sun and moon and of the five planets,
nor the same proofs. Some employ only concentric circles, others use
eccentric and epicyclic ones, with which, however, they do not fully
attain the desired end. They could not even discover nor compute the
main thing--namely, the form of the universe and the symmetry of its
parts. It was with them as if some should, from different places, take
hands, feet, head, and other parts of the body, which, although very
beautiful, were not drawn in their proper relations, and, without making
them in any way correspond, should construct a monster instead of a
human being.

"Accordingly, when I had long reflected on this uncertainty of
mathematical tradition, I took the trouble to read again the books of
all the philosophers I could get hold of, to see if some one of them had
not once believed that there were other motions of the heavenly bodies.
First I found in Cicero that Niceties had believed in the motion of the
earth. Afterwards I found in Plutarch, likewise, that some others had
held the same opinion. This induced me also to begin to consider the
movability of the earth, and, although the theory appeared contrary to
reason, I did so because I knew that others before me had been allowed
to assume rotary movements at will, in order to explain the phenomena
of these celestial bodies. I was of the opinion that I, too, might be
permitted to see whether, by presupposing motion in the earth, more
reliable conclusions than hitherto reached could not be discovered for
the rotary motions of the spheres. And thus, acting on the hypothesis of
the motion which, in the following book, I ascribe to the earth, and by
long and continued observations, I have finally discovered that if the
motion of the other planets be carried over to the relation of the earth
and this is made the basis for the rotation of every star, not only will
the phenomena of the planets be explained thereby, but also the laws and
the size of the stars; all their spheres and the heavens themselves will
appear so harmoniously connected that nothing could be changed in any
part of them without confusion in the remaining parts and in the whole
universe. I do not doubt that clever and learned men will agree with me
if they are willing fully to comprehend and to consider the proofs
which I advance in the book before us. In order, however, that both
the learned and the unlearned may see that I fear no man's judgment, I
wanted to dedicate these, my night labors, to your holiness, rather than
to any one else, because you, even in this remote corner of the earth
where I live, are held to be the greatest in dignity of station and in
love for all sciences and for mathematics, so that you, through your
position and judgment, can easily suppress the bites of slanderers,
although the proverb says that there is no remedy against the bite of
calumny."


In chapter X. of book I., "On the Order of the Spheres," occurs a more
detailed presentation of the system, as follows:

"That which Martianus Capella, and a few other Latins, very well knew,
appears to me extremely noteworthy. He believed that Venus and Mercury
revolve about the sun as their centre and that they cannot go farther
away from it than the circles of their orbits permit, since they do
not revolve about the earth like the other planets. According to this
theory, then, Mercury's orbit would be included within that of Venus,
which is more than twice as great, and would find room enough within it
for its revolution.

"If, acting upon this supposition, we connect Saturn, Jupiter, and
Mars with the same centre, keeping in mind the greater extent of their
orbits, which include the earth's sphere besides those of Mercury and
Venus, we cannot fail to see the explanation of the regular order of
their motions. He is certain that Saturn, Jupiter, and Mars are always
nearest the earth when they rise in the evening--that is, when they
appear over against the sun, or the earth stands between them and the
sun--but that they are farthest from the earth when they set in the
evening--that is, when we have the sun between them and the earth. This
proves sufficiently that their centre belongs to the sun and is the same
about which the orbits of Venus and Mercury circle. Since, however, all
have one centre, it is necessary for the space intervening between the
orbits of Venus and Mars to include the earth with her accompanying
moon and all that is beneath the moon; for the moon, which stands
unquestionably nearest the earth, can in no way be separated from her,
especially as there is sufficient room for the moon in the aforesaid
space. Hence we do not hesitate to claim that the whole system, which
includes the moon with the earth for its centre, makes the round of that
great circle between the planets, in yearly motion about the sun,
and revolves about the centre of the universe, in which the sun rests
motionless, and that all which looks like motion in the sun is explained
by the motion of the earth. The extent of the universe, however, is
so great that, whereas the distance of the earth from the sun is
considerable in comparison with the size of the other planetary orbits,
it disappears when compared with the sphere of the fixed stars. I hold
this to be more easily comprehensible than when the mind is confused by
an almost endless number of circles, which is necessarily the case with
those who keep the earth in the middle of the universe. Although this
may appear incomprehensible and contrary to the opinion of many, I
shall, if God wills, make it clearer than the sun, at least to those who
are not ignorant of mathematics.

"The order of the spheres is as follows: The first and lightest of all
the spheres is that of the fixed stars, which includes itself and all
others, and hence is motionless as the place in the universe to which
the motion and position of all other stars is referred.

"Then follows the outermost planet, Saturn, which completes its
revolution around the sun in thirty years; next comes Jupiter with a
twelve years' revolution; then Mars, which completes its course in two
years. The fourth one in order is the yearly revolution which includes
the earth with the moon's orbit as an epicycle. In the fifth place is
Venus with a revolution of nine months. The sixth place is taken by
Mercury, which completes its course in eighty days. In the middle of
all stands the sun, and who could wish to place the lamp of this most
beautiful temple in another or better place. Thus, in fact, the sun,
seated upon the royal throne, controls the family of the stars which
circle around him. We find in their order a harmonious connection which
cannot be found elsewhere. Here the attentive observer can see why the
waxing and waning of Jupiter seems greater than with Saturn and smaller
than with Mars, and again greater with Venus than with Mercury. Also,
why Saturn, Jupiter, and Mars are nearer to the earth when they rise
in the evening than when they disappear in the rays of the sun. More
prominently, however, is it seen in the case of Mars, which when it
appears in the heavens at night, seems to equal Jupiter in size, but
soon afterwards is found among the stars of second magnitude. All of
this results from the same cause--namely, from the earth's motion. The
fact that nothing of this is to be seen in the case of the fixed stars
is a proof of their immeasurable distance, which makes even the orbit of
yearly motion or its counterpart invisible to us."(1)


The fact that the stars show no parallax had been regarded as an
important argument against the motion of the earth, and it was still so
considered by the opponents of the system of Copernicus. It had, indeed,
been necessary for Aristarchus to explain the fact as due to the extreme
distance of the stars; a perfectly correct explanation, but one that
implies distances that are altogether inconceivable. It remained for
nineteenth-century astronomers to show, with the aid of instruments of
greater precision, that certain of the stars have a parallax. But
long before this demonstration had been brought forward, the system of
Copernicus had been accepted as a part of common knowledge.

While Copernicus postulated a cosmical scheme that was correct as to its
main features, he did not altogether break away from certain defects of
the Ptolemaic hypothesis. Indeed, he seems to have retained as much of
this as practicable, in deference to the prejudice of his time. Thus
he records the planetary orbits as circular, and explains their
eccentricities by resorting to the theory of epicycles, quite after
the Ptolemaic method. But now, of course, a much more simple mechanism
sufficed to explain the planetary motions, since the orbits were
correctly referred to the central sun and not to the earth.

Needless to say, the revolutionary conception of Copernicus did not meet
with immediate acceptance. A number of prominent astronomers, however,
took it up almost at once, among these being Rhaeticus, who wrote
a commentary on the evolutions; Erasmus Reinhold, the author of the
Prutenic tables; Rothmann, astronomer to the Landgrave of Hesse, and
Maestlin, the instructor of Kepler. The Prutenic tables, just referred
to, so called because of their Prussian origin, were considered an
improvement on the tables of Copernicus, and were highly esteemed by
the astronomers of the time. The commentary of Rhaeticus gives us the
interesting information that it was the observation of the orbit of
Mars and of the very great difference between his apparent diameters at
different times which first led Copernicus to conceive the heliocentric
idea. Of Reinhold it is recorded that he considered the orbit of Mercury
elliptical, and that he advocated a theory of the moon, according to
which her epicycle revolved on an elliptical orbit, thus in a measure
anticipating one of the great discoveries of Kepler to which we shall
refer presently. The Landgrave of Hesse was a practical astronomer, who
produced a catalogue of fixed stars which has been compared with that
of Tycho Brahe. He was assisted by Rothmann and by Justus Byrgius.
Maestlin, the preceptor of Kepler, is reputed to have been the first
modern observer to give a correct explanation of the light seen on
portions of the moon not directly illumined by the sun. He explained
this as not due to any proper light of the moon itself, but as light
reflected from the earth. Certain of the Greek philosophers, however,
are said to have given the same explanation, and it is alleged also that
Leonardo da Vinci anticipated Maestlin in this regard.(2)

While, various astronomers of some eminence thus gave support to the
Copernican system, almost from the beginning, it unfortunately chanced
that by far the most famous of the immediate successors of Copernicus
declined to accept the theory of the earth's motion. This was Tycho
Brahe, one of the greatest observing astronomers of any age. Tycho
Brahe was a Dane, born at Knudstrup in the year 1546. He died in 1601 at
Prague, in Bohemia. During a considerable portion of his life he found
a patron in Frederick, King of Denmark, who assisted him to build a
splendid observatory on the Island of Huene. On the death of his patron
Tycho moved to Germany, where, as good luck would have it, he came in
contact with the youthful Kepler, and thus, no doubt, was instrumental
in stimulating the ambitions of one who in later years was to be known
as a far greater theorist than himself. As has been said, Tycho rejected
the Copernican theory of the earth's motion. It should be added,
however, that he accepted that part of the Copernican theory which
makes the sun the centre of all the planetary motions, the earth being
excepted. He thus developed a system of his own, which was in some sort
a compromise between the Ptolemaic and the Copernican systems. As Tycho
conceived it, the sun revolves about the earth, carrying with it the
planets-Mercury, Venus, Mars, Jupiter, and Saturn, which planets have
the sun and not the earth as the centre of their orbits. This cosmical
scheme, it should be added, may be made to explain the observed motions
of the heavenly bodies, but it involves a much more complex mechanism
than is postulated by the Copernican theory.

Various explanations have been offered of the conservatism which held
the great Danish astronomer back from full acceptance of the relatively
simple and, as we now know, correct Copernican doctrine. From our
latter-day point of view, it seems so much more natural to accept
than to reject the Copernican system, that we find it difficult to put
ourselves in the place of a sixteenth-century observer. Yet if we recall
that the traditional view, having warrant of acceptance by nearly all
thinkers of every age, recorded the earth as a fixed, immovable body, we
shall see that our surprise should be excited rather by the thinker who
can break away from this view than by the one who still tends to cling
to it.

Moreover, it is useless to attempt to disguise the fact that something
more than a mere vague tradition was supposed to support the idea of
the earth's overshadowing importance in the cosmical scheme.
The sixteenth-century mind was overmastered by the tenets of
ecclesiasticism, and it was a dangerous heresy to doubt that the Hebrew
writings, upon which ecclesiasticism based its claim, contained the last
word regarding matters of science. But the writers of the Hebrew text
had been under the influence of that Babylonian conception of the
universe which accepted the earth as unqualifiedly central--which,
indeed, had never so much as conceived a contradictory hypothesis;
and so the Western world, which had come to accept these writings as
actually supernatural in origin, lay under the spell of Oriental ideas
of a pre-scientific era. In our own day, no one speaking with authority
thinks of these Hebrew writings as having any scientific weight
whatever. Their interest in this regard is purely antiquarian; hence
from our changed point of view it seems scarcely credible that Tycho
Brahe can have been in earnest when he quotes the Hebrew traditions as
proof that the sun revolves about the earth. Yet we shall see that for
almost three centuries after the time of Tycho, these same dreamings
continued to be cited in opposition to those scientific advances which
new observations made necessary; and this notwithstanding the fact that
the Oriental phrasing is, for the most part, poetically ambiguous and
susceptible of shifting interpretations, as the criticism of successive
generations has amply testified.

As we have said, Tycho Brahe, great observer as he was, could not shake
himself free from the Oriental incubus. He began his objections, then,
to the Copernican system by quoting the adverse testimony of a Hebrew
prophet who lived more than a thousand years B.C. All of this shows
sufficiently that Tycho Brahe was not a great theorist. He was
essentially an observer, but in this regard he won a secure place in the
very first rank. Indeed, he was easily the greatest observing astronomer
since Hipparchus, between whom and himself there were many points of
resemblance. Hipparchus, it will be recalled, rejected the Aristarchian
conception of the universe just as Tycho rejected the conception of
Copernicus.

But if Tycho propounded no great generalizations, the list of specific
advances due to him is a long one, and some of these were to prove
important aids in the hands of later workers to the secure demonstration
of the Copernican idea. One of his most important series of studies had
to do with comets. Regarding these bodies there had been the greatest
uncertainty in the minds of astronomers. The greatest variety of
opinions regarding them prevailed; they were thought on the one hand to
be divine messengers, and on the other to be merely igneous phenomena
of the earth's atmosphere. Tycho Brahe declared that a comet which he
observed in the year 1577 had no parallax, proving its extreme distance.
The observed course of the comet intersected the planetary orbits,
which fact gave a quietus to the long-mooted question as to whether the
Ptolemaic spheres were transparent solids or merely imaginary; since the
comet was seen to intersect these alleged spheres, it was obvious that
they could not be the solid substance that they were commonly imagined
to be, and this fact in itself went far towards discrediting the
Ptolemaic system. It should be recalled, however, that this supposition
of tangible spheres for the various planetary and stellar orbits was
a mediaeval interpretation of Ptolemy's theory rather than an
interpretation of Ptolemy himself, there being nothing to show that the
Alexandrian astronomer regarded his cycles and epicycles as other than
theoretical.

An interesting practical discovery made by Tycho was his method of
determining the latitude of a place by means of two observations made at
an interval of twelve hours. Hitherto it had been necessary to observe
the sun's angle on the equinoctial days, a period of six months being
therefore required. Tycho measured the angle of elevation of some star
situated near the pole, when on the meridian, and then, twelve hours
later, measured the angle of elevation of the same star when it again
came to the meridian at the opposite point of its apparent circle about
the polestar. Half the sum of these angles gives the latitude of the
place of observation.

As illustrating the accuracy of Tycho's observations, it may be noted
that he rediscovered a third inequality of the moon's motion at its
variation, he, in common with other European astronomers, being then
quite unaware that this inequality had been observed by an Arabian
astronomer. Tycho proved also that the angle of inclination of the
moon's orbit to the ecliptic is subject to slight variation.

The very brilliant new star which shone forth suddenly in the
constellation of Cassiopeia in the year 1572, was made the object of
special studies by Tycho, who proved that the star had no sensible
parallax and consequently was far beyond the planetary regions. The
appearance of a new star was a phenomenon not unknown to the ancients,
since Pliny records that Hipparchus was led by such an appearance
to make his catalogue of the fixed stars. But the phenomenon is
sufficiently uncommon to attract unusual attention. A similar phenomenon
occurred in the year 1604, when the new star--in this case appearing in
the constellation of Serpentarius--was explained by Kepler as probably
proceeding from a vast combustion. This explanation--in which Kepler is
said to have followed. Tycho--is fully in accord with the most recent
theories on the subject, as we shall see in due course. It is surprising
to hear Tycho credited with so startling a theory, but, on the other
hand, such an explanation is precisely what should be expected from
the other astronomer named. For Johann Kepler, or, as he was originally
named, Johann von Kappel, was one of the most speculative astronomers of
any age. He was forever theorizing, but such was the peculiar quality of
his mind that his theories never satisfied him for long unless he could
put them to the test of observation. Thanks to this happy combination
of qualities, Kepler became the discoverer of three famous laws of
planetary motion which lie at the very foundation of modern astronomy,
and which were to be largely instrumental in guiding Newton to his
still greater generalization. These laws of planetary motion were vastly
important as corroborating the Copernican theory of the universe,
though their position in this regard was not immediately recognized
by contemporary thinkers. Let us examine with some detail into their
discovery, meantime catching a glimpse of the life history of the
remarkable man whose name they bear.


JOHANN KEPLER AND THE LAWS OF PLANETARY MOTION

Johann Kepler was born the 27th of December, 1571, in the little town of
Weil, in Wurtemburg. He was a weak, sickly child, further enfeebled by a
severe attack of small-pox. It would seem paradoxical to assert that the
parents of such a genius were mismated, but their home was not a happy
one, the mother being of a nervous temperament, which perhaps in some
measure accounted for the genius of the child. The father led the life
of a soldier, and finally perished in the campaign against the Turks.
Young Kepler's studies were directed with an eye to the ministry. After
a preliminary training he attended the university at Tubingen, where
he came under the influence of the celebrated Maestlin and became his
life-long friend.

Curiously enough, it is recorded that at first Kepler had no taste
for astronomy or for mathematics. But the doors of the ministry being
presently barred to him, he turned with enthusiasm to the study of
astronomy, being from the first an ardent advocate of the Copernican
system. His teacher, Maestlin, accepted the same doctrine, though he was
obliged, for theological reasons, to teach the Ptolemaic system, as also
to oppose the Gregorian reform of the calendar.

The Gregorian calendar, it should be explained, is so called because it
was instituted by Pope Gregory XIII., who put it into effect in the year
1582, up to which time the so-called Julian calendar, as introduced by
Julius Caesar, had been everywhere accepted in Christendom. This Julian
calendar, as we have seen, was a great improvement on preceding ones,
but still lacked something of perfection inasmuch as its theoretical
day differed appreciably from the actual day. In the course of fifteen
hundred years, since the time of Caesar, this defect amounted to a
discrepancy of about eleven days. Pope Gregory proposed to correct this
by omitting ten days from the calendar, which was done in September,
1582. To prevent similar inaccuracies in the future, the Gregorian
calendar provided that once in four centuries the additional day to make
a leap-year should be omitted, the date selected for such omission being
the last year of every fourth century. Thus the years 1500, 1900, and
2300, A.D., would not be leap-years. By this arrangement an approximate
rectification of the calendar was effected, though even this does not
make it absolutely exact.

Such a rectification as this was obviously desirable, but there was
really no necessity for the omission of the ten days from the calendar.
The equinoctial day had shifted so that in the year 1582 it fell on the
10th of March and September. There was no reason why it should not have
remained there. It would greatly have simplified the task of future
historians had Gregory contented himself with providing for the future
stability of the calendar without making the needless shift in question.
We are so accustomed to think of the 21st of March and 21st of September
as the natural periods of the equinox, that we are likely to forget
that these are purely arbitrary dates for which the 10th might have been
substituted without any inconvenience or inconsistency.

But the opposition to the new calendar, to which reference has been
made, was not based on any such considerations as these. It was due,
largely at any rate, to the fact that Germany at this time was under
sway of the Lutheran revolt against the papacy. So effective was the
opposition that the Gregorian calendar did not come into vogue in
Germany until the year 1699. It may be added that England, under stress
of the same manner of prejudice, held out against the new reckoning
until the year 1751, while Russia does not accept it even now.

As the Protestant leaders thus opposed the papal attitude in a matter
of so practical a character as the calendar, it might perhaps have
been expected that the Lutherans would have had a leaning towards the
Copernican theory of the universe, since this theory was opposed by the
papacy. Such, however, was not the case. Luther himself pointed out with
great strenuousness, as a final and demonstrative argument, the fact
that Joshua commanded the sun and not the earth to stand still; and
his followers were quite as intolerant towards the new teaching as were
their ultramontane opponents. Kepler himself was, at various times, to
feel the restraint of ecclesiastical opposition, though he was never
subjected to direct persecution, as was his friend and contemporary,
Galileo. At the very outset of Kepler's career there was, indeed,
question as to the publication of a work he had written, because that
work took for granted the truth of the Copernican doctrine. This
work appeared, however, in the year 1596. It bore the title Mysterium
Cosmographium, and it attempted to explain the positions of the various
planetary bodies. Copernicus had devoted much time to observation of the
planets with reference to measuring their distance, and his efforts had
been attended with considerable success. He did not, indeed, know the
actual distance of the sun, and, therefore, was quite unable to fix
the distance of any planet; but, on the other hand, he determined the
relative distance of all the planets then known, as measured in terms of
the sun's distance, with remarkable accuracy.

With these measurements as a guide, Kepler was led to a very fanciful
theory, according to which the orbits of the five principal planets
sustain a peculiar relation to the five regular solids of geometry.
His theory was this: "Around the orbit of the earth describe a
dodecahedron--the circle comprising it will be that of Mars; around
Mars describe a tetrahedron--the circle comprising it will be that of
Jupiter; around Jupiter describe a cube--the circle comprising it
will be that of Saturn; now within the earth's orbit inscribe an
icosahedron--the inscribed circle will be that of Venus; in the orbit
of Venus inscribe an octahedron--the circle inscribed will be that of
Mercury."(3)

Though this arrangement was a fanciful one, which no one would
now recall had not the theorizer obtained subsequent fame on more
substantial grounds, yet it evidenced a philosophical spirit on the
part of the astronomer which, misdirected as it was in this instance,
promised well for the future. Tycho Brahe, to whom a copy of the
work was sent, had the acumen to recognize it as a work of genius. He
summoned the young astronomer to be his assistant at Prague, and no
doubt the association thus begun was instrumental in determining the
character of Kepler's future work. It was precisely the training
in minute observation that could avail most for a mind which, like
Kepler's, tended instinctively to the formulation of theories. When
Tycho Brahe died, in 1601, Kepler became his successor. In due time
he secured access to all the unpublished observations of his great
predecessor, and these were of inestimable value to him in the progress
of his own studies.

Kepler was not only an ardent worker and an enthusiastic theorizer, but
he was an indefatigable writer, and it pleased him to take the public
fully into his confidence, not merely as to his successes, but as to
his failures. Thus his works elaborate false theories as well as correct
ones, and detail the observations through which the incorrect guesses
were refuted by their originator. Some of these accounts are highly
interesting, but they must not detain us here. For our present purpose
it must suffice to point out the three important theories, which, as
culled from among a score or so of incorrect ones, Kepler was able to
demonstrate to his own satisfaction and to that of subsequent observers.
Stated in a few words, these theories, which have come to bear the name
of Kepler's Laws, are the following:

1. That the planetary orbits are not circular, but elliptical, the sun
occupying one focus of the ellipses.

2. That the speed of planetary motion varies in different parts of the
orbit in such a way that an imaginary line drawn from the sun to the
planet--that is to say, the radius vector of the planet's orbit--always
sweeps the same area in a given time.


These two laws Kepler published as early as 1609. Many years more of
patient investigation were required before he found out the secret of
the relation between planetary distances and times of revolution which
his third law expresses. In 1618, however, he was able to formulate this
relation also, as follows:

3. The squares of the distance of the various planets from the sun are
proportional to the cubes of their periods of revolution about the sun.


All these laws, it will be observed, take for granted the fact that the
sun is the centre of the planetary orbits. It must be understood, too,
that the earth is constantly regarded, in accordance with the Copernican
system, as being itself a member of the planetary system, subject to
precisely the same laws as the other planets. Long familiarity has made
these wonderful laws of Kepler seem such a matter of course that it is
difficult now to appreciate them at their full value. Yet, as has been
already pointed out, it was the knowledge of these marvellously simple
relations between the planetary orbits that laid the foundation for the
Newtonian law of universal gravitation. Contemporary judgment could not,
of course, anticipate this culmination of a later generation. What it
could understand was that the first law of Kepler attacked one of the
most time-honored of metaphysical conceptions--namely, the Aristotelian
idea that the circle is the perfect figure, and hence that the planetary
orbits must be circular. Not even Copernicus had doubted the validity of
this assumption. That Kepler dared dispute so firmly fixed a belief,
and one that seemingly had so sound a philosophical basis, evidenced the
iconoclastic nature of his genius. That he did not rest content until he
had demonstrated the validity of his revolutionary assumption shows how
truly this great theorizer made his hypotheses subservient to the most
rigid inductions.


GALILEO GALILEI

While Kepler was solving these riddles of planetary motion, there was
an even more famous man in Italy whose championship of the Copernican
doctrine was destined to give the greatest possible publicity to the
new ideas. This was Galileo Galilei, one of the most extraordinary
scientific observers of any age. Galileo was born at Pisa, on the 18th
of February (old style), 1564. The day of his birth is doubly memorable,
since on the same day the greatest Italian of the preceding epoch,
Michael Angelo, breathed his last. Persons fond of symbolism have found
in the coincidence a forecast of the transit from the artistic to
the scientific epoch of the later Renaissance. Galileo came of an
impoverished noble family. He was educated for the profession of
medicine, but did not progress far before his natural proclivities
directed him towards the physical sciences. Meeting with opposition in
Pisa, he early accepted a call to the chair of natural philosophy in the
University of Padua, and later in life he made his home at Florence. The
mechanical and physical discoveries of Galileo will claim our attention
in another chapter. Our present concern is with his contribution to the
Copernican theory.

Galileo himself records in a letter to Kepler that he became a convert
to this theory at an early day. He was not enabled, however, to make any
marked contribution to the subject, beyond the influence of his general
teachings, until about the year 1610. The brilliant contributions which
he made were due largely to a single discovery--namely, that of the
telescope. Hitherto the astronomical observations had been made with the
unaided eye. Glass lenses had been known since the thirteenth century,
but, until now, no one had thought of their possible use as aids to
distant vision. The question of priority of discovery has never been
settled. It is admitted, however, that the chief honors belong to the
opticians of the Netherlands.

As early as the year 1590 the Dutch optician Zacharias Jensen placed
a concave and a convex lens respectively at the ends of a tube about
eighteen inches long, and used this instrument for the purpose of
magnifying small objects--producing, in short, a crude microscope. Some
years later, Johannes Lippershey, of whom not much is known except that
he died in 1619, experimented with a somewhat similar combination of
lenses, and made the startling observation that the weather-vane on
a distant church-steeple seemed to be brought much nearer when viewed
through the lens. The combination of lenses he employed is that still
used in the construction of opera-glasses; the Germans still call such a
combination a Dutch telescope.

Doubtless a large number of experimenters took the matter up and the
fame of the new instrument spread rapidly abroad. Galileo, down in
Italy, heard rumors of this remarkable contrivance, through the use of
which it was said "distant objects might be seen as clearly as those
near at hand." He at once set to work to construct for himself a similar
instrument, and his efforts were so far successful that at first he "saw
objects three times as near and nine times enlarged." Continuing his
efforts, he presently so improved his glass that objects were enlarged
almost a thousand times and made to appear thirty times nearer than
when seen with the naked eye. Naturally enough, Galileo turned this
fascinating instrument towards the skies, and he was almost immediately
rewarded by several startling discoveries. At the very outset, his
magnifying-glass brought to view a vast number of stars that are
invisible to the naked eye, and enabled the observer to reach the
conclusion that the hazy light of the Milky Way is merely due to the
aggregation of a vast number of tiny stars.

Turning his telescope towards the moon, Galileo found that body rough
and earth-like in contour, its surface covered with mountains, whose
height could be approximately measured through study of their shadows.
This was disquieting, because the current Aristotelian doctrine supposed
the moon, in common with the planets, to be a perfectly spherical,
smooth body. The metaphysical idea of a perfect universe was sure to
be disturbed by this seemingly rough workmanship of the moon. Thus
far, however, there was nothing in the observations of Galileo to bear
directly upon the Copernican theory; but when an inspection was made of
the planets the case was quite different. With the aid of his telescope,
Galileo saw that Venus, for example, passes through phases precisely
similar to those of the moon, due, of course, to the same cause. Here,
then, was demonstrative evidence that the planets are dark bodies
reflecting the light of the sun, and an explanation was given of the
fact, hitherto urged in opposition to the Copernican theory, that the
inferior planets do not seem many times brighter when nearer the earth
than when in the most distant parts of their orbits; the explanation
being, of course, that when the planets are between the earth and the
sun only a small portion of their illumined surfaces is visible from the
earth.

On inspecting the planet Jupiter, a still more striking revelation was
made, as four tiny stars were observed to occupy an equatorial position
near that planet, and were seen, when watched night after night, to
be circling about the planet, precisely as the moon circles about
the earth. Here, obviously, was a miniature solar system--a tangible
object-lesson in the Copernican theory. In honor of the ruling
Florentine house of the period, Galileo named these moons of Jupiter,
Medicean stars.

Turning attention to the sun itself, Galileo observed on the surface
of that luminary a spot or blemish which gradually changed its shape,
suggesting that changes were taking place in the substance of the
sun--changes obviously incompatible with the perfect condition
demanded by the metaphysical theorists. But however disquieting for the
conservative, the sun's spots served a most useful purpose in enabling
Galileo to demonstrate that the sun itself revolves on its axis, since
a given spot was seen to pass across the disk and after disappearing
to reappear in due course. The period of rotation was found to be about
twenty-four days.

It must be added that various observers disputed priority of discovery
of the sun's spots with Galileo. Unquestionably a sun-spot had been
seen by earlier observers, and by them mistaken for the transit of an
inferior planet. Kepler himself had made this mistake. Before the day of
the telescope, he had viewed the image of the sun as thrown on a screen
in a camera-obscura, and had observed a spot on the disk which be
interpreted as representing the planet Mercury, but which, as is now
known, must have been a sun-spot, since the planetary disk is too
small to have been revealed by this method. Such observations as these,
however interesting, cannot be claimed as discoveries of the sun-spots.
It is probable, however, that several discoverers (notably Johann
Fabricius) made the telescopic observation of the spots, and recognized
them as having to do with the sun's surface, almost simultaneously with
Galileo. One of these claimants was a Jesuit named Scheiner, and the
jealousy of this man is said to have had a share in bringing about that
persecution to which we must now refer.

There is no more famous incident in the history of science than the
heresy trial through which Galileo was led to the nominal renunciation
of his cherished doctrines. There is scarcely another incident that has
been commented upon so variously. Each succeeding generation has put
its own interpretation on it. The facts, however, have been but little
questioned. It appears that in the year 1616 the church became at
last aroused to the implications of the heliocentric doctrine of the
universe. Apparently it seemed clear to the church authorities that the
authors of the Bible believed the world to be immovably fixed at the
centre of the universe. Such, indeed, would seem to be the natural
inference from various familiar phrases of the Hebrew text, and what
we now know of the status of Oriental science in antiquity gives full
warrant to this interpretation. There is no reason to suppose that the
conception of the subordinate place of the world in the solar system had
ever so much as occurred, even as a vague speculation, to the authors of
Genesis. In common with their contemporaries, they believed the earth to
be the all-important body in the universe, and the sun a luminary placed
in the sky for the sole purpose of giving light to the earth. There is
nothing strange, nothing anomalous, in this view; it merely reflects the
current notions of Oriental peoples in antiquity. What is strange and
anomalous is the fact that the Oriental dreamings thus expressed could
have been supposed to represent the acme of scientific knowledge. Yet
such a hold had these writings taken upon the Western world that not
even a Galileo dared contradict them openly; and when the church fathers
gravely declared the heliocentric theory necessarily false, because
contradictory to Scripture, there were probably few people in
Christendom whose mental attitude would permit them justly to appreciate
the humor of such a pronouncement. And, indeed, if here and there a man
might have risen to such an appreciation, there were abundant reasons
for the repression of the impulse, for there was nothing humorous about
the response with which the authorities of the time were wont to meet
the expression of iconoclastic opinions. The burning at the stake of
Giordano Bruno, in the year 1600, was, for example, an object-lesson
well calculated to restrain the enthusiasm of other similarly minded
teachers.

Doubtless it was such considerations that explained the relative silence
of the champions of the Copernican theory, accounting for the otherwise
inexplicable fact that about eighty years elapsed after the death of
Copernicus himself before a single text-book expounded his theory. The
text-book which then appeared, under date of 1622, was written by the
famous Kepler, who perhaps was shielded in a measure from the papal
consequences of such hardihood by the fact of residence in a Protestant
country. Not that the Protestants of the time favored the heliocentric
doctrine--we have already quoted Luther in an adverse sense--but of
course it was characteristic of the Reformation temper to oppose any
papal pronouncement, hence the ultramontane declaration of 1616 may
indirectly have aided the doctrine which it attacked, by making that
doctrine less obnoxious to Lutheran eyes. Be that as it may, the work of
Kepler brought its author into no direct conflict with the authorities.
But the result was quite different when, in 1632, Galileo at last broke
silence and gave the world, under cover of the form of dialogue, an
elaborate exposition of the Copernican theory. Galileo, it must be
explained, had previously been warned to keep silent on the subject,
hence his publication doubly offended the authorities. To be sure, he
could reply that his dialogue introduced a champion of the Ptolemaic
system to dispute with the upholder of the opposite view, and that, both
views being presented with full array of argument, the reader was left
to reach a verdict for himself, the author having nowhere pointedly
expressed an opinion. But such an argument, of course, was specious, for
no one who read the dialogue could be in doubt as to the opinion of the
author. Moreover, it was hinted that Simplicio, the character who upheld
the Ptolemaic doctrine and who was everywhere worsted in the argument,
was intended to represent the pope himself--a suggestion which probably
did no good to Galileo's cause.

The character of Galileo's artistic presentation may best be judged from
an example, illustrating the vigorous assault of Salviati, the
champion of the new theory, and the feeble retorts of his conservative
antagonist:

"Salviati. Let us then begin our discussion with the consideration that,
whatever motion may be attributed to the earth, yet we, as dwellers upon
it, and hence as participators in its motion, cannot possibly perceive
anything of it, presupposing that we are to consider only earthly
things. On the other hand, it is just as necessary that this same motion
belong apparently to all other bodies and visible objects, which, being
separated from the earth, do not take part in its motion. The correct
method to discover whether one can ascribe motion to the earth, and what
kind of motion, is, therefore, to investigate and observe whether in
bodies outside the earth a perceptible motion may be discovered which
belongs to all alike. Because a movement which is perceptible only in
the moon, for instance, and has nothing to do with Venus or Jupiter or
other stars, cannot possibly be peculiar to the earth, nor can its
seat be anywhere else than in the moon. Now there is one such universal
movement which controls all others--namely, that which the sun, moon,
the other planets, the fixed stars--in short, the whole universe, with
the single exception of the earth--appears to execute from east to west
in the space of twenty-four hours. This now, as it appears at the first
glance anyway, might just as well be a motion of the earth alone as of
all the rest of the universe with the exception of the earth, for the
same phenomena would result from either hypothesis. Beginning with the
most general, I will enumerate the reasons which seem to speak in favor
of the earth's motion. When we merely consider the immensity of the
starry sphere in comparison with the smallness of the terrestrial ball,
which is contained many million times in the former, and then think of
the rapidity of the motion which completes a whole rotation in one day
and night, I cannot persuade myself how any one can hold it to be more
reasonable and credible that it is the heavenly sphere which rotates,
while the earth stands still.

"Simplicio. I do not well understand how that powerful motion may be
said to as good as not exist for the sun, the moon, the other planets,
and the innumerable host of fixed stars. Do you call that nothing when
the sun goes from one meridian to another, rises up over this horizon
and sinks behind that one, brings now day, and now night; when the moon
goes through similar changes, and the other planets and fixed stars in
the same way?

"Salviati. All the changes you mention are such only in respect to
the earth. To convince yourself of it, only imagine the earth out of
existence. There would then be no rising and setting of the sun or of
the moon, no horizon, no meridian, no day, no night--in short, the said
motion causes no change of any sort in the relation of the sun to the
moon or to any of the other heavenly bodies, be they planets or fixed
stars. All changes are rather in respect to the earth; they may all be
reduced to the simple fact that the sun is first visible in China, then
in Persia, afterwards in Egypt, Greece, France, Spain, America, etc.,
and that the same thing happens with the moon and the other heavenly
bodies. Exactly the same thing happens and in exactly the same way if,
instead of disturbing so large a part of the universe, you let the earth
revolve about itself. The difficulty is, however, doubled, inasmuch as a
second very important problem presents itself. If, namely, that powerful
motion is ascribed to the heavens, it is absolutely necessary to regard
it as opposed to the individual motion of all the planets, every one of
which indubitably has its own very leisurely and moderate movement
from west to east. If, on the other hand, you let the earth move about
itself, this opposition of motion disappears.

"The improbability is tripled by the complete overthrow of that order
which rules all the heavenly bodies in which the revolving motion is
definitely established. The greater the sphere is in such a case, so
much longer is the time required for its revolution; the smaller the
sphere the shorter the time. Saturn, whose orbit surpasses those of all
the planets in size, traverses it in thirty years. Jupiter(4) completes
its smaller course in twelve years, Mars in two; the moon performs its
much smaller revolution within a month. Just as clearly in the Medicean
stars, we see that the one nearest Jupiter completes its revolution in
a very short time--about forty-two hours; the next in about three and
one-half days, the third in seven, and the most distant one in sixteen
days. This rule, which is followed throughout, will still remain if we
ascribe the twenty-four-hourly motion to a rotation of the earth. If,
however, the earth is left motionless, we must go first from the very
short rule of the moon to ever greater ones--to the two-yearly rule of
Mars, from that to the twelve-yearly one of Jupiter, from here to
the thirty-yearly one of Saturn, and then suddenly to an incomparably
greater sphere, to which also we must ascribe a complete rotation in
twenty-four hours. If, however, we assume a motion of the earth, the
rapidity of the periods is very well preserved; from the slowest sphere
of Saturn we come to the wholly motionless fixed stars. We also escape
thereby a fourth difficulty, which arises as soon as we assume that
there is motion in the sphere of the stars. I mean the great unevenness
in the movement of these very stars, some of which would have to revolve
with extraordinary rapidity in immense circles, while others moved very
slowly in small circles, since some of them are at a greater, others at
a less, distance from the pole. That is likewise an inconvenience,
for, on the one hand, we see all those stars, the motion of which is
indubitable, revolve in great circles, while, on the other hand, there
seems to be little object in placing bodies, which are to move in
circles, at an enormous distance from the centre and then let them
move in very small circles. And not only are the size of the different
circles and therewith the rapidity of the movement very different in the
different fixed stars, but the same stars also change their orbits and
their rapidity of motion. Therein consists the fifth inconvenience.
Those stars, namely, which were at the equator two thousand years ago,
and hence described great circles in their revolutions, must to-day
move more slowly and in smaller circles, because they are many degrees
removed from it. It will even happen, after not so very long a time,
that one of those which have hitherto been continually in motion will
finally coincide with the pole and stand still, but after a period of
repose will again begin to move. The other stars in the mean while,
which unquestionably move, all have, as was said, a great circle for an
orbit and keep this unchangeably.

"The improbability is further increased--this may be considered the
sixth inconvenience--by the fact that it is impossible to conceive what
degree of solidity those immense spheres must have, in the depths of
which so many stars are fixed so enduringly that they are kept revolving
evenly in spite of such difference of motion without changing their
respective positions. Or if, according to the much more probable theory,
the heavens are fluid, and every star describes an orbit of its own,
according to what law then, or for what reason, are their orbits
so arranged that, when looked at from the earth, they appear to be
contained in one single sphere? To attain this it seems to me much
easier and more convenient to make them motionless instead of moving,
just as the paving-stones on the market-place, for instance, remain in
order more easily than the swarms of children running about on them.

"Finally, the seventh difficulty: If we attribute the daily rotation to
the higher region of the heavens, we should have to endow it with force
and power sufficient to carry with it the innumerable host of the fixed
stars--every one a body of very great compass and much larger than the
earth--and all the planets, although the latter, like the earth, move
naturally in an opposite direction. In the midst of all this the little
earth, single and alone, would obstinately and wilfully withstand such
force--a supposition which, it appears to me, has much against it. I
could also not explain why the earth, a freely poised body, balancing
itself about its centre, and surrounded on all sides by a fluid medium,
should not be affected by the universal rotation. Such difficulties,
however, do not confront us if we attribute motion to the earth--such
a small, insignificant body in comparison with the whole universe, and
which for that very reason cannot exercise any power over the latter.

"Simplicio. You support your arguments throughout, it seems to me,
on the greater ease and simplicity with which the said effects are
produced. You mean that as a cause the motion of the earth alone is just
as satisfactory as the motion of all the rest of the universe with the
exception of the earth; you hold the actual event to be much easier
in the former case than in the latter. For the ruler of the universe,
however, whose might is infinite, it is no less easy to move the
universe than the earth or a straw balm. But if his power is infinite,
why should not a greater, rather than a very small, part of it be
revealed to me?

"Salviati. If I had said that the universe does not move on account of
the impotence of its ruler, I should have been wrong and your rebuke
would have been in order. I admit that it is just as easy for an
infinite power to move a hundred thousand as to move one. What I said,
however, does not refer to him who causes the motion, but to that
which is moved. In answer to your remark that it is more fitting for an
infinite power to reveal a large part of itself rather than a little, I
answer that, in relation to the infinite, one part is not greater than
another, if both are finite. Hence it is unallowable to say that a
hundred thousand is a larger part of an infinite number than two,
although the former is fifty thousand times greater than the latter. If,
therefore, we consider the moving bodies, we must unquestionably regard
the motion of the earth as a much simpler process than that of the
universe; if, furthermore, we direct our attention to so many other
simplifications which may be reached only by this theory, the daily
movement of the earth must appear much more probable than the motion
of the universe without the earth, for, according to Aristotle's just
axiom, 'Frustra fit per plura, quod potest fieri per p auciora' (It is
vain to expend many means where a few are sufficient)."(2)


The work was widely circulated, and it was received with an interest
which bespeaks a wide-spread undercurrent of belief in the Copernican
doctrine. Naturally enough, it attracted immediate attention from the
church authorities. Galileo was summoned to appear at Rome to defend his
conduct. The philosopher, who was now in his seventieth year, pleaded
age and infirmity. He had no desire for personal experience of the
tribunal of the Inquisition; but the mandate was repeated, and Galileo
went to Rome. There, as every one knows, he disavowed any intention to
oppose the teachings of Scripture, and formally renounced the heretical
doctrine of the earth's motion. According to a tale which so long passed
current that every historian must still repeat it though no one now
believes it authentic, Galileo qualified his renunciation by muttering
to himself, "E pur si muove" (It does move, none the less), as he rose
to his feet and retired from the presence of his persecutors. The tale
is one of those fictions which the dramatic sense of humanity is wont
to impose upon history, but, like most such fictions, it expresses the
spirit if not the letter of truth; for just as no one believes that
Galileo's lips uttered the phrase, so no one doubts that the rebellious
words were in his mind.

After his formal renunciation, Galileo was allowed to depart, but with
the injunction that he abstain in future from heretical teaching. The
remaining ten years of his life were devoted chiefly to mechanics, where
his experiments fortunately opposed the Aristotelian rather than the
Hebrew teachings. Galileo's death occurred in 1642, a hundred years
after the death of Copernicus. Kepler had died thirteen years before,
and there remained no astronomer in the field who is conspicuous in
the history of science as a champion of the Copernican doctrine. But in
truth it might be said that the theory no longer needed a champion. The
researches of Kepler and Galileo had produced a mass of evidence for the
Copernican theory which amounted to demonstration. A generation or two
might be required for this evidence to make itself everywhere known
among men of science, and of course the ecclesiastical authorities must
be expected to stand by their guns for a somewhat longer period. In
point of fact, the ecclesiastical ban was not technically removed by
the striking of the Copernican books from the list of the Index
Expurgatorius until the year 1822, almost two hundred years after the
date of Galileo's dialogue. But this, of course, is in no sense a guide
to the state of general opinion regarding the theory. We shall gain a
true gauge as to this if we assume that the greater number of important
thinkers had accepted the heliocentric doctrine before the middle of the
seventeenth century, and that before the close of that century the old
Ptolemaic idea had been quite abandoned. A wonderful revolution in
man's estimate of the universe had thus been effected within about two
centuries after the birth of Copernicus.




V. GALILEO AND THE NEW PHYSICS

After Galileo had felt the strong hand of the Inquisition, in 1632, he
was careful to confine his researches, or at least his publications, to
topics that seemed free from theological implications. In doing so he
reverted to the field of his earliest studies--namely, the field of
mechanics; and the Dialoghi delle Nuove Scienze, which he finished in
1636, and which was printed two years later, attained a celebrity no
less than that of the heretical dialogue that had preceded it. The
later work was free from all apparent heresies, yet perhaps it did
more towards the establishment of the Copernican doctrine, through
the teaching of correct mechanical principles, than the other work had
accomplished by a more direct method.

Galileo's astronomical discoveries were, as we have seen, in a sense
accidental; at least, they received their inception through the
inventive genius of another. His mechanical discoveries, on the other
hand, were the natural output of his own creative genius. At the very
beginning of his career, while yet a very young man, though a professor
of mathematics at Pisa, he had begun that onslaught upon the old
Aristotelian ideas which he was to continue throughout his life. At the
famous leaning tower in Pisa, the young iconoclast performed, in the
year 1590, one of the most theatrical demonstrations in the history
of science. Assembling a multitude of champions of the old ideas, he
proposed to demonstrate the falsity of the Aristotelian doctrine that
the velocity of falling bodies is proportionate to their weight. There
is perhaps no fact more strongly illustrative of the temper of
the Middle Ages than the fact that this doctrine, as taught by the
Aristotelian philosopher, should so long have gone unchallenged. Now,
however, it was put to the test; Galileo released a half-pound weight
and a hundred-pound cannon-ball from near the top of the tower, and,
needless to say, they reached the ground together. Of course, the
spectators were but little pleased with what they saw. They could not
doubt the evidence of their own senses as to the particular experiment
in question; they could suggest, however, that the experiment involved
a violation of the laws of nature through the practice of magic. To
controvert so firmly established an idea savored of heresy. The young
man guilty of such iconoclasm was naturally looked at askance by the
scholarship of his time. Instead of being applauded, he was hissed, and
he found it expedient presently to retire from Pisa.

Fortunately, however, the new spirit of progress had made itself felt
more effectively in some other portions of Italy, and so Galileo found a
refuge and a following in Padua, and afterwards in Florence; and while,
as we have seen, he was obliged to curb his enthusiasm regarding the
subject that was perhaps nearest his heart--the promulgation of the
Copernican theory--yet he was permitted in the main to carry on his
experimental observations unrestrained. These experiments gave him a
place of unquestioned authority among his contemporaries, and they have
transmitted his name to posterity as that of one of the greatest of
experimenters and the virtual founder of modern mechanical science. The
experiments in question range over a wide field; but for the most part
they have to do with moving bodies and with questions of force, or, as
we should now say, of energy. The experiment at the leaning tower showed
that the velocity of falling bodies is independent of the weight of the
bodies, provided the weight is sufficient to overcome the resistance
of the atmosphere. Later experiments with falling bodies led to the
discovery of laws regarding the accelerated velocity of fall. Such
velocities were found to bear a simple relation to the period of time
from the beginning of the fall. Other experiments, in which balls were
allowed to roll down inclined planes, corroborated the observation that
the pull of gravitation gave a velocity proportionate to the length of
fall, whether such fall were direct or in a slanting direction.

These studies were associated with observations on projectiles,
regarding which Galileo was the first to entertain correct notions.
According to the current idea, a projectile fired, for example, from a
cannon, moved in a straight horizontal line until the propulsive force
was exhausted, and then fell to the ground in a perpendicular line.
Galileo taught that the projectile begins to fall at once on leaving the
mouth of the cannon and traverses a parabolic course. According to his
idea, which is now familiar to every one, a cannon-ball dropped from the
level of the cannon's muzzle will strike the ground simultaneously with
a ball fired horizontally from the cannon. As to the paraboloid course
pursued by the projectile, the resistance of the air is a factor which
Galileo could not accurately compute, and which interferes with the
practical realization of his theory. But this is a minor consideration.
The great importance of his idea consists in the recognition that such
a force as that of gravitation acts in precisely the same way upon all
unsupported bodies, whether or not such bodies be at the same time acted
upon by a force of translation.

Out of these studies of moving bodies was gradually developed a correct
notion of several important general laws of mechanics--laws a knowledge
of which was absolutely essential to the progress of physical science.
The belief in the rotation of the earth made necessary a clear
conception that all bodies at the surface of the earth partake of that
motion quite independently of their various observed motions in relation
to one another. This idea was hard to grasp, as an oft-repeated argument
shows. It was asserted again and again that, if the earth rotates, a
stone dropped from the top of a tower could not fall at the foot of the
tower, since the earth's motion would sweep the tower far away from its
original position while the stone is in transit.

This was one of the stock arguments against the earth's motion, yet it
was one that could be refuted with the greatest ease by reasoning
from strictly analogous experiments. It might readily be observed, for
example, that a stone dropped from a moving cart does not strike the
ground directly below the point from which it is dropped, but partakes
of the forward motion of the cart. If any one doubt this he has but to
jump from a moving cart to be given a practical demonstration of the
fact that his entire body was in some way influenced by the motion of
translation. Similarly, the simple experiment of tossing a ball from the
deck of a moving ship will convince any one that the ball partakes of
the motion of the ship, so that it can be manipulated precisely as
if the manipulator were standing on the earth. In short, every-day
experience gives us illustrations of what might be called compound
motion, which makes it seem altogether plausible that, if the earth is
in motion, objects at its surface will partake of that motion in a way
that does not interfere with any other movements to which they may
be subjected. As the Copernican doctrine made its way, this idea of
compound motion naturally received more and more attention, and
such experiments as those of Galileo prepared the way for a new
interpretation of the mechanical principles involved.

The great difficulty was that the subject of moving bodies had all
along been contemplated from a wrong point of view. Since force must be
applied to an object to put it in motion, it was perhaps not unnaturally
assumed that similar force must continue to be applied to keep the
object in motion. When, for example, a stone is thrown from the hand,
the direct force applied necessarily ceases as soon as the projectile
leaves the hand. The stone, nevertheless, flies on for a certain
distance and then falls to the ground. How is this flight of the stone
to be explained? The ancient philosophers puzzled more than a little
over this problem, and the Aristotelians reached the conclusion that the
motion of the hand had imparted a propulsive motion to the air, and that
this propulsive motion was transmitted to the stone, pushing it on. Just
how the air took on this propulsive property was not explained, and
the vagueness of thought that characterized the time did not demand
an explanation. Possibly the dying away of ripples in water may have
furnished, by analogy, an explanation of the gradual dying out of the
impulse which propels the stone.

All of this was, of course, an unfortunate maladjustment of the point of
view. As every one nowadays knows, the air retards the progress of the
stone, enabling the pull of gravitation to drag it to the earth earlier
than it otherwise could. Were the resistance of the air and the pull of
gravitation removed, the stone as projected from the hand would fly on
in a straight line, at an unchanged velocity, forever. But this fact,
which is expressed in what we now term the first law of motion, was
extremely difficult to grasp. The first important step towards it was
perhaps implied in Galileo's study of falling bodies. These studies, as
we have seen, demonstrated that a half-pound weight and a hundred-pound
weight fall with the same velocity. It is, however, matter of common
experience that certain bodies, as, for example, feathers, do not
fall at the same rate of speed with these heavier bodies. This anomaly
demands an explanation, and the explanation is found in the resistance
offered the relatively light object by the air. Once the idea that the
air may thus act as an impeding force was grasped, the investigator of
mechanical principles had entered on a new and promising course.

Galileo could not demonstrate the retarding influence of air in the
way which became familiar a generation or two later; he could not put a
feather and a coin in a vacuum tube and prove that the two would there
fall with equal velocity, because, in his day, the air-pump had not yet
been invented. The experiment was made only a generation after the time
of Galileo, as we shall see; but, meantime, the great Italian had fully
grasped the idea that atmospheric resistance plays a most important part
in regard to the motion of falling and projected bodies. Thanks largely
to his own experiments, but partly also to the efforts of others, he had
come, before the end of his life, pretty definitely to realize that the
motion of a projectile, for example, must be thought of as inherent in
the projectile itself, and that the retardation or ultimate cessation of
that motion is due to the action of antagonistic forces. In other
words, he had come to grasp the meaning of the first law of motion. It
remained, however, for the great Frenchman Descartes to give precise
expression to this law two years after Galileo's death. As Descartes
expressed it in his Principia Philosophiae, published in 1644, any body
once in motion tends to go on in a straight line, at a uniform rate of
speed, forever. Contrariwise, a stationary body will remain forever at
rest unless acted on by some disturbing force.

This all-important law, which lies at the very foundation of all true
conceptions of mechanics, was thus worked out during the first half of
the seventeenth century, as the outcome of numberless experiments
for which Galileo's experiments with failing bodies furnished the
foundation. So numerous and so gradual were the steps by which the
reversal of view regarding moving bodies was effected that it is
impossible to trace them in detail. We must be content to reflect that
at the beginning of the Galilean epoch utterly false notions regarding
the subject were entertained by the very greatest philosophers--by
Galileo himself, for example, and by Kepler--whereas at the close of
that epoch the correct and highly illuminative view had been attained.

We must now consider some other experiments of Galileo which led to
scarcely less-important results. The experiments in question had to do
with the movements of bodies passing down an inclined plane, and
with the allied subject of the motion of a pendulum. The elaborate
experiments of Galileo regarding the former subject were made by
measuring the velocity of a ball rolling down a plane inclined at
various angles. He found that the velocity acquired by a ball was
proportional to the height from which the ball descended regardless of
the steepness of the incline. Experiments were made also with a ball
rolling down a curved gutter, the curve representing the are of a
circle. These experiments led to the study of the curvilinear motions of
a weight suspended by a cord; in other words, of the pendulum.

Regarding the motion of the pendulum, some very curious facts were soon
ascertained. Galileo found, for example, that a pendulum of a given
length performs its oscillations with the same frequency though the arc
described by the pendulum be varied greatly.(1) He found, also, that the
rate of oscillation for pendulums of different lengths varies according
to a simple law. In order that one pendulum shall oscillate one-half
as fast as another, the length of the pendulums must be as four to one.
Similarly, by lengthening the pendulums nine times, the oscillation
is reduced to one-third, In other words, the rate of oscillation of
pendulums varies inversely as the square of their length. Here, then, is
a simple relation between the motions of swinging bodies which suggests
the relation which Kepler bad discovered between the relative motions of
the planets. Every such discovery coming in this age of the rejuvenation
of experimental science had a peculiar force in teaching men the
all-important lesson that simple laws lie back of most of the diverse
phenomena of nature, if only these laws can be discovered.

Galileo further observed that his pendulum might be constructed of
any weight sufficiently heavy readily to overcome the atmospheric
resistance, and that, with this qualification, neither the weight nor
the material had any influence upon the time of oscillation, this being
solely determined by the length of the cord. Naturally, the practical
utility of these discoveries was not overlooked by Galileo. Since a
pendulum of a given length oscillates with unvarying rapidity, here is
an obvious means of measuring time. Galileo, however, appears not to
have met with any great measure of success in putting this idea into
practice. It remained for the mechanical ingenuity of Huyghens to
construct a satisfactory pendulum clock.

As a theoretical result of the studies of rolling and oscillating
bodies, there was developed what is usually spoken of as the third law
of motion--namely, the law that a given force operates upon a moving
body with an effect proportionate to its effect upon the same body when
at rest. Or, as Whewell states the law: "The dynamical effect of
force is as the statical effect; that is, the velocity which any
force generates in a given time, when it puts the body in motion, is
proportional to the pressure which this same force produces in a body
at rest."(2) According to the second law of motion, each one of the
different forces, operating at the same time upon a moving body,
produces the same effect as if it operated upon the body while at rest.


STEVINUS AND THE LAW OF EQUILIBRIUM

It appears, then, that the mechanical studies of Galileo, taken as a
whole, were nothing less than revolutionary. They constituted the first
great advance upon the dynamic studies of Archimedes, and then led to
the secure foundation for one of the most important of modern sciences.
We shall see that an important company of students entered the field
immediately after the time of Galileo, and carried forward the work he
had so well begun. But before passing on to the consideration of their
labors, we must consider work in allied fields of two men who were
contemporaries of Galileo and whose original labors were in some
respects scarcely less important than his own. These men are the
Dutchman Stevinus, who must always be remembered as a co-laborer with
Galileo in the foundation of the science of dynamics, and the Englishman
Gilbert, to whom is due the unqualified praise of first subjecting the
phenomenon of magnetism to a strictly scientific investigation.

Stevinus was born in the year 1548, and died in 1620. He was a man of a
practical genius, and he attracted the attention of his non-scientific
contemporaries, among other ways, by the construction of a curious
land-craft, which, mounted on wheels, was to be propelled by sails like
a boat. Not only did he write a book on this curious horseless carriage,
but he put his idea into practical application, producing a vehicle
which actually traversed the distance between Scheveningen and Petton,
with no fewer than twenty-seven passengers, one of them being Prince
Maurice of Orange. This demonstration was made about the year 1600. It
does not appear, however, that any important use was made of the strange
vehicle; but the man who invented it put his mechanical ingenuity
to other use with better effect. It was he who solved the problem of
oblique forces, and who discovered the important hydrostatic principle
that the pressure of fluids is proportionate to their depth, without
regard to the shape of the including vessel.

The study of oblique forces was made by Stevinus with the aid of
inclined planes. His most demonstrative experiment was a very simple
one, in which a chain of balls of equal weight was hung from a triangle;
the triangle being so constructed as to rest on a horizontal base, the
oblique sides bearing the relation to each other of two to one. Stevinus
found that his chain of balls just balanced when four balls were on the
longer side and two on the shorter and steeper side. The balancing of
force thus brought about constituted a stable equilibrium, Stevinus
being the first to discriminate between such a condition and the
unbalanced condition called unstable equilibrium. By this simple
experiment was laid the foundation of the science of statics. Stevinus
had a full grasp of the principle which his experiment involved, and he
applied it to the solution of oblique forces in all directions. Earlier
investigations of Stevinus were published in 1608. His collected works
were published at Leyden in 1634.

This study of the equilibrium of pressure of bodies at rest led
Stevinus, not unnaturally, to consider the allied subject of the
pressure of liquids. He is to be credited with the explanation of the
so-called hydrostatic paradox. The familiar modern experiment which
illustrates this paradox is made by inserting a long perpendicular tube
of small caliber into the top of a tight barrel. On filling the barrel
and tube with water, it is possible to produce a pressure which will
burst the barrel, though it be a strong one, and though the actual
weight of water in the tube is comparatively insignificant. This
illustrates the fact that the pressure at the bottom of a column of
liquid is proportionate to the height of the column, and not to its
bulk, this being the hydrostatic paradox in question. The explanation
is that an enclosed fluid under pressure exerts an equal force upon all
parts of the circumscribing wall; the aggregate pressure may, therefore,
be increased indefinitely by increasing the surface. It is this
principle, of course, which is utilized in the familiar hydrostatic
press. Theoretical explanations of the pressure of liquids were supplied
a generation or two later by numerous investigators, including Newton,
but the practical refoundation of the science of hydrostatics in modern
times dates from the experiments of Stevinus.


GALILEO AND THE EQUILIBRIUM OF FLUIDS

Experiments of an allied character, having to do with the equilibrium of
fluids, exercised the ingenuity of Galileo. Some of his most interesting
experiments have to do with the subject of floating bodies. It will be
recalled that Archimedes, away back in the Alexandrian epoch, had solved
the most important problems of hydrostatic equilibrium. Now, however,
his experiments were overlooked or forgotten, and Galileo was obliged
to make experiments anew, and to combat fallacious views that ought long
since to have been abandoned. Perhaps the most illuminative view of
the spirit of the times can be gained by quoting at length a paper of
Galileo's, in which he details his own experiments with floating bodies
and controverts the views of his opponents. The paper has further
value as illustrating Galileo's methods both as experimenter and as
speculative reasoner.

The current view, which Galileo here undertakes to refute, asserts that
water offers resistance to penetration, and that this resistance is
instrumental in determining whether a body placed in water will float
or sink. Galileo contends that water is non-resistant, and that bodies
float or sink in virtue of their respective weights. This, of course, is
merely a restatement of the law of Archimedes. But it remains to explain
the fact that bodies of a certain shape will float, while bodies of the
same material and weight, but of a different shape, will sink. We shall
see what explanation Galileo finds of this anomaly as we proceed.

In the first place, Galileo makes a cone of wood or of wax, and shows
that when it floats with either its point or its base in the water, it
displaces exactly the same amount of fluid, although the apex is by its
shape better adapted to overcome the resistance of the water, if that
were the cause of buoyancy. Again, the experiment may be varied by
tempering the wax with filings of lead till it sinks in the water, when
it will be found that in any figure the same quantity of cork must be
added to it to raise the surface.

"But," says Galileo, "this silences not my antagonists; they say that
all the discourse hitherto made by me imports little to them, and that
it serves their turn; that they have demonstrated in one instance, and
in such manner and figure as pleases them best--namely, in a board
and in a ball of ebony--that one when put into the water sinks to the
bottom, and that the other stays to swim on the top; and the matter
being the same, and the two bodies differing in nothing but in figure,
they affirm that with all perspicuity they have demonstrated and
sensibly manifested what they undertook. Nevertheless, I believe, and
think I can prove, that this very experiment proves nothing against my
theory. And first, it is false that the ball sinks and the board not;
for the board will sink, too, if you do to both the figures as the words
of our question require; that is, if you put them both in the water; for
to be in the water implies to be placed in the water, and by Aristotle's
own definition of place, to be placed imports to be environed by the
surface of the ambient body; but when my antagonists show the floating
board of ebony, they put it not into the water, but upon the water;
where, being detained by a certain impediment (of which more anon), it
is surrounded, partly with water, partly with air, which is contrary to
our agreement, for that was that bodies should be in the water, and not
part in the water, part in the air.

"I will not omit another reason, founded also upon experience, and, if
I deceive not myself, conclusive against the notion that figure, and
the resistance of the water to penetration, have anything to do with
the buoyancy of bodies. Choose a piece of wood or other matter, as,
for instance, walnut-wood, of which a ball rises from the bottom of the
water to the surface more slowly than a ball of ebony of the same
size sinks, so that, clearly, the ball of ebony divides the water more
readily in sinking than the ball of wood does in rising. Then take
a board of walnut-tree equal to and like the floating one of my
antagonists; and if it be true that this latter floats by reason of the
figure being unable to penetrate the water, the other of walnut-tree,
without a question, if thrust to the bottom, ought to stay there, as
having the same impeding figure, and being less apt to overcome the said
resistance of the water. But if we find by experience that not only the
thin board, but every other figure of the same walnut-tree, will return
to float, as unquestionably we shall, then I must desire my opponents
to forbear to attribute the floating of the ebony to the figure of the
board, since the resistance of the water is the same in rising as in
sinking, and the force of ascension of the walnut-tree is less than the
ebony's force for going to the bottom.

"Now let us return to the thin plate of gold or silver, or the thin
board of ebony, and let us lay it lightly upon the water, so that it may
stay there without sinking, and carefully observe the effect. It will
appear clearly that the plates are a considerable matter lower than the
surface of the water, which rises up and makes a kind of rampart round
them on every side. But if it has already penetrated and overcome the
continuity of the water, and is of its own nature heavier than the
water, why does it not continue to sink, but stop and suspend itself in
that little dimple that its weight has made in the water? My answer is,
because in sinking till its surface is below the water, which rises up
in a bank round it, it draws after and carries along with it the air
above it, so that that which, in this case, descends in the water is not
only the board of ebony or the plate of iron, but a compound of ebony
and air, from which composition results a solid no longer specifically
heavier than the water, as was the ebony or gold alone. But, gentlemen,
we want the same matter; you are to alter nothing but the shape, and,
therefore, have the goodness to remove this air, which may be done
simply by washing the surface of the board, for the water having once
got between the board and the air will run together, and the ebony will
go to the bottom; and if it does not, you have won the day.

"But methinks I hear some of my antagonists cunningly opposing this, and
telling me that they will not on any account allow their boards to be
wetted, because the weight of the water so added, by making it heavier
than it was before, draws it to the bottom, and that the addition of new
weight is contrary to our agreement, which was that the matter should be
the same.

"To this I answer, first, that nobody can suppose bodies to be put into
the water without their being wet, nor do I wish to do more to the board
than you may do to the ball. Moreover, it is not true that the board
sinks on account of the weight of the water added in the washing; for I
will put ten or twenty drops on the floating board, and so long as they
stand separate it shall not sink; but if the board be taken out and all
that water wiped off, and the whole surface bathed with one single drop,
and put it again upon the water, there is no question but it will sink,
the other water running to cover it, being no longer hindered by the
air. In the next place, it is altogether false that water can in any way
increase the weight of bodies immersed in it, for water has no weight in
water, since it does not sink. Now just as he who should say that brass
by its own nature sinks, but that when formed into the shape of a
kettle it acquires from that figure the virtue of lying in water without
sinking, would say what is false, because that is not purely brass which
then is put into the water, but a compound of brass and air; so is it
neither more nor less false that a thin plate of brass or ebony swims by
virtue of its dilated and broad figure. Also, I cannot omit to tell
my opponents that this conceit of refusing to bathe the surface of the
board might beget an opinion in a third person of a poverty of argument
on their side, especially as the conversation began about flakes of ice,
in which it would be simple to require that the surfaces should be kept
dry; not to mention that such pieces of ice, whether wet or dry, always
float, and so my antagonists say, because of their shape.

"Some may wonder that I affirm this power to be in the air of keeping
plate of brass or silver above water, as if in a certain sense I would
attribute to the air a kind of magnetic virtue for sustaining heavy
bodies with which it is in contact. To satisfy all these doubts I have
contrived the following experiment to demonstrate how truly the air does
support these bodies; for I have found, when one of these bodies which
floats when placed lightly on the water is thoroughly bathed and sunk to
the bottom, that by carrying down to it a little air without otherwise
touching it in the least, I am able to raise and carry it back to the
top, where it floats as before. To this effect, I take a ball of wax,
and with a little lead make it just heavy enough to sink very slowly to
the bottom, taking care that its surface be quite smooth and even. This,
if put gently into the water, submerges almost entirely, there remaining
visible only a little of the very top, which, so long as it is joined to
the air, keeps the ball afloat; but if we take away the contact of the
air by wetting this top, the ball sinks to the bottom and remains there.
Now to make it return to the surface by virtue of the air which before
sustained it, thrust into the water a glass with the mouth downward,
which will carry with it the air it contains, and move this down towards
the ball until you see, by the transparency of the glass, that the air
has reached the top of it; then gently draw the glass upward, and you
will see the ball rise, and afterwards stay on the top of the water,
if you carefully part the glass and water without too much disturbing
it."(3)

It will be seen that Galileo, while holding in the main to a correct
thesis, yet mingles with it some false ideas. At the very outset, of
course, it is not true that water has no resistance to penetration; it
is true, however, in the sense in which Galileo uses the term--that
is to say, the resistance of the water to penetration is not the
determining factor ordinarily in deciding whether a body sinks
or floats. Yet in the case of the flat body it is not altogether
inappropriate to say that the water resists penetration and thus
supports the body. The modern physicist explains the phenomenon as due
to surface-tension of the fluid. Of course, Galileo's disquisition
on the mixing of air with the floating body is utterly fanciful. His
experiments were beautifully exact; his theorizing from them was, in
this instance, altogether fallacious. Thus, as already intimated, his
paper is admirably adapted to convey a double lesson to the student of
science.


WILLIAM GILBERT AND THE STUDY OF MAGNETISM

It will be observed that the studies of Galileo and Stevinus were
chiefly concerned with the force of gravitation. Meanwhile, there was
an English philosopher of corresponding genius, whose attention was
directed towards investigation of the equally mysterious force of
terrestrial magnetism. With the doubtful exception of Bacon, Gilbert
was the most distinguished man of science in England during the reign
of Queen Elizabeth. He was for many years court physician, and Queen
Elizabeth ultimately settled upon him a pension that enabled him to
continue his researches in pure science.

His investigations in chemistry, although supposed to be of great
importance, are mostly lost; but his great work, De Magnete, on which
he labored for upwards of eighteen years, is a work of sufficient
importance, as Hallam says, "to raise a lasting reputation for its
author." From its first appearance it created a profound impression upon
the learned men of the continent, although in England Gilbert's theories
seem to have been somewhat less favorably received. Galileo freely
expressed his admiration for the work and its author; Bacon, who admired
the author, did not express the same admiration for his theories;
but Dr. Priestley, later, declared him to be "the father of modern
electricity."

Strangely enough, Gilbert's book had never been translated into English,
or apparently into any other language, until recent years, although at
the time of its publication certain learned men, unable to read the
book in the original, had asked that it should be. By this neglect, or
oversight, a great number of general readers as well as many scientists,
through succeeding centuries, have been deprived of the benefit of
writings that contained a good share of the fundamental facts about
magnetism as known to-day.

Gilbert was the first to discover that the earth is a great magnet, and
he not only gave the name of "pole" to the extremities of the magnetic
needle, but also spoke of these "poles" as north and south pole,
although he used these names in the opposite sense from that in which we
now use them, his south pole being the extremity which pointed towards
the north, and vice versa. He was also first to make use of the terms
"electric force," "electric emanations," and "electric attractions."

It is hardly necessary to say that some of the views taken by Gilbert,
many of his theories, and the accuracy of some of his experiments
have in recent times been found to be erroneous. As a pioneer in an
unexplored field of science, however, his work is remarkably accurate.
"On the whole," says Dr. John Robinson, "this performance contains more
real information than any writing of the age in which he lived, and is
scarcely exceeded by any that has appeared since."(4)

In the preface to his work Gilbert says: "Since in the discovery of
secret things, and in the investigation of hidden causes, stronger
reasons are obtained from sure experiments and demonstrated arguments
than from probable conjectures and the opinions of philosophical
speculators of the common sort, therefore, to the end of that noble
substance of that great loadstone, our common mother (the earth), still
quite unknown, and also that the forces extraordinary and exalted of
this globe may the better be understood, we have decided, first, to
begin with the common stony and ferruginous matter, and magnetic bodies,
and the part of the earth that we may handle and may perceive with
senses, and then to proceed with plain magnetic experiments, and to
penetrate to the inner parts of the earth."(5)

Before taking up the demonstration that the earth is simply a giant
loadstone, Gilbert demonstrated in an ingenious way that every
loadstone, of whatever size, has definite and fixed poles. He did this
by placing the stone in a metal lathe and converting it into a sphere,
and upon this sphere demonstrated how the poles can be found. To this
round loadstone he gave the name of terrella--that is, little earth.

"To find, then, poles answering to the earth," he says, "take in your
hand the round stone, and lay on it a needle or a piece of iron wire:
the ends of the wire move round their middle point, and suddenly come
to a standstill. Now, with ochre or with chalk, mark where the wire lies
still and sticks. Then move the middle or centre of the wire to another
spot, and so to a third and fourth, always marking the stone along
the length of the wire where it stands still; the lines so marked will
exhibit meridian circles, or circles like meridians, on the stone or
terrella; and manifestly they will all come together at the poles of the
stone. The circle being continued in this way, the poles appear, both
the north and the south, and betwixt these, midway, we may draw a large
circle for an equator, as is done by the astronomer in the heavens and
on his spheres, and by the geographer on the terrestrial globe."(6)

Gilbert had tried the familiar experiment of placing the loadstone on a
float in water, and observed that the poles always revolved until
they pointed north and south, which he explained as due to the earth's
magnetic attraction. In this same connection he noticed that a piece of
wrought iron mounted on a cork float was attracted by other metals to
a slight degree, and he observed also that an ordinary iron bar, if
suspended horizontally by a thread, assumes invariably a north and
south direction. These, with many other experiments of a similar nature,
convinced him that the earth "is a magnet and a loadstone," which he
says is a "new and till now unheard-of view of the earth."

Fully to appreciate Gilbert's revolutionary views concerning the earth
as a magnet, it should be remembered that numberless theories to explain
the action of the electric needle had been advanced. Columbus and
Paracelsus, for example, believed that the magnet was attracted by some
point in the heavens, such as a magnetic star. Gilbert himself tells of
some of the beliefs that had been held by his predecessors, many of whom
he declares "wilfully falsify." One of his first steps was to refute
by experiment such assertions as that of Cardan, that "a wound by a
magnetized needle was painless"; and also the assertion of Fracastoni
that loadstone attracts silver; or that of Scalinger, that the diamond
will attract iron; and the statement of Matthiolus that "iron rubbed
with garlic is no longer attracted to the loadstone."

Gilbert made extensive experiments to explain the dipping of the needle,
which had been first noticed by William Norman. His deduction as to
this phenomenon led him to believe that this was also explained by the
magnetic attraction of the earth, and to predict where the vertical dip
would be found. These deductions seem the more wonderful because at the
time he made them the dip had just been discovered, and had not been
studied except at London. His theory of the dip was, therefore, a
scientific prediction, based on a preconceived hypothesis. Gilbert found
the dip to be 72 degrees at London; eight years later Hudson found the
dip at 75 degrees 22' north latitude to be 89 degrees 30'; but it was
not until over two hundred years later, in 1831, that the vertical
dip was first observed by Sir James Ross at about 70 degrees 5' north
latitude, and 96 degrees 43' west longitude. This was not the exact
point assumed by Gilbert, and his scientific predictions, therefore,
were not quite correct; but such comparatively slight and excusable
errors mar but little the excellence of his work as a whole.

A brief epitome of some of his other important discoveries suffices
to show that the exalted position in science accorded him by
contemporaries, as well as succeeding generations of scientists,
was well merited. He was first to distinguish between magnetism
and electricity, giving the latter its name. He discovered also the
"electrical charge," and pointed the way to the discovery of insulation
by showing that the charge could be retained some time in the excited
body by covering it with some non-conducting substance, such as silk;
although, of course, electrical conduction can hardly be said to have
been more than vaguely surmised, if understood at all by him. The first
electrical instrument ever made, and known as such, was invented by him,
as was also the first magnetometer, and the first electrical indicating
device. Although three centuries have elapsed since his death, the
method of magnetizing iron first introduced by him is in common use
to-day.

He made exhaustive experiments with a needle balanced on a pivot to see
how many substances he could find which, like amber, on being rubbed
affected the needle. In this way he discovered that light substances
were attracted by alum, mica, arsenic, sealing-wax, lac sulphur, slags,
beryl, amethyst, rock-crystal, sapphire, jet, carbuncle, diamond,
opal, Bristol stone, glass, glass of antimony, gum-mastic, hard resin,
rock-salt, and, of course, amber. He discovered also that atmospheric
conditions affected the production of electricity, dryness being
unfavorable and moisture favorable.

Galileo's estimate of this first electrician is the verdict of
succeeding generations. "I extremely admire and envy this author," he
said. "I think him worthy of the greatest praise for the many new and
true observations which he has made, to the disgrace of so many vain and
fabling authors."


STUDIES OF LIGHT, HEAT, AND ATMOSPHERIC PRESSURE

We have seen that Gilbert was by no means lacking in versatility, yet
the investigations upon which his fame is founded were all pursued along
one line, so that the father of magnetism may be considered one of the
earliest of specialists in physical science. Most workers of the time,
on the other band, extended their investigations in many directions. The
sum total of scientific knowledge of that day had not bulked so large as
to exclude the possibility that one man might master it all. So we find
a Galileo, for example, making revolutionary discoveries in astronomy,
and performing fundamental experiments in various fields of physics.
Galileo's great contemporary, Kepler, was almost equally versatile,
though his astronomical studies were of such pre-eminent importance
that his other investigations sink into relative insignificance. Yet
he performed some notable experiments in at least one department of
physics. These experiments had to do with the refraction of light, a
subject which Kepler was led to investigate, in part at least, through
his interest in the telescope.

We have seen that Ptolemy in the Alexandrian time, and Alhazen, the
Arab, made studies of refraction. Kepler repeated their experiments,
and, striving as always to generalize his observations, he attempted to
find the law that governed the observed change of direction which a ray
of light assumes in passing from one medium to another. Kepler measured
the angle of refraction by means of a simple yet ingenious trough-like
apparatus which enabled him to compare readily the direct and refracted
rays. He discovered that when a ray of light passes through a glass
plate, if it strikes the farther surface of the glass at an angle
greater than 45 degrees it will be totally refracted instead of passing
through into the air. He could not well fail to know that different
mediums refract light differently, and that for the same medium the
amount of light valies with the change in the angle of incidence. He was
not able, however, to generalize his observations as he desired, and to
the last the law that governs refraction escaped him. It remained for
Willebrord Snell, a Dutchman, about the year 1621, to discover the
law in question, and for Descartes, a little later, to formulate it.
Descartes, indeed, has sometimes been supposed to be the discoverer of
the law. There is reason to believe that he based his generalizations
on the experiment of Snell, though he did not openly acknowledge his
indebtedness. The law, as Descartes expressed it, states that the sine
of the angle of incidence bears a fixed ratio to the sine of the angle
of refraction for any given medium. Here, then, was another illustration
of the fact that almost infinitely varied phenomena may be brought
within the scope of a simple law. Once the law had been expressed, it
could be tested and verified with the greatest ease; and, as usual, the
discovery being made, it seems surprising that earlier investigators--in
particular so sagacious a guesser as Kepler--should have missed it.

Galileo himself must have been to some extent a student of light, since,
as we have seen, he made such notable contributions to practical
optics through perfecting the telescope; but he seems not to have added
anything to the theory of light. The subject of heat, however, attracted
his attention in a somewhat different way, and he was led to the
invention of the first contrivance for measuring temperatures. His
thermometer was based on the afterwards familiar principle of the
expansion of a liquid under the influence of heat; but as a practical
means of measuring temperature it was a very crude affair, because the
tube that contained the measuring liquid was exposed to the air, hence
barometric changes of pressure vitiated the experiment. It remained for
Galileo's Italian successors of the Accademia del Cimento of Florence
to improve upon the apparatus, after the experiments of Torricelli--to
which we shall refer in a moment--had thrown new light on the question
of atmospheric pressure. Still later the celebrated Huygens hit upon the
idea of using the melting and the boiling point of water as fixed
points in a scale of measurements, which first gave definiteness to
thermometric tests.


TORRICELLI

In the closing years of his life Galileo took into his family, as
his adopted disciple in science, a young man, Evangelista Torricelli
(1608-1647), who proved himself, during his short lifetime, to be a
worthy follower of his great master. Not only worthy on account of his
great scientific discoveries, but grateful as well, for when he had
made the great discovery that the "suction" made by a vacuum was really
nothing but air pressure, and not suction at all, he regretted that
so important a step in science might not have been made by his
great teacher, Galileo, instead of by himself. "This generosity of
Torricelli," says Playfair, "was, perhaps, rarer than his genius: there
are more who might have discovered the suspension of mercury in the
barometer than who would have been willing to part with the honor of the
discovery to a master or a friend."

Torricelli's discovery was made in 1643, less than two years after the
death of his master. Galileo had observed that water will not rise in
an exhausted tube, such as a pump, to a height greater than thirty-three
feet, but he was never able to offer a satisfactory explanation of the
principle. Torricelli was able to demonstrate that the height at which
the water stood depended upon nothing but its weight as compared with
the weight of air. If this be true, it is evident that any fluid will
be supported at a definite height, according to its relative weight
as compared with air. Thus mercury, which is about thirteen times more
dense than water, should only rise to one-thirteenth the height of a
column of water--that is, about thirty inches. Reasoning in this way,
Torricelli proceeded to prove that his theory was correct. Filling a
long tube, closed at one end, with mercury, he inverted the tube with
its open orifice in a vessel of mercury. The column of mercury fell at
once, but at a height of about thirty inches it stopped and remained
stationary, the pressure of the air on the mercury in the vessel
maintaining it at that height. This discovery was a shattering blow
to the old theory that had dominated that field of physics for so many
centuries. It was completely revolutionary to prove that, instead of
a mysterious something within the tube being responsible for the
suspension of liquids at certain heights, it was simply the ordinary
atmospheric pressure mysterious enough, it is true--pushing upon them
from without. The pressure exerted by the atmosphere was but little
understood at that time, but Torricelli's discovery aided materially
in solving the mystery. The whole class of similar phenomena of air
pressure, which had been held in the trammel of long-established but
false doctrines, was now reduced to one simple law, and the door to a
solution of a host of unsolved problems thrown open.

It had long been suspected and believed that the density of the
atmosphere varies at certain times. That the air is sometimes "heavy"
and at other times "light" is apparent to the senses without scientific
apparatus for demonstration. It is evident, then, that Torricelli's
column of mercury should rise and fall just in proportion to the
lightness or heaviness of the air. A short series of observations
proved that it did so, and with those observations went naturally
the observations as to changes in the weather. It was only necessary,
therefore, to scratch a scale on the glass tube, indicating relative
atmospheric pressures, and the Torricellian barometer was complete.

Such a revolutionary theory and such an important discovery were, of
course, not to be accepted without controversy, but the feeble arguments
of the opponents showed how untenable the old theory had become. In
1648 Pascal suggested that if the theory of the pressure of air upon the
mercury was correct, it could be demonstrated by ascending a mountain
with the mercury tube. As the air was known to get progressively lighter
from base to summit, the height of the column should be progressively
lessened as the ascent was made, and increase again on the descent
into the denser air. The experiment was made on the mountain called
the Puy-de-Dome, in Auvergne, and the column of mercury fell and rose
progressively through a space of about three inches as the ascent and
descent were made.

This experiment practically sealed the verdict on the new theory, but
it also suggested something more. If the mercury descended to a certain
mark on the scale on a mountain-top whose height was known, why was not
this a means of measuring the heights of all other elevations? And so
the beginning was made which, with certain modifications and corrections
in details, is now the basis of barometrical measurements of heights.

In hydraulics, also, Torricelli seems to have taken one of the first
steps. He did this by showing that the water which issues from a hole
in the side or bottom of a vessel does so at the same velocity as that
which a body would acquire by falling from the level of the surface of
the water to that of the orifice. This discovery was of the greatest
importance to a correct understanding of the science of the motions of
fluids. He also discovered the valuable mechanical principle that if any
number of bodies be connected so that by their motion there is neither
ascent nor descent of their centre of gravity, these bodies are in
equilibrium.

Besides making these discoveries, he greatly improved the microscope
and the telescope, and invented a simple microscope made of a globule of
glass. In 1644 he published a tract on the properties of the cycloid in
which he suggested a solution of the problem of its quadrature. As soon
as this pamphlet appeared its author was accused by Gilles Roberval
(1602-1675) of having appropriated a solution already offered by him.
This led to a long debate, during which Torricelli was seized with a
fever, from the effects of which he died, in Florence, October 25, 1647.
There is reason to believe, however, that while Roberval's discovery
was made before Torricelli's, the latter reached his conclusions
independently.




VI. TWO PSEUDO-SCIENCES--ALCHEMY AND ASTROLOGY

In recent chapters we have seen science come forward with tremendous
strides. A new era is obviously at hand. But we shall misconceive the
spirit of the times if we fail to understand that in the midst of all
this progress there was still room for mediaeval superstition and for
the pursuit of fallacious ideals. Two forms of pseudo-science were
peculiarly prevalent--alchemy and astrology. Neither of these can with
full propriety be called a science, yet both were pursued by many of the
greatest scientific workers of the period. Moreover, the studies of the
alchemist may with some propriety be said to have laid the foundation
for the latter-day science of chemistry; while astrology was closely
allied to astronomy, though its relations to that science are not as
intimate as has sometimes been supposed.

Just when the study of alchemy began is undetermined. It was certainly
of very ancient origin, perhaps Egyptian, but its most flourishing time
was from about the eighth century A.D. to the eighteenth century. The
stories of the Old Testament formed a basis for some of the
strange beliefs regarding the properties of the magic "elixir,"
or "philosopher's stone." Alchemists believed that most of the
antediluvians, perhaps all of them, possessed a knowledge of this stone.
How, otherwise, could they have prolonged their lives to nine and a half
centuries? And Moses was surely a first-rate alchemist, as is proved by
the story of the Golden Calf.(1) After Aaron had made the calf of gold,
Moses performed the much more difficult task of grinding it to powder
and "strewing it upon the waters," thus showing that he had transmuted
it into some lighter substance.

But antediluvians and Biblical characters were not the only persons who
were thought to have discovered the coveted "elixir." Hundreds of aged
mediaeval chemists were credited with having made the discovery, and
were thought to be living on through the centuries by its means. Alaies
de Lisle, for example, who died in 1298, at the age of 110, was alleged
to have been at the point of death at the age of fifty, but just at
this time he made the fortunate discovery of the magic stone, and so
continued to live in health and affluence for sixty years more. And De
Lisle was but one case among hundreds.

An aged and wealthy alchemist could claim with seeming plausibility that
he was prolonging his life by his magic; whereas a younger man might
assert that, knowing the great secret, he was keeping himself young
through the centuries. In either case such a statement, or rumor, about
a learned and wealthy alchemist was likely to be believed, particularly
among strangers; and as such a man would, of course, be the object
of much attention, the claim was frequently made by persons seeking
notoriety. One of the most celebrated of these impostors was a certain
Count de Saint-Germain, who was connected with the court of Louis XV.
His statements carried the more weight because, having apparently no
means of maintenance, he continued to live in affluence year after
year--for two thousand years, as he himself admitted--by means of the
magic stone. If at any time his statements were doubted, he was in the
habit of referring to his valet for confirmation, this valet being also
under the influence of the elixir of life.

"Upon one occasion his master was telling a party of ladies and
gentlemen, at dinner, some conversation he had had in Palestine, with
King Richard I., of England, whom he described as a very particular
friend of his. Signs of astonishment and incredulity were visible on the
faces of the company, upon which Saint-Germain very coolly turned to his
servant, who stood behind his chair, and asked him if he had not spoken
the truth. 'I really cannot say,' replied the man, without moving a
muscle; 'you forget, sir, I have been only five hundred years in your
service.' 'Ah, true,' said his master, 'I remember now; it was a little
before your time!'"(2)

In the time of Saint-Germain, only a little over a century ago, belief
in alchemy had almost disappeared, and his extraordinary tales were
probably regarded in the light of amusing stories. Still there was
undoubtedly a lingering suspicion in the minds of many that this man
possessed some peculiar secret. A few centuries earlier his tales
would hardly have been questioned, for at that time the belief in the
existence of this magic something was so strong that the search for it
became almost a form of mania; and once a man was seized with it, lie
gambled away health, position, and life itself in pursuing the coveted
stake. An example of this is seen in Albertus Magnus, one of the most
learned men of his time, who it is said resigned his position as bishop
of Ratisbon in order that he might pursue his researches in alchemy.

If self-sacrifice was not sufficient to secure the prize, crime would
naturally follow, for there could be no limit to the price of the
stakes in this game. The notorious Marechal de Reys, failing to find the
coveted stone by ordinary methods of laboratory research, was persuaded
by an impostor that if he would propitiate the friendship of the
devil the secret would be revealed. To this end De Reys began secretly
capturi

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