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A History of Science, Volume 1 by Henry Smith Williams

Part 4 out of 5

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their height. Hipparchus, at a later day, was enabled to compare
his own observations with those made by Aristarchus, and, as we
have just seen, his work was well known to so distant a
contemporary as Archimedes. Yet the facts of his life are almost
a blank for us, and of his writings only a single one has been
preserved. That one, however, is a most important and interesting
paper on the measurements of the sun and the moon. Unfortunately,
this paper gives us no direct clew as to the opinions of
Aristarchus concerning the relative positions of the earth and
sun. But the testimony of Archimedes as to this is unequivocal,
and this testimony is supported by other rumors in themselves
less authoritative.

In contemplating this astronomer of Samos, then, we are in the
presence of a man who had solved in its essentials the problem of
the mechanism of the solar system. It appears from the words of
Archimedes that Aristarchus; had propounded his theory in
explicit writings. Unquestionably, then, he held to it as a
positive doctrine, not as a mere vague guess. We shall show, in a
moment, on what grounds he based his opinion. Had his teaching
found vogue, the story of science would be very different from
what it is. We should then have no tale to tell of a Copernicus
coming upon the scene fully seventeen hundred years later with
the revolutionary doctrine that our world is not the centre of
the universe. We should not have to tell of the persecution of a
Bruno or of a Galileo for teaching this doctrine in the
seventeenth century of an era which did not begin till two
hundred years after the death of Aristarchus. But, as we know,
the teaching of the astronomer of Samos did not win its way. The
old conservative geocentric doctrine, seemingly so much more in
accordance with the every-day observations of mankind, supported
by the majority of astronomers with the Peripatetic philosophers
at their head, held its place. It found fresh supporters
presently among the later Alexandrians, and so fully eclipsed the
heliocentric view that we should scarcely know that view had even
found an advocate were it not for here and there such a chance
record as the phrases we have just quoted from Archimedes. Yet,
as we now see, the heliocentric doctrine, which we know to be
true, had been thought out and advocated as the correct theory of
celestial mechanics by at least one worker of the third century
B.C. Such an idea, we may be sure, did not spring into the mind
of its originator except as the culmination of a long series of
observations and inferences. The precise character of the
evolution we perhaps cannot trace, but its broader outlines are
open to our observation, and we may not leave so important a
topic without at least briefly noting them.

Fully to understand the theory of Aristarchus, we must go back a
century or two and recall that as long ago as the time of that
other great native of Samos, Pythagoras, the conception had been
reached that the earth is in motion. We saw, in dealing with
Pythagoras, that we could not be sure as to precisely what he
himself taught, but there is no question that the idea of the
world's motion became from an early day a so-called Pythagorean
doctrine. While all the other philosophers, so far as we know,
still believed that the world was flat, the Pythagoreans out in
Italy taught that the world is a sphere and that the apparent
motions of the heavenly bodies are really due to the actual
motion of the earth itself. They did not, however, vault to the
conclusion that this true motion of the earth takes place in the
form of a circuit about the sun. Instead of that, they conceived
the central body of the universe to be a great fire, invisible
from the earth, because the inhabited side of the terrestrial
ball was turned away from it. The sun, it was held, is but a
great mirror, which reflects the light from the central fire. Sun
and earth alike revolve about this great fire, each in its own
orbit. Between the earth and the central fire there was,
curiously enough, supposed to be an invisible earthlike body
which was given the name of Anticthon, or counter-earth. This
body, itself revolving about the central fire, was supposed to
shut off the central light now and again from the sun or from the
moon, and thus to account for certain eclipses for which the
shadow of the earth did not seem responsible. It was, perhaps,
largely to account for such eclipses that the counter-earth was
invented. But it is supposed that there was another reason. The
Pythagoreans held that there is a peculiar sacredness in the
number ten. Just as the Babylonians of the early day and the
Hegelian philosophers of a more recent epoch saw a sacred
connection between the number seven and the number of planetary
bodies, so the Pythagoreans thought that the universe must be
arranged in accordance with the number ten. Their count of the
heavenly bodies, including the sphere of the fixed stars, seemed
to show nine, and the counter-earth supplied the missing body.

The precise genesis and development of this idea cannot now be
followed, but that it was prevalent about the fifth century B.C.
as a Pythagorean doctrine cannot be questioned. Anaxagoras also
is said to have taken account of the hypothetical counter-earth
in his explanation of eclipses; though, as we have seen, he
probably did not accept that part of the doctrine which held the
earth to be a sphere. The names of Philolaus and Heraclides have
been linked with certain of these Pythagorean doctrines. Eudoxus,
too, who, like the others, lived in Asia Minor in the fourth
century B.C., was held to have made special studies of the
heavenly spheres and perhaps to have taught that the earth moves.
So, too, Nicetas must be named among those whom rumor credited
with having taught that the world is in motion. In a word, the
evidence, so far as we can garner it from the remaining
fragments, tends to show that all along, from the time of the
early Pythagoreans, there had been an undercurrent of opinion in
the philosophical world which questioned the fixity of the earth;
and it would seem that the school of thinkers who tended to
accept the revolutionary view centred in Asia Minor, not far from
the early home of the founder of the Pythagorean doctrines. It
was not strange, then, that the man who was finally to carry
these new opinions to their logical conclusion should hail from
Samos.

But what was the support which observation could give to this
new, strange conception that the heavenly bodies do not in
reality move as they seem to move, but that their apparent motion
is due to the actual revolution of the earth? It is extremely
difficult for any one nowadays to put himself in a mental
position to answer this question. We are so accustomed to
conceive the solar system as we know it to be, that we are wont
to forget how very different it is from what it seems. Yet one
needs but to glance up at the sky, and then to glance about one
at the solid earth, to grant, on a moment's reflection, that the
geocentric idea is of all others the most natural; and that to
conceive the sun as the actual Centre of the solar system is an
idea which must look for support to some other evidence than that
which ordinary observation can give. Such was the view of most of
the ancient philosophers, and such continued to be the opinion of
the majority of mankind long after the time of Copernicus. We
must not forget that even so great an observing astronomer as
Tycho Brahe, so late as the seventeenth century, declined to
accept the heliocentric theory, though admitting that all the
planets except the earth revolve about the sun. We shall see that
before the Alexandrian school lost its influence a geocentric
scheme had been evolved which fully explained all the apparent
motions of the heavenly bodies. All this, then, makes us but
wonder the more that the genius of an Aristarchus could give
precedence to scientific induction as against the seemingly clear
evidence of the senses.

What, then, was the line of scientific induction that led
Aristarchus to this wonderful goal? Fortunately, we are able to
answer that query, at least in part. Aristarchus gained his
evidence through some wonderful measurements. First, he measured
the disks of the sun and the moon. This, of course, could in
itself give him no clew to the distance of these bodies, and
therefore no clew as to their relative size; but in attempting to
obtain such a clew he hit upon a wonderful yet altogether simple
experiment. It occurred to him that when the moon is precisely
dichotomized-- that is to say, precisely at the half-the line of
vision from the earth to the moon must be precisely at right
angles with the line of light passing from the sun to the moon.
At this moment, then, the imaginary lines joining the sun, the
moon, and the earth, make a right angle triangle. But the
properties of the right-angle triangle had long been studied and
were well under stood. One acute angle of such a triangle
determines the figure of the triangle itself. We have already
seen that Thales, the very earliest of the Greek philosophers,
measured the distance of a ship at sea by the application of this
principle. Now Aristarchus sights the sun in place of Thales'
ship, and, sighting the moon at the same time, measures the angle
and establishes the shape of his right-angle triangle. This does
not tell him the distance of the sun, to be sure, for he does not
know the length of his base-line--that is to say, of the line
between the moon and the earth. But it does establish the
relation of that base-line to the other lines of the triangle; in
other words, it tells him the distance of the sun in terms of the
moon's distance. As Aristarchus strikes the angle, it shows that
the sun is eighteen times as distant as the moon. Now, by
comparing the apparent size of the sun with the apparent size of
the moon--which, as we have seen, Aristarchus has already
measured--he is able to tell us that, the sun is "more than 5832
times, and less than 8000" times larger than the moon; though his
measurements, taken by themselves, give no clew to the actual
bulk of either body. These conclusions, be it understood, are
absolutely valid inferences--nay, demonstrations--from the
measurements involved, provided only that these measurements have
been correct. Unfortunately, the angle of the triangle we have
just seen measured is exceedingly difficult to determine with
accuracy, while at the same time, as a moment's reflection will
show, it is so large an angle that a very slight deviation from
the truth will greatly affect the distance at which its line
joins the other side of the triangle. Then again, it is virtually
impossible to tell the precise moment when the moon is at half,
as the line it gives is not so sharp that we can fix it with
absolute accuracy. There is, moreover, another element of error
due to the refraction of light by the earth's atmosphere. The
experiment was probably made when the sun was near the horizon,
at which time, as we now know, but as Aristarchus probably did
not suspect, the apparent displacement of the sun's position is
considerable; and this displacement, it will be observed, is in
the direction to lessen the angle in question.

In point of fact, Aristarchus estimated the angle at eighty-seven
degrees. Had his instrument been more precise, and had he been
able to take account of all the elements of error, he would have
found it eighty-seven degrees and fifty-two minutes. The
difference of measurement seems slight; but it sufficed to make
the computations differ absurdly from the truth. The sun is
really not merely eighteen times but more than two hundred times
the distance of the moon, as Wendelein discovered on repeating
the experiment of Aristarchus about two thousand years later. Yet
this discrepancy does not in the least take away from the
validity of the method which Aristarchus employed. Moreover, his
conclusion, stated in general terms, was perfectly correct: the
sun is many times more distant than the moon and vastly larger
than that body. Granted, then, that the moon is, as Aristarchus
correctly believed, considerably less in size than the earth, the
sun must be enormously larger than the earth; and this is the
vital inference which, more than any other, must have seemed to
Aristarchus to confirm the suspicion that the sun and not the
earth is the centre of the planetary system. It seemed to him
inherently improbable that an enormously large body like the sun
should revolve about a small one such as the earth. And again, it
seemed inconceivable that a body so distant as the sun should
whirl through space so rapidly as to make the circuit of its
orbit in twenty- four hours. But, on the other hand, that a small
body like the earth should revolve about the gigantic sun seemed
inherently probable. This proposition granted, the rotation of
the earth on its axis follows as a necessary consequence in
explanation of the seeming motion of the stars. Here, then, was
the heliocentric doctrine reduced to a virtual demonstration by
Aristarchus of Samos, somewhere about the middle of the third
century B.C.

It must be understood that in following out the, steps of
reasoning by which we suppose Aristarchus to have reached so
remarkable a conclusion, we have to some extent guessed at the
processes of thought- development; for no line of explication
written by the astronomer himself on this particular point has
come down to us. There does exist, however, as we have already
stated, a very remarkable treatise by Aristarchus on the Size and
Distance of the Sun and the Moon, which so clearly suggests the
methods of reasoning of the great astronomer, and so explicitly
cites the results of his measurements, that we cannot well pass
it by without quoting from it at some length. It is certainly one
of the most remarkable scientific documents of antiquity. As
already noted, the heliocentric doctrine is not expressly stated
here. It seems to be tacitly implied throughout, but it is not a
necessary consequence of any of the propositions expressly
stated. These propositions have to do with certain observations
and measurements and what Aristarchus believes to be inevitable
deductions from them, and he perhaps did not wish to have these
deductions challenged through associating them with a theory
which his contemporaries did not accept. In a word, the paper of
Aristarchus is a rigidly scientific document unvitiated by
association with any theorizings that are not directly germane to
its central theme. The treatise opens with certain hypotheses as
follows:

"First. The moon receives its light from the sun.

"Second. The earth may be considered as a point and as the centre
of the orbit of the moon.

"Third. When the moon appears to us dichotomized it offers to our
view a great circle [or actual meridian] of its circumference
which divides the illuminated part from the dark part.

"Fourth. When the moon appears dichotomized its distance from the
sun is less than a quarter of the circumference [of its orbit] by
a thirtieth part of that quarter."

That is to say, in modern terminology, the moon at this time
lacks three degrees (one thirtieth of ninety degrees) of being at
right angles with the line of the sun as viewed from the earth;
or, stated otherwise, the angular distance of the moon from the
sun as viewed from the earth is at this time eighty-seven
degrees--this being, as we have already observed, the fundamental
measurement upon which so much depends. We may fairly suppose
that some previous paper of Aristarchus's has detailed the
measurement which here is taken for granted, yet which of course
could depend solely on observation.

"Fifth. The diameter of the shadow [cast by the earth at the
point where the moon's orbit cuts that shadow when the moon is
eclipsed] is double the diameter of the moon."

Here again a knowledge of previously established measurements is
taken for granted; but, indeed, this is the case throughout the
treatise.

"Sixth. The arc subtended in the sky by the moon is a fifteenth
part of a sign" of the zodiac; that is to say, since there are
twenty-four, signs in the zodiac, one-fifteenth of one
twenty-fourth, or in modern terminology, one degree of arc. This
is Aristarchus's measurement of the moon to which we have already
referred when speaking of the measurements of Archimedes.

"If we admit these six hypotheses," Aristarchus continues, "it
follows that the sun is more than eighteen times more distant
from the earth than is the moon, and that it is less than twenty
times more distant, and that the diameter of the sun bears a
corresponding relation to the diameter of the moon; which is
proved by the position of the moon when dichotomized. But the
ratio of the diameter of the sun to that of the earth is greater
than nineteen to three and less than forty-three to six. This is
demonstrated by the relation of the distances, by the position
[of the moon] in relation to the earth's shadow, and by the fact
that the arc subtended by the moon is a fifteenth part of a
sign."

Aristarchus follows with nineteen propositions intended to
elucidate his hypotheses and to demonstrate his various
contentions. These show a singularly clear grasp of geometrical
problems and an altogether correct conception of the general
relations as to size and position of the earth, the moon, and the
sun. His reasoning has to do largely with the shadow cast by the
earth and by the moon, and it presupposes a considerable
knowledge of the phenomena of eclipses. His first proposition is
that "two equal spheres may always be circumscribed in a
cylinder; two unequal spheres in a cone of which the apex is
found on the side of the smaller sphere; and a straight line
joining the centres of these spheres is perpendicular to each of
the two circles made by the contact of the surface of the
cylinder or of the cone with the spheres."

It will be observed that Aristarchus has in mind here the moon,
the earth, and the sun as spheres to be circumscribed within a
cone, which cone is made tangible and measurable by the shadows
cast by the non-luminous bodies; since, continuing, he clearly
states in proposition nine, that "when the sun is totally
eclipsed, an observer on the earth's surface is at an apex of a
cone comprising the moon and the sun." Various propositions deal
with other relations of the shadows which need not detain us
since they are not fundamentally important, and we may pass to
the final conclusions of Aristarchus, as reached in his
propositions ten to nineteen.

Now, since (proposition ten) "the diameter of the sun is more
than eighteen times and less than twenty times greater than that
of the moon," it follows (proposition eleven) "that the bulk of
the sun is to that of the moon in ratio, greater than 5832 to 1,
and less than 8000 to 1."

"Proposition sixteen. The diameter of the sun is to the diameter
of the earth in greater proportion than nineteen to three, and
less than forty-three to six.

"Proposition seventeen. The bulk of the sun is to that of the
earth in greater proportion than 6859 to 27, and less than 79,507
to 216.

"Proposition eighteen. The diameter of the earth is to the
diameter of the moon in greater proportion than 108 to 43 and
less than 60 to 19.

"Proposition nineteen. The bulk of the earth is to that of the
moon in greater proportion than 1,259,712 to 79,507 and less than
20,000 to 6859."

Such then are the more important conclusions of this very
remarkable paper--a paper which seems to have interest to the
successors of Aristarchus generation after generation, since this
alone of all the writings of the great astronomer has been
preserved. How widely the exact results of the measurements of
Aristarchus, differ from the truth, we have pointed out as we
progressed. But let it be repeated that this detracts little from
the credit of the astronomer who had such clear and correct
conceptions of the relations of the heavenly bodies and who
invented such correct methods of measurement. Let it be
particularly observed, however, that all the conclusions of
Aristarchus are stated in relative terms. He nowhere attempts to
estimate the precise size of the earth, of the moon, or of the
sun, or the actual distance of one of these bodies from another.
The obvious reason for this is that no data were at hand from
which to make such precise measurements. Had Aristarchus known
the size of any one of the bodies in question, he might readily,
of course, have determined the size of the others by the mere
application of his relative scale; but he had no means of
determining the size of the earth, and to this extent his system
of measurements remained imperfect. Where Aristarchus halted,
however, another worker of the same period took the task in hand
and by an altogether wonderful measurement determined the size of
the earth, and thus brought the scientific theories of cosmology
to their climax. This worthy supplementor of the work of
Aristarchus was Eratosthenes of Alexandria.

ERATOSTHENES, "THE SURVEYOR OF THE WORLD"

An altogether remarkable man was this native of Cyrene, who came
to Alexandria from Athens to be the chief librarian of Ptolemy
Euergetes. He was not merely an astronomer and a geographer, but
a poet and grammarian as well. His contemporaries jestingly
called him Beta the Second, because he was said through the
universality of his attainments to be "a second Plato" in
philosophy, "a second Thales" in astronomy, and so on throughout
the list. He was also called the "surveyor of the world," in
recognition of his services to geography. Hipparchus said of him,
perhaps half jestingly, that he had studied astronomy as a
geographer and geography as an astronomer. It is not quite clear
whether the epigram was meant as compliment or as criticism.
Similar phrases have been turned against men of versatile talent
in every age. Be that as it may, Eratosthenes passed into history
as the father of scientific geography and of scientific
chronology; as the astronomer who first measured the obliquity of
the ecliptic; and as the inventive genius who performed the
astounding feat of measuring the size of the globe on which we
live at a time when only a relatively small portion of that
globe's surface was known to civilized man. It is no discredit to
approach astronomy as a geographer and geography as an
astronomer if the results are such as these. What
Eratosthenes really did was to approach both astronomy and
geography from two seemingly divergent points of attack--namely,
from the stand-point of the geometer and also from that of the
poet. Perhaps no man in any age has brought a better combination
of observing and imaginative faculties to the aid of science.

Nearly all the discoveries of Eratosthenes are associated with
observations of the shadows cast by the sun. We have seen that,
in the study of the heavenly bodies, much depends on the
measurement of angles. Now the easiest way in which angles can be
measured, when solar angles are in question, is to pay attention,
not to the sun itself, but to the shadow that it casts. We saw
that Thales made some remarkable measurements with the aid of
shadows, and we have more than once referred to the gnomon, which
is the most primitive, but which long remained the most
important, of astronomical instruments. It is believed that
Eratosthenes invented an important modification of the gnomon
which was elaborated afterwards by Hipparchus and called an
armillary sphere. This consists essentially of a small gnomon, or
perpendicular post, attached to a plane representing the earth's
equator and a hemisphere in imitation of the earth's surface.
With the aid of this, the shadow cast by the sun could be very
accurately measured. It involves no new principle. Every
perpendicular post or object of any kind placed in the sunlight
casts a shadow from which the angles now in question could be
roughly measured. The province of the armillary sphere was to
make these measurements extremely accurate.

With the aid of this implement, Eratosthenes carefully noted the
longest and the shortest shadows cast by the gnomon--that is to
say, the shadows cast on the days of the solstices. He found that
the distance between the tropics thus measured represented 47
degrees 42' 39" of arc. One-half of this, or 23 degrees 5,'
19.5", represented the obliquity of the ecliptic--that is to say,
the angle by which the earth's axis dipped from the perpendicular
with reference to its orbit. This was a most important
observation, and because of its accuracy it has served modern
astronomers well for comparison in measuring the trifling change
due to our earth's slow, swinging wobble. For the earth, be it
understood, like a great top spinning through space, holds its
position with relative but not quite absolute fixity. It must not
be supposed, however, that the experiment in question was quite
new with Eratosthenes. His merit consists rather in the accuracy
with which he made his observation than in the novelty of the
conception; for it is recorded that Eudoxus, a full century
earlier, had remarked the obliquity of the ecliptic. That
observer had said that the obliquity corresponded to the side of
a pentadecagon, or fifteen-sided figure, which is equivalent in
modern phraseology to twenty- four degrees of arc. But so little
is known regarding the way in which Eudoxus reached his estimate
that the measurement of Eratosthenes is usually spoken of as if
it were the first effort of the kind.

Much more striking, at least in its appeal to the popular
imagination, was that other great feat which Eratosthenes
performed with the aid of his perfected gnomon--the measurement
of the earth itself. When we reflect that at this period the
portion of the earth open to observation extended only from the
Straits of Gibraltar on the west to India on the east, and from
the North Sea to Upper Egypt, it certainly seems enigmatical--at
first thought almost miraculous--that an observer should have
been able to measure the entire globe. That he should have
accomplished this through observation of nothing more than a tiny
bit of Egyptian territory and a glimpse of the sun's shadow makes
it seem but the more wonderful. Yet the method of Eratosthenes,
like many another enigma, seems simple enough once it is
explained. It required but the application of a very elementary
knowledge of the geometry of circles, combined with the use of a
fact or two from local geography--which detracts nothing from the
genius of the man who could reason from such simple premises to
so wonderful a conclusion.

Stated in a few words, the experiment of Eratosthenes was this.
His geographical studies had taught him that the town of Syene
lay directly south of Alexandria, or, as we should say, on the
same meridian of latitude. He had learned, further, that Syene
lay directly under the tropic, since it was reported that at noon
on the day of the summer solstice the gnomon there cast no
shadow, while a deep well was illumined to the bottom by the sun.
A third item of knowledge, supplied by the surveyors of Ptolemy,
made the distance between Syene and Alexandria five thousand
stadia. These, then, were the preliminary data required by
Eratosthenes. Their significance consists in the fact that here
is a measured bit of the earth's arc five thousand stadia in
length. If we could find out what angle that bit of arc subtends,
a mere matter of multiplication would give us the size of the
earth. But how determine this all-important number? The answer
came through reflection on the relations of concentric circles.
If you draw any number of circles, of whatever size, about a
given centre, a pair of radii drawn from that centre will cut
arcs of the same relative size from all the circles. One circle
may be so small that the actual arc subtended by the radii in a
given case may be but an inch in length, while another circle is
so large that its corresponding are is measured in millions of
miles; but in each case the same number of so-called degrees will
represent the relation of each arc to its circumference. Now,
Eratosthenes knew, as just stated, that the sun, when on the
meridian on the day of the summer solstice, was directly over the
town of Syene. This meant that at that moment a radius of the
earth projected from Syene would point directly towards the sun.
Meanwhile, of course, the zenith would represent the projection
of the radius of the earth passing through Alexandria. All that
was required, then, was to measure, at Alexandria, the angular
distance of the sun from the zenith at noon on the day of the
solstice to secure an approximate measurement of the arc of the
sun's circumference, corresponding to the arc of the earth's
surface represented by the measured distance between Alexandria
and Syene.

The reader will observe that the measurement could not be
absolutely accurate, because it is made from the surface of the
earth, and not from the earth's centre, but the size of the earth
is so insignificant in comparison with the distance of the sun
that this slight discrepancy could be disregarded.

The way in which Eratosthenes measured this angle was very
simple. He merely measured the angle of the shadow which his
perpendicular gnomon at Alexandria cast at mid-day on the day of
the solstice, when, as already noted, the sun was directly
perpendicular at Syene. Now a glance at the diagram will make it
clear that the measurement of this angle of the shadow is merely
a convenient means of determining the precisely equal opposite
angle subtending an arc of an imaginary circle passing through
the sun; the are which, as already explained, corresponds with
the arc of the earth's surface represented by the distance
between Alexandria and Syene. He found this angle to represent 7
degrees 12', or one-fiftieth of the circle. Five thousand stadia,
then, represent one-fiftieth of the earth's circumference; the
entire circumference being, therefore, 250,000 stadia.
Unfortunately, we do not know which one of the various
measurements used in antiquity is represented by the stadia of
Eratosthenes. According to the researches of Lepsius, however,
the stadium in question represented 180 meters, and this would
make the earth, according to the measurement of Eratosthenes,
about twenty-eight thousand miles in circumference, an answer
sufficiently exact to justify the wonder which the experiment
excited in antiquity, and the admiration with which it has ever
since been regarded.

{illustration caption = DIAGRAM TO ILLUSTRATE ERATOSTHENES'
MEASUREMENT OF THE GLOBE

FIG. 1. AF is a gnomon at Alexandria; SB a gnomon at Svene; IS
and JK represent the sun's rays. The angle actually measured by
Eratosthenes is KFA, as determined by the shadow cast by the
gnomon AF. This angle is equal to the opposite angle JFL, which
measures the sun's distance from the zenith; and which is also
equal to the angle AES--to determine the Size of which is the
real object of the entire measurement.

FIG. 2 shows the form of the gnomon actually employed in
antiquity. The hemisphere KA being marked with a scale, it is
obvious that in actual practice Eratosthenes required only to set
his gnomon in the sunlight at the proper moment, and read off the
answer to his problem at a glance. The simplicity of the method
makes the result seem all the more wonderful.}

Of course it is the method, and not its details or its exact
results, that excites our interest. And beyond question the
method was an admirable one. Its result, however, could not have
been absolutely accurate, because, while correct in principle,
its data were defective. In point of fact Syene did not lie
precisely on the same meridian as Alexandria, neither did it lie
exactly on the tropic. Here, then, are two elements of
inaccuracy. Moreover, it is doubtful whether Eratosthenes made
allowance, as he should have done, for the semi-diameter of the
sun in measuring the angle of the shadow. But these are mere
details, scarcely worthy of mention from our present stand-point.
What perhaps is deserving of more attention is the fact that this
epoch-making measurement of Eratosthenes may not have been the
first one to be made. A passage of Aristotle records that the
size of the earth was said to be 400,000 stadia. Some
commentators have thought that Aristotle merely referred to the
area of the inhabited portion of the earth and not to the
circumference of the earth itself, but his words seem doubtfully
susceptible of this interpretation; and if he meant, as his words
seem to imply, that philosophers of his day had a tolerably
precise idea of the globe, we must assume that this idea was
based upon some sort of measurement. The recorded size, 400,000
stadia, is a sufficient approximation to the truth to suggest
something more than a mere unsupported guess. Now, since
Aristotle died more than fifty years before Eratosthenes was
born, his report as to the alleged size of the earth certainly
has a suggestiveness that cannot be overlooked; but it arouses
speculations without giving an inkling as to their solution. If
Eratosthenes had a precursor as an earth-measurer, no hint or
rumor has come down to us that would enable us to guess who that
precursor may have been. His personality is as deeply enveloped
in the mists of the past as are the personalities of the great
prehistoric discoverers. For the purpose of the historian,
Eratosthenes must stand as the inventor of the method with which
his name is associated, and as the first man of whom we can say
with certainty that he measured the size of the earth. Right
worthily, then, had the Alexandrian philosopher won his proud
title of "surveyor of the world."

HIPPARCHUS, "THE LOVER OF TRUTH"

Eratosthenes outlived most of his great contemporaries. He saw
the turning of that first and greatest century of Alexandrian
science, the third century before our era. He died in the year
196 B.C., having, it is said, starved himself to death to escape
the miseries of blindness;--to the measurer of shadows, life
without light seemed not worth the living. Eratosthenes left no
immediate successor. A generation later, however, another great
figure appeared in the astronomical world in the person of
Hipparchus, a man who, as a technical observer, had perhaps no
peer in the ancient world: one who set so high a value upon
accuracy of observation as to earn the title of "the lover of
truth." Hipparchus was born at Nicaea, in Bithynia, in the year
160 B.C. His life, all too short for the interests of science,
ended in the year 125 B.C. The observations of the great
astronomer were made chiefly, perhaps entirely, at Rhodes. A
misinterpretation of Ptolemy's writings led to the idea that
Hipparchus, performed his chief labors in Alexandria, but it is
now admitted that there is no evidence for this. Delambre
doubted, and most subsequent writers follow him here, whether
Hipparchus ever so much as visited Alexandria. In any event there
seems to be no question that Rhodes may claim the honor of being
the chief site of his activities.

It was Hipparchus whose somewhat equivocal comment on the work of
Eratosthenes we have already noted. No counter-charge in kind
could be made against the critic himself; he was an astronomer
pure and simple. His gift was the gift of accurate observation
rather than the gift of imagination. No scientific progress is
possible without scientific guessing, but Hipparchus belonged to
that class of observers with whom hypothesis is held rigidly
subservient to fact. It was not to be expected that his mind
would be attracted by the heliocentric theory of Aristarchus. He
used the facts and observations gathered by his great predecessor
of Samos, but he declined to accept his theories. For him the
world was central; his problem was to explain, if he could, the
irregularities of motion which sun, moon, and planets showed in
their seeming circuits about the earth. Hipparchus had the gnomon
of Eratosthenes--doubtless in a perfected form--to aid him, and
he soon proved himself a master in its use. For him, as we have
said, accuracy was everything; this was the one element that led
to all his great successes.

Perhaps his greatest feat was to demonstrate the eccentricity of
the sun's seeming orbit. We of to-day, thanks to Keppler and his
followers, know that the earth and the other planetary bodies in
their circuit about the sun describe an ellipse and not a circle.
But in the day of Hipparchus, though the ellipse was recognized
as a geometrical figure (it had been described and named along
with the parabola and hyperbola by Apollonius of Perga, the pupil
of Euclid), yet it would have been the rankest heresy to suggest
an elliptical course for any heavenly body. A metaphysical
theory, as propounded perhaps by the Pythagoreans but ardently
supported by Aristotle, declared that the circle is the perfect
figure, and pronounced it inconceivable that the motions of the
spheres should be other than circular. This thought dominated the
mind of Hipparchus, and so when his careful measurements led him
to the discovery that the northward and southward journeyings of
the sun did not divide the year into four equal parts, there was
nothing open to him but to either assume that the earth does not
lie precisely at the centre of the sun's circular orbit or to
find some alternative hypothesis.

In point of fact, the sun (reversing the point of view in
accordance with modern discoveries) does lie at one focus of the
earth's elliptical orbit, and therefore away from the physical
centre of that orbit; in other words, the observations of
Hipparchus were absolutely accurate. He was quite correct in
finding that the sun spends more time on one side of the equator
than on the other. When, therefore, he estimated the relative
distance of the earth from the geometrical centre of the sun's
supposed circular orbit, and spoke of this as the measure of the
sun's eccentricity, he propounded a theory in which true data of
observation were curiously mingled with a positively inverted
theory. That the theory of Hipparchus was absolutely consistent
with all the facts of this particular observation is the best
evidence that could be given of the difficulties that stood in
the way of a true explanation of the mechanism of the heavens.

But it is not merely the sun which was observed to vary in the
speed of its orbital progress; the moon and the planets also show
curious accelerations and retardations of motion. The moon in
particular received most careful attention from Hipparchus.
Dominated by his conception of the perfect spheres, he could find
but one explanation of the anomalous motions which he observed,
and this was to assume that the various heavenly bodies do not
fly on in an unvarying arc in their circuit about the earth, but
describe minor circles as they go which can be likened to nothing
so tangibly as to a light attached to the rim of a wagon-wheel in
motion. If such an invisible wheel be imagined as carrying the
sun, for example, on its rim, while its invisible hub follows
unswervingly the circle of the sun's mean orbit (this wheel, be
it understood, lying in the plane of the orbit, not at right-
angles to it), then it must be obvious that while the hub remains
always at the same distance from the earth, the circling rim will
carry the sun nearer the earth, then farther away, and that while
it is traversing that portion of the are which brings it towards
the earth, the actual forward progress of the sun will be
retarded notwithstanding the uniform motion of the hub, just as
it will be accelerated in the opposite arc. Now, if we suppose
our sun-bearing wheel to turn so slowly that the sun revolves but
once about its imaginary hub while the wheel itself is making the
entire circuit of the orbit, we shall have accounted for the
observed fact that the sun passes more quickly through one-half
of the orbit than through the other. Moreover, if we can
visualize the process and imagine the sun to have left a visible
line of fire behind him throughout the course, we shall see that
in reality the two circular motions involved have really resulted
in producing an elliptical orbit.

The idea is perhaps made clearer if we picture the actual
progress of the lantern attached to the rim of an ordinary
cart-wheel. When the cart is drawn forward the lantern is made to
revolve in a circle as regards the hub of the wheel, but since
that hub is constantly going forward, the actual path described
by the lantern is not a circle at all but a waving line. It is
precisely the same with the imagined course of the sun in its
orbit, only that we view these lines just as we should view the
lantern on the wheel if we looked at it from directly above and
not from the side. The proof that the sun is describing this
waving line, and therefore must be considered as attached to an
imaginary wheel, is furnished, as it seemed to Hipparchus, by the
observed fact of the sun's varying speed.

That is one way of looking at the matter. It is an hypothesis
that explains the observed facts--after a fashion, and indeed a
very remarkable fashion. The idea of such an explanation did not
originate with Hipparchus. The germs of the thought were as old
as the Pythagorean doctrine that the earth revolves about a
centre that we cannot see. Eudoxus gave the conception greater
tangibility, and may be considered as the father of this doctrine
of wheels--epicycles, as they came to be called. Two centuries
before the time of Hipparchus he conceived a doctrine of spheres
which Aristotle found most interesting, and which served to
explain, along the lines we have just followed, the observed
motions of the heavenly bodies. Calippus, the reformer of the
calendar, is said to have carried an account of this theory to
Aristotle. As new irregularities of motion of the sun, moon, and
planetary bodies were pointed out, new epicycles were invented.
There is no limit to the number of imaginary circles that may be
inscribed about an imaginary centre, and if we conceive each one
of these circles to have a proper motion of its own, and each one
to carry the sun in the line of that motion, except as it is
diverted by the other motions--if we can visualize this complex
mingling of wheels--we shall certainly be able to imagine the
heavenly body which lies at the juncture of all the rims, as
being carried forward in as erratic and wobbly a manner as could
be desired. In other words, the theory of epicycles will account
for all the facts of the observed motions of all the heavenly
bodies, but in so doing it fills the universe with a most
bewildering network of intersecting circles. Even in the time of
Calippus fifty-five of these spheres were computed.

We may well believe that the clear-seeing Aristarchus would look
askance at such a complex system of imaginary machinery. But
Hipparchus, pre-eminently an observer rather than a theorizer,
seems to have been content to accept the theory of epicycles as
he found it, though his studies added to its complexities; and
Hipparchus was the dominant scientific personality of his
century. What he believed became as a law to his immediate
successors. His tenets were accepted as final by their great
popularizer, Ptolemy, three centuries later; and so the
heliocentric theory of Aristarchus passed under a cloud almost at
the hour of its dawning, there to remain obscured and forgotten
for the long lapse of centuries. A thousand pities that the
greatest observing astronomer of antiquity could not, like one of
his great precursors, have approached astronomy from the
stand-point of geography and poetry. Had he done so, perhaps he
might have reflected, like Aristarchus before him, that it seems
absurd for our earth to hold the giant sun in thraldom; then
perhaps his imagination would have reached out to the
heliocentric doctrine, and the cobweb hypothesis of epicycles,
with that yet more intangible figment of the perfect circle,
might have been wiped away.

But it was not to be. With Aristarchus the scientific imagination
had reached its highest flight; but with Hipparchus it was
beginning to settle back into regions of foggier atmosphere and
narrower horizons. For what, after all, does it matter that
Hipparchus should go on to measure the precise length of the year
and the apparent size of the moon's disk; that he should make a
chart of the heavens showing the place of 1080 stars; even that
he should discover the precession of the equinox;--what, after
all, is the significance of these details as against the
all-essential fact that the greatest scientific authority of his
century--the one truly heroic scientific figure of his
epoch--should have lent all the forces of his commanding
influence to the old, false theory of cosmology, when the true
theory had been propounded and when he, perhaps, was the only man
in the world who might have substantiated and vitalized that
theory? It is easy to overestimate the influence of any single
man, and, contrariwise, to underestimate the power of the
Zeitgeist. But when we reflect that the doctrines of Hipparchus,
as promulgated by Ptolemy, became, as it were, the last word of
astronomical science for both the Eastern and Western worlds, and
so continued after a thousand years, it is perhaps not too much
to say that Hipparchus, "the lover of truth," missed one of the
greatest opportunities for the promulgation of truth ever
vouchsafed to a devotee of pure science.

But all this, of course, detracts nothing from the merits of
Hipparchus as an observing astronomer. A few words more must be
said as to his specific discoveries in this field. According to
his measurement, the tropic year consists of 365 days, 5 hours,
and 49 minutes, varying thus only 12 seconds from the true year,
as the modern astronomer estimates it. Yet more remarkable,
because of the greater difficulties involved, was Hipparchus's
attempt to measure the actual distance of the moon. Aristarchus
had made a similar attempt before him. Hipparchus based his
computations on studies of the moon in eclipse, and he reached
the conclusion that the distance of the moon is equal to 59 radii
of the earth (in reality it is 60.27 radii). Here, then, was the
measure of the base-line of that famous triangle with which
Aristarchus had measured the distance of the sun. Hipparchus must
have known of that measurement, since he quotes the work of
Aristarchus in other fields. Had he now but repeated the
experiment of Aristarchus, with his perfected instruments and his
perhaps greater observational skill, he was in position to
compute the actual distance of the sun in terms not merely of the
moon's distance but of the earth's radius. And now there was the
experiment of Eratosthenes to give the length of that radius in
precise terms. In other words, Hipparchus might have measured the
distance of the sun in stadia. But if he had made the
attempt--and, indeed, it is more than likely that he did so--the
elements of error in his measurements would still have kept him
wide of the true figures.

The chief studies of Hipparchus were directed, as we have seen,
towards the sun and the moon, but a phenomenon that occurred in
the year 134 B.C. led him for a time to give more particular
attention to the fixed stars. The phenomenon in question was the
sudden outburst of a new star; a phenomenon which has been
repeated now and again, but which is sufficiently rare and
sufficiently mysterious to have excited the unusual attention of
astronomers in all generations. Modern science offers an
explanation of the phenomenon, as we shall see in due course. We
do not know that Hipparchus attempted to explain it, but he was
led to make a chart of the heavens, probably with the idea of
guiding future observers in the observation of new stars. Here
again Hipparchus was not altogether an innovator, since a chart
showing the brightest stars had been made by Eratosthenes; but
the new charts were much elaborated.

The studies of Hipparchus led him to observe the stars chiefly
with reference to the meridian rather than with reference to
their rising, as had hitherto been the custom. In making these
studies of the relative position of the stars, Hipparchus was led
to compare his observations with those of the Babylonians, which,
it was said, Alexander had caused to be transmitted to Greece. He
made use also of the observations of Aristarchus and others of
his Greek precursors. The result of his comparisons proved that
the sphere of the fixed stars had apparently shifted its position
in reference to the plane of the sun's orbit--that is to say, the
plane of the ecliptic no longer seemed to cut the sphere of the
fixed stars at precisely the point where the two coincided in
former centuries. The plane of the ecliptic must therefore be
conceived as slowly revolving in such a way as gradually to
circumnavigate the heavens. This important phenomenon is
described as the precession of the equinoxes.

It is much in question whether this phenomenon was not known to
the ancient Egyptian astronomers; but in any event, Hipparchus is
to be credited with demonstrating the fact and making it known to
the Western world. A further service was rendered theoretical
astronomy by Hipparchus through his invention of the planosphere,
an instrument for the representation of the mechanism of the
heavens. His computations of the properties of the spheres led
him also to what was virtually a discovery of the method of
trigonometry, giving him, therefore, a high position in the field
of mathematics. All in all, then, Hipparchus is a most heroic
figure. He may well be considered the greatest star-gazer of
antiquity, though he cannot, without injustice to his great
precursors, be allowed the title which is sometimes given him of
"father of systematic astronomy."

CTESIBIUS AND HERO: MAGICIANS OF ALEXANDRIA

Just about the time when Hipparchus was working out at Rhodes his
puzzles of celestial mechanics, there was a man in Alexandria who
was exercising a strangely inventive genius over mechanical
problems of another sort; a man who, following the example set by
Archimedes a century before, was studying the problems of matter
and putting his studies to practical application through the
invention of weird devices. The man's name was Ctesibius. We know
scarcely more of him than that he lived in Alexandria, probably
in the first half of the second century B.C. His antecedents, the
place and exact time of his birth and death, are quite unknown.
Neither are we quite certain as to the precise range of his
studies or the exact number of his discoveries. It appears that
he had a pupil named Hero, whose personality, unfortunately, is
scarcely less obscure than that of his master, but who wrote a
book through which the record of the master's inventions was
preserved to posterity. Hero, indeed, wrote several books, though
only one of them has been preserved. The ones that are lost bear
the following suggestive titles: On the Construction of Slings;
On the Construction of Missiles; On the Automaton; On the Method
of Lifting Heavy Bodies; On the Dioptric or Spying-tube. The work
that remains is called Pneumatics, and so interesting a work it
is as to make us doubly regret the loss of its companion volumes.
Had these other books been preserved we should doubtless have a
clearer insight than is now possible into some at least of the
mechanical problems that exercised the minds of the ancient
philosophers. The book that remains is chiefly concerned, as its
name implies, with the study of gases, or, rather, with the study
of a single gas, this being, of course, the air. But it tells us
also of certain studies in the dynamics of water that are most
interesting, and for the historian of science most important.

Unfortunately, the pupil of Ctesibius, whatever his ingenuity,
was a man with a deficient sense of the ethics of science. He
tells us in his preface that the object of his book is to record
some ingenious discoveries of others, together with additional
discoveries of his own, but nowhere in the book itself does he
give us the, slightest clew as to where the line is drawn between
the old and the new. Once, in discussing the weight of water, he
mentions the law of Archimedes regarding a floating body, but
this is the only case in which a scientific principle is traced
to its source or in which credit is given to any one for a
discovery. This is the more to be regretted because Hero has
discussed at some length the theories involved in the treatment
of his subject. This reticence on the part of Hero, combined with
the fact that such somewhat later writers as Pliny and Vitruvius
do not mention Hero's name, while they frequently mention the
name of his master, Ctesibius, has led modern critics to a
somewhat sceptical attitude regarding the position of Hero as an
actual discoverer.

The man who would coolly appropriate some discoveries of others
under cloak of a mere prefatorial reference was perhaps an
expounder rather than an innovator, and had, it is shrewdly
suspected, not much of his own to offer. Meanwhile, it is
tolerably certain that Ctesibius was the discoverer of the
principle of the siphon, of the forcing-pump, and of a pneumatic
organ. An examination of Hero's book will show that these are
really the chief principles involved in most of the various
interesting mechanisms which he describes. We are constrained,
then, to believe that the inventive genius who was really
responsible for the mechanisms we are about to describe was
Ctesibius, the master. Yet we owe a debt of gratitude to Hero,
the pupil, for having given wider vogue to these discoveries, and
in particular for the discussion of the principles of
hydrostatics and pneumatics contained in the introduction to his
book. This discussion furnishes us almost our only knowledge as
to the progress of Greek philosophers in the field of mechanics
since the time of Archimedes.

The main purpose of Hero in his preliminary thesis has to do with
the nature of matter, and recalls, therefore, the studies of
Anaxagoras and Democritus. Hero, however, approaches his subject
from a purely material or practical stand-point. He is an
explicit champion of what we nowadays call the molecular theory
of matter. "Every body," he tells us, "is composed of minute
particles, between which are empty spaces less than these
particles of the body. It is, therefore, erroneous to say that
there is no vacuum except by the application of force, and that
every space is full either of air or water or some other
substance. But in proportion as any one of these particles
recedes, some other follows it and fills the vacant space;
therefore there is no continuous vacuum, except by the
application of some force [like suction]--that is to say, an
absolute vacuum is never found, except as it is produced
artificially." Hero brings forward some thoroughly convincing
proofs of the thesis he is maintaining. "If there were no void
places between the particles of water," he says, "the rays of
light could not penetrate the water; moreover, another liquid,
such as wine, could not spread itself through the water, as it is
observed to do, were the particles of water absolutely
continuous." The latter illustration is one the validity of which
appeals as forcibly to the physicists of to-day as it did to
Hero. The same is true of the argument drawn from the
compressibility of gases. Hero has evidently made a careful study
of this subject. He knows that an inverted tube full of air may
be immersed in water without becoming wet on the inside, proving
that air is a physical substance; but he knows also that this
same air may be caused to expand to a much greater bulk by the
application of heat, or may, on the other hand, be condensed by
pressure, in which case, as he is well aware, the air exerts
force in the attempt to regain its normal bulk. But, he argues,
surely we are not to believe that the particles of air expand to
fill all the space when the bulk of air as a whole expands under
the influence of heat; nor can we conceive that the particles of
normal air are in actual contact, else we should not be able to
compress the air. Hence his conclusion, which, as we have seen,
he makes general in its application to all matter, that there are
spaces, or, as he calls them, vacua, between the particles that
go to make up all substances, whether liquid, solid, or gaseous.

Here, clearly enough, was the idea of the "atomic" nature of
matter accepted as a fundamental notion. The argumentative
attitude assumed by Hero shows that the doctrine could not be
expected to go unchallenged. But, on the other hand, there is
nothing in his phrasing to suggest an intention to claim
originality for any phase of the doctrine. We may infer that in
the three hundred years that had elapsed since the time of
Anaxagoras, that philosopher's idea of the molecular nature of
matter had gained fairly wide currency. As to the expansive power
of gas, which Hero describes at some length without giving us a
clew to his authorities, we may assume that Ctesibius was an
original worker, yet the general facts involved were doubtless
much older than his day. Hero, for example, tells us of the
cupping-glass used by physicians, which he says is made into a
vacuum by burning up the air in it; but this apparatus had
probably been long in use, and Hero mentions it not in order to
describe the ordinary cupping-glass which is referred to, but a
modification of it. He refers to the old form as if it were
something familiar to all.

Again, we know that Empedocles studied the pressure of the air in
the fifth century B.C., and discovered that it would support a
column of water in a closed tube, so this phase of the subject is
not new. But there is no hint anywhere before this work of Hero
of a clear understanding that the expansive properties of the air
when compressed, or when heated, may be made available as a motor
power. Hero, however, has the clearest notions on the subject and
puts them to the practical test of experiment. Thus he constructs
numerous mechanisms in which the expansive power of air under
pressure is made to do work, and others in which the same end is
accomplished through the expansive power of heated air. For
example, the doors of a temple are made to swing open
automatically when a fire is lighted on a distant altar, closing
again when the fire dies out--effects which must have filled the
minds of the pious observers with bewilderment and wonder,
serving a most useful purpose for the priests, who alone, we may
assume, were in the secret. There were two methods by which this
apparatus was worked. In one the heated air pressed on the water
in a close retort connected with the altar, forcing water out of
the retort into a bucket, which by its weight applied a force
through pulleys and ropes that turned the standards on which the
temple doors revolved. When the fire died down the air
contracted, the water was siphoned back from the bucket, which,
being thus lightened, let the doors close again through the
action of an ordinary weight. The other method was a slight
modification, in which the retort of water was dispensed with and
a leather sack like a large football substitued. The ropes
and pulleys were connected with this sack, which exerted a pull
when the hot air expanded, and which collapsed and thus relaxed
its strain when the air cooled. A glance at the illustrations
taken from Hero's book will make the details clear.

Other mechanisms utilized a somewhat different combination of
weights, pulleys, and siphons, operated by the expansive power of
air, unheated but under pressure, such pressure being applied
with a force- pump, or by the weight of water running into a
closed receptacle. One such mechanism gives us a constant jet of
water or perpetual fountain. Another curious application of the
principle furnishes us with an elaborate toy, consisting of a
group of birds which alternately whistle or are silent, while an
owl seated on a neighboring perch turns towards the birds when
their song begins and away from them when it ends. The "singing"
of the birds, it must be explained, is produced by the expulsion
of air through tiny tubes passing up through their throats from a
tank below. The owl is made to turn by a mechanism similar to
that which manipulates the temple doors. The pressure is supplied
merely by a stream of running water, and the periodical silence
of the birds is due to the fact that this pressure is relieved
through the automatic siphoning off of the water when it reaches
a certain height. The action of the siphon, it may be added, is
correctly explained by Hero as due to the greater weight of the
water in the longer arm of the bent tube. As before mentioned,
the siphon is repeatedly used in these mechanisms of Hero. The
diagram will make clear the exact application of it in the
present most ingenious mechanism. We may add that the principle
of the whistle was a favorite one of Hero. By the aid of a
similar mechanism he brought about the blowing of trumpets when
the temple doors were opened, a phenomenon which must greatly
have enhanced the mystification. It is possible that this
principle was utilized also in connection with statues to produce
seemingly supernatural effects. This may be the explanation of
the tradition of the speaking statue in the temple of Ammon at
Thebes.

{illustration caption = DEVICE FOR CAUSING THE DOORS OF THE
TEMPLE TO OPEN WHEN THE FIRE ON THE ALTAR IS LIGHTED (Air heated
in the altar F drives water from the closed receptacle H through
the tube KL into the bucket M, which descends through gravity,
thus opening the doors. When the altar cools, the air contracts,
the water is sucked from the bucket, and the weight and pulley
close the doors.)}

{illustration caption = THE STEAM-ENGINE OF HERO (The steam
generated in the receptacle AB passes through the tube EF into
the globe, and escapes through the bent tubes H and K, causing
the globe to rotate on the axis LG.)}

The utilization of the properties of compressed air was not
confined, however, exclusively to mere toys, or to produce
miraculous effects. The same principle was applied to a practical
fire-engine, worked by levers and force-pumps; an apparatus, in
short, altogether similar to that still in use in rural
districts. A slightly different application of the motive power
of expanding air is furnished in a very curious toy called "the
dancing figures." In this, air heated in a retort like a
miniature altar is allowed to escape through the sides of two
pairs of revolving arms precisely like those of the ordinary
revolving fountain with which we are accustomed to water our
lawns, the revolving arms being attached to a plane on which
several pairs of statuettes representing dancers are placed, An
even more interesting application of this principle of setting a
wheel in motion is furnished in a mechanism which must be
considered the earliest of steam-engines. Here, as the name
implies, the gas supplying the motive power is actually steam.
The apparatus made to revolve is a globe connected with the
steam-retort by a tube which serves as one of its axes, the steam
escaping from the globe through two bent tubes placed at either
end of an equatorial diameter. It does not appear that Hero had
any thought of making practical use of this steam- engine. It was
merely a curious toy--nothing more. Yet had not the age that
succeeded that of Hero been one in which inventive genius was
dormant, some one must soon have hit upon the idea that this
steam- engine might be improved and made to serve a useful
purpose. As the case stands, however, there was no advance made
upon the steam motor of Hero for almost two thousand years. And,
indeed, when the practical application of steam was made, towards
the close of the eighteenth century, it was made probably quite
without reference to the experiment of Hero, though knowledge of
his toy may perhaps have given a clew to Watt or his
predecessors.

{illustration caption = THE SLOT-MACHINE OF HERO (The coin
introduced at A falls on the lever R, and by its weight opens the
valve S, permitting the liquid to escape through the invisible
tube LM. As the lever tips, the coin slides off and the valve
closes. The liquid in tank must of course be kept above F.)}

In recent times there has been a tendency to give to this
steam-engine of Hero something more than full meed of
appreciation. To be sure, it marked a most important principle in
the conception that steam might be used as a motive power, but,
except in the demonstration of this principle, the mechanism of
Hero was much too primitive to be of any importance. But there is
one mechanism described by Hero which was a most explicit
anticipation of a device, which presumably soon went out of use,
and which was not reinvented until towards the close of the
nineteenth century. This was a device which has become familiar
in recent times as the penny-in-the-slot machine. When towards
the close of the nineteenth century some inventive craftsman hit
upon the idea of an automatic machine to supply candy, a box of
cigarettes, or a whiff of perfumery, he may or may not have
borrowed his idea from the slot-machine of Hero; but in any
event, instead of being an innovator he was really two thousand
years behind the times, for the slot-machine of Hero is the
precise prototype of these modern ones.

The particular function which the mechanism of Hero was destined
to fulfil was the distribution of a jet of water, presumably used
for sacramental purposes, which was given out automatically when
a five- drachma coin was dropped into the slot at the top of the
machine. The internal mechanism of the machine was simple enough,
consisting merely of a lever operating a valve which was opened
by the weight of the coin dropping on the little shelf at the end
of the lever, and which closed again when the coin slid off the
shelf. The illustration will show how simple this mechanism was.
Yet to the worshippers, who probably had entered the temple
through doors miraculously opened, and who now witnessed this
seemingly intelligent response of a machine, the result must have
seemed mystifying enough; and, indeed, for us also, when we
consider how relatively crude was the mechanical knowledge of the
time, this must seem nothing less than marvellous. As in
imagination we walk up to the sacred tank, drop our drachma in
the slot, and hold our hand for the spurt of holy-water, can we
realize that this is the land of the Pharaohs, not England or
America; that the kingdom of the Ptolemies is still at its
height; that the republic of Rome is mistress of the world; that
all Europe north of the Alps is inhabited solely by barbarians;
that Cleopatra and Julius Caesar are yet unborn; that the
Christian era has not yet begun? Truly, it seems as if there
could be no new thing under the sun.

X. SCIENCE OF THE ROMAN PERIOD

We have seen that the third century B.C. was a time when
Alexandrian science was at its height, but that the second
century produced also in Hipparchus at least one investigator of
the very first rank; though, to be sure, Hipparchus can be called
an Alexandrian only by courtesy. In the ensuing generations the
Greek capital at the mouth of the Nile continued to hold its
place as the centre of scientific and philosophical thought. The
kingdom of the Ptolemies still flourished with at least the
outward appearances of its old-time glory, and a company of
grammarians and commentators of no small merit could always be
found in the service of the famous museum and library; but the
whole aspect of world-history was rapidly changing. Greece, after
her brief day of political supremacy, was sinking rapidly
into desuetude, and the hard-headed Roman in the West was making
himself master everywhere. While Hipparchus of Rhodes was in his
prime, Corinth, the last stronghold of the main-land of Greece,
had fallen before the prowess of the Roman, and the kingdom of
the Ptolemies, though still nominally free, had begun to come
within the sphere of Roman influence.

Just what share these political changes had in changing the
aspect of Greek thought is a question regarding which difference
of opinion might easily prevail; but there can be no question
that, for one reason or another, the Alexandrian school as a
creative centre went into a rapid decline at about the time of
the Roman rise to world-power. There are some distinguished
names, but, as a general rule, the spirit of the times is
reminiscent rather than creative; the workers tend to collate the
researches of their predecessors rather than to make new and
original researches for themselves. Eratosthenes, the inventive
world-measurer, was succeeded by Strabo, the industrious collator
of facts; Aristarchus and Hipparchus, the originators of new
astronomical methods, were succeeded by Ptolemy, the perfecter of
their methods and the systematizer of their knowledge. Meanwhile,
in the West, Rome never became a true culture-centre. The great
genius of the Roman was political; the Augustan Age produced a
few great historians and poets, but not a single great
philosopher or creative devotee of science. Cicero, Lucian,
Seneca, Marcus Aurelius, give us at best a reflection of Greek
philosophy. Pliny, the one world-famous name in the scientific
annals of Rome, can lay claim to no higher credit than that of a
marvellously industrious collector of facts--the compiler of an
encyclopaedia which contains not one creative touch.

All in all, then, this epoch of Roman domination is one that need
detain the historian of science but a brief moment. With the
culmination of Greek effort in the so-called Hellenistic period
we have seen ancient science at its climax. The Roman period is
but a time of transition, marking, as it were, a plateau on the
slope between those earlier heights and the deep, dark valleys of
the Middle Ages. Yet we cannot quite disregard the efforts of
such workers as those we have just named. Let us take a more
specific glance at their accomplishments.

STRABO THE GEOGRAPHER

The earliest of these workers in point of time is Strabo. This
most famous of ancient geographers was born in Amasia, Pontus,
about 63 B.C., and lived to the year 24 A.D., living, therefore,
in the age of Caesar and Augustus, during which the final
transformation in the political position of the kingdom of Egypt
was effected. The name of Strabo in a modified form has become
popularized through a curious circumstance. The geographer, it
appears, was afflicted with a peculiar squint of the eyes, hence
the name strabismus, which the modern oculist applies to that
particular infirmity.

Fortunately, the great geographer has not been forced to depend
upon hearsay evidence for recognition. His comprehensive work on
geography has been preserved in its entirety, being one of the
few expansive classical writings of which this is true. The other
writings of Strabo, however, including certain histories of which
reports have come down to us, are entirely lost. The geography is
in many ways a remarkable book. It is not, however, a work in
which any important new principles are involved. Rather is it
typical of its age in that it is an elaborate compilation and a
critical review of the labors of Strabo's predecessors. Doubtless
it contains a vast deal of new information as to the details of
geography--precise areas and distance, questions of geographical
locations as to latitude and zones, and the like. But however
important these details may have been from a contemporary
stand-point, they, of course, can have nothing more than
historical interest to posterity. The value of the work from our
present stand-point is chiefly due to the criticisms which Strabo
passes upon his forerunners, and to the incidental historical and
scientific references with which his work abounds. Being written
in this closing period of ancient progress, and summarizing, as
it does, in full detail the geographical knowledge of the time,
it serves as an important guide-mark for the student of the
progress of scientific thought. We cannot do better than briefly
to follow Strabo in his estimates and criticisms of the work of
his predecessors, taking note thus of the point of view from
which he himself looked out upon the world. We shall thus gain a
clear idea as to the state of scientific geography towards the
close of the classical epoch.

"If the scientific investigation of any subject be the proper
avocation of the philosopher," says Strabo, "geography, the
science of which we propose to treat, is certainly entitled to a
high place; and this is evident from many considerations. They
who first undertook to handle the matter were distinguished men.
Homer, Anaximander the Milesian, and Hecaeus (his fellow-citizen
according to Eratosthenes), Democritus, Eudoxus, Dicaearchus, and
Ephorus, with many others, and after these, Eratosthenes,
Polybius, and Posidonius, all of them philosophers. Nor is the
great learning through which alone this subject can be approached
possessed by any but a person acquainted with both human and
divine things, and these attainments constitute what is called
philosophy. In addition to its vast importance in regard to
social life and the art of government, geography unfolds to us a
celestial phenomena, acquaints us with the occupants of the land
and ocean, and the vegetation, fruits, and peculiarities of the
various quarters of the earth, a knowledge of which marks him who
cultivates it as a man earnest in the great problem of life and
happiness."

Strabo goes on to say that in common with other critics,
including Hipparchus, he regards Homer as the first great
geographer. He has much to say on the geographical knowledge of
the bard, but this need not detain us. We are chiefly concerned
with his comment upon his more recent predecessors, beginning
with Eratosthenes. The constant reference to this worker shows
the important position which he held. Strabo appears neither as
detractor nor as partisan, but as one who earnestly desires the
truth. Sometimes he seems captious in his criticisms regarding
some detail, nor is he always correct in his emendations of the
labors of others; but, on the whole, his work is marked by an
evident attempt at fairness. In reading his book, however, one is
forced to the conclusion that Strabo is an investigator of
details, not an original thinker. He seems more concerned with
precise measurements than with questionings as to the open
problems of his science. Whatever he accepts, then, may be taken
as virtually the stock doctrine of the period.

"As the size of the earth," he says, "has been demonstrated by
other writers, we shall here take for granted and receive as
accurate what they have advanced. We shall also assume that the
earth is spheroidal, that its surface is likewise spheroidal and,
above all, that bodies have a tendency towards its centre, which
latter point is clear to the perception of the most average
understanding. However, we may show summarily that the earth is
spheroidal, from the consideration that all things, however
distant, tend to its centre, and that every body is attracted
towards its centre by gravity. This is more distinctly proved
from observations of the sea and sky, for here the evidence of
the senses and common observation is alone requisite. The
convexity of the sea is a further proof of this to those who have
sailed, for they cannot perceive lights at a distance when placed
at the same level as their eyes, and if raised on high they at
once become perceptible to vision though at the same time farther
removed. So when the eye is raised it sees what before was
utterly imperceptible. Homer speaks of this when he says:

" 'Lifted up on the vast wave he quickly beheld afar.'

Sailors as they approach their destination behold the shore
continually raising itself to their view, and objects which had
at first seemed low begin to lift themselves. Our gnomons, also,
are, among other things, evidence of the revolution of the
heavenly bodies, and common-sense at once shows us that if the
depth of the earth were infinite such a revolution could not take
place."[1]

Elsewhere Strabo criticises Eratosthenes for having entered into
a long discussion as to the form of the earth. This matter,
Strabo thinks, "should have been disposed of in the compass of a
few words." Obviously this doctrine of the globe's sphericity
had, in the course of 600 years, become so firmly established
among the Greek thinkers as to seem almost axiomatic. We shall
see later on how the Western world made a curious recession from
this seemingly secure position under stimulus of an Oriental
misconception. As to the size of the globe, Strabo is disposed to
accept without particular comment the measurements of
Eratosthenes. He speaks, however, of "more recent measurements,"
referring in particular to that adopted by Posidonius, according
to which the circumference is only about one hundred and eighty
thousand stadia. Posidonius, we may note in passing, was a
contemporary and friend of Cicero, and hence lived shortly before
the time of Strabo. His measurement of the earth was based on
observations of a star which barely rose above the southern
horizon at Rhodes as compared with the height of the same star
when observed at Alexandria. This measurement of Posidonius,
together with the even more famous measurement of Eratosthenes,
appears to have been practically the sole guide as to the size of
the earth throughout the later periods of antiquity, and, indeed,
until the later Middle Ages.

As becomes a writer who is primarily geographer and historian
rather than astronomer, Strabo shows a much keener interest in
the habitable portions of the globe than in the globe as a whole.
He assures us that this habitable portion of the earth is a great
island, "since wherever men have approached the termination of
the land, the sea, which we designate ocean, has been met with,
and reason assures us of the similarity of this place which our
senses have not been tempted to survey." He points out that
whereas sailors have not circumnavigated the globe, that they had
not been prevented from doing so by any continent, and it seems
to him altogether unlikely that the Atlantic Ocean is divided
into two seas by narrow isthmuses so placed as to prevent
circumnavigation. "How much more probable that it is confluent
and uninterrupted. This theory," he adds, "goes better with the
ebb and flow of the ocean. Moreover (and here his reasoning
becomes more fanciful), the greater the amount of moisture
surrounding the earth, the easier would the heavenly bodies be
supplied with vapor from thence." Yet he is disposed to believe,
following Plato, that the tradition "concerning the island of
Atlantos might be received as something more than idle fiction,
it having been related by Solon, on the authority of the Egyptian
priests, that this island, almost as large as a continent, was
formerly in existence although now it had disappeared."[2]

In a word, then, Strabo entertains no doubt whatever that it
would be possible to sail around the globe from Spain to India.
Indeed, so matter-of-fact an inference was this that the feat of
Columbus would have seemed less surprising in the first century
of our era than it did when actually performed in the fifteenth
century. The terrors of the great ocean held the mariner back,
rather than any doubt as to where he would arrive at the end of
the voyage.

Coupled with the idea that the habitable portion of the earth is
an island, there was linked a tolerably definite notion as to the
shape of this island. This shape Strabo likens to a military
cloak. The comparison does not seem peculiarly apt when we are
told presently that the length of the habitable earth is more
than twice its breadth. This idea, Strabo assures us, accords
with the most accurate observations "both ancient and modern."
These observations seemed to show that it is not possible to live
in the region close to the equator, and that, on the other hand,
the cold temperature sharply limits the habitability of the globe
towards the north. All the civilization of antiquity clustered
about the Mediterranean, or extended off towards the east at
about the same latitude. Hence geographers came to think of the
habitable globe as having the somewhat lenticular shape which a
crude map of these regions suggests. We have already had occasion
to see that at an earlier day Anaxagoras was perhaps influenced
in his conception of the shape of the earth by this idea, and the
constant references of Strabo impress upon us the thought that
this long, relatively narrow area of the earth's surface is the
only one which can be conceived of as habitable.

Strabo had much to tell us concerning zones, which, following
Posidonius, he believes to have been first described by
Parmenides. We may note, however, that other traditions assert
that both Thales and Pythagoras had divided the earth into zones.
The number of zones accepted by Strabo is five, and he
criticises Polybius for making the number six. The five
zones accepted by Strabo are as follows: the uninhabitable torrid
zone lying in the region of the equator; a zone on either side of
this extending to the tropic; and then the temperate zones
extending in either direction from the tropic to the arctic
regions. There seems to have been a good deal of dispute among
the scholars of the time as to the exact arrangement of these
zones, but the general idea that the north-temperate zone is the
part of the earth with which the geographer deals seemed clearly
established. That the south-temperate zone would also present a
habitable area is an idea that is sometimes suggested, though
seldom or never distinctly expressed. It is probable that
different opinions were held as to this, and no direct evidence
being available, a cautiously scientific geographer like Strabo
would naturally avoid the expression of an opinion regarding it.
Indeed, his own words leave us somewhat in doubt as to the
precise character of his notion regarding the zones. Perhaps we
shall do best to quote them:

"Let the earth be supposed to consist of five zones. (1) The
equatorial circle described around it. (2) Another parallel to
this, and defining the frigid zone of the northern hemisphere.
(3) A circle passing through the poles and cutting the two
preceding circles at right- angles. The northern hemisphere
contains two quarters of the earth, which are bounded by the
equator and circle passing through the poles. Each of these
quarters should be supposed to contain a four-sided district, its
northern side being of one-half of the parallel next the pole,
its southern by the half of the equator, and its remaining sides
by two segments of the circle drawn through the poles, opposite
to each other, and equal in length. In one of these (which of
them is of no consequence) the earth which we inhabit is
situated, surrounded by a sea and similar to an island. This, as
we said before, is evident both to our senses and to our reason.
But let any one doubt this, it makes no difference so far as
geography is concerned whether you believe the portion of the
earth which we inhabit to be an island or only admit what we know
from experience --namely, that whether you start from the east or
the west you may sail all around it. Certain intermediate spaces
may have been left (unexplored), but these are as likely to be
occupied by sea as uninhabited land. The object of the geographer
is to describe known countries. Those which are unknown he passes
over equally with those beyond the limits of the inhabited earth.
It will, therefore, be sufficient for describing the contour of
the island we have been speaking of, if we join by a right line
the outmost points which, up to this time, have been explored by
voyagers along the coast on either side."[3]

We may pass over the specific criticisms of Strabo upon various
explorations that seem to have been of great interest to his
contemporaries, including an alleged trip of one Eudoxus out into
the Atlantic, and the journeyings of Pytheas in the far north. It
is Pytheas, we may add, who was cited by Hipparchus as having
made the mistaken observation that the length of the shadow of
the gnomon is the same at Marseilles and Byzantium, hence that
these two places are on the same parallel. Modern commentators
have defended Pytheas as regards this observation, claiming that
it was Hipparchus and not Pytheas who made the second observation
from which the faulty induction was drawn. The point is of no
great significance, however, except as showing that a correct
method of determining the problems of latitude had thus early
been suggested. That faulty observations and faulty application
of the correct principle should have been made is not surprising.
Neither need we concern ourselves with the details as to the
geographical distances, which Strabo found so worthy of criticism
and controversy. But in leaving the great geographer we may
emphasize his point of view and that of his contemporaries by
quoting three fundamental principles which he reiterates as being
among the "facts established by natural philosophers." He tells
us that "(1) The earth and heavens are spheroidal. (2) The
tendency of all bodies having weight is towards a centre. (3)
Further, the earth being spheroidal and having the same centre as
the heavens, is motionless, as well as the axis that passes
through both it and the heavens. The heavens turn round both the
earth and its axis, from east to west. The fixed stars turn round
with it at the same rate as the whole. These fixed stars follow
in their course parallel circles, the principal of which are the
equator, two tropics, and the arctic circles; while the planets,
the sun, and the moon describe certain circles comprehended
within the zodiac."[4]

Here, then, is a curious mingling of truth and error. The
Pythagorean doctrine that the earth is round had become a
commonplace, but it would appear that the theory of Aristarchus,
according to which the earth is in motion, has been almost
absolutely forgotten. Strabo does not so much as refer to it;
neither, as we shall see, is it treated with greater respect by
the other writers of the period.

TWO FAMOUS EXPOSITORS--PLINY AND PTOLEMY

While Strabo was pursuing his geographical studies at Alexandria,
a young man came to Rome who was destined to make his name more
widely known in scientific annals than that of any other Latin
writer of antiquity. This man was Plinius Secundus, who, to
distinguish him from his nephew, a famous writer in another
field, is usually spoken of as Pliny the Elder. There is a famous
story to the effect that the great Roman historian Livy on one
occasion addressed a casual associate in the amphitheatre at
Rome, and on learning that the stranger hailed from the outlying
Spanish province of the empire, remarked to him, "Yet you have
doubtless heard of my writings even there." "Then," replied the
stranger, "you must be either Livy or Pliny."

The anecdote illustrates the wide fame which the Roman naturalist
achieved in his own day. And the records of the Middle Ages show
that this popularity did not abate in succeeding times. Indeed,
the Natural History of Pliny is one of the comparatively few
bulky writings of antiquity that the efforts of copyists have
preserved to us almost entire. It is, indeed, a remarkable work
and eminently typical of its time; but its author was an
industrious compiler, not a creative genius. As a monument of
industry it has seldom been equalled, and in this regard it seems
the more remarkable inasmuch as Pliny was a practical man of
affairs who occupied most of his life as a soldier fighting the
battles of the empire. He compiled his book in the leisure hours
stolen from sleep, often writing by the light of the camp-fire.
Yet he cites or quotes from about four thousand works, most of
which are known to us only by his references. Doubtless Pliny
added much through his own observations. We know how keen was his
desire to investigate, since he lost his life through attempting
to approach the crater of Vesuvius on the occasion of that
memorable eruption which buried the cities of Herculaneum and
Pompeii.

Doubtless the wandering life of the soldier had given Pliny
abundant opportunity for personal observation in his favorite
fields of botany and zoology. But the records of his own
observations are so intermingled with knowledge drawn from books
that it is difficult to distinguish the one from the other. Nor
does this greatly matter, for whether as closet-student or
field-naturalist, Pliny's trait of mind is essentially that of
the compiler. He was no philosophical thinker, no generalizer, no
path-maker in science. He lived at the close of a great
progressive epoch of thought; in one of those static periods when
numberless observers piled up an immense mass of details which
might advantageously be sorted into a kind of encyclopaedia. Such
an encyclopaedia is the so-called Natural History of Pliny. It is
a vast jumble of more or less uncritical statements regarding
almost every field of contemporary knowledge. The descriptions of
animals and plants predominate, but the work as a whole would
have been immensely improved had the compiler shown a more
critical spirit. As it is, he seems rather disposed to quote any
interesting citation that he comes across in his omnivorous
readings, shielding himself behind an equivocal "it is said," or
"so and so alleges." A single illustration will suffice to show
what manner of thing is thought worthy of repetition.

"It is asserted," he says, "that if the fish called a sea-star is
smeared with the fox's blood and then nailed to the upper lintel
of the door, or to the door itself, with a copper nail, no
noxious spell will be able to obtain admittance, or, at all
events, be productive of any ill effects."

It is easily comprehensible that a work fortified with such
practical details as this should have gained wide popularity.
Doubtless the natural histories of our own day would find readier
sale were they to pander to various superstitions not altogether
different from that here suggested. The man, for example, who
believes that to have a black cat cross his path is a lucky omen
would naturally find himself attracted by a book which took
account of this and similar important details of natural history.
Perhaps, therefore, it was its inclusion of absurdities, quite as
much as its legitimate value, that gave vogue to the celebrated
work of Pliny. But be that as it may, the most famous scientist
of Rome must be remembered as a popular writer rather than as an
experimental worker. In the history of the promulgation of
scientific knowledge his work is important; in the history of
scientific principles it may virtually be disregarded.

PTOLEMY, THE LAST GREAT ASTRONOMER OF ANTIQUITY

Almost the same thing may be said of Ptolemy, an even more
celebrated writer, who was born not very long after the death of
Pliny. The exact dates of Ptolemy's life are not known, but his
recorded observations extend to the year 151 A.D. He was a
working astronomer, and he made at least one original discovery
of some significance--namely, the observation of a hitherto
unrecorded irregularity of the moon's motion, which came to be
spoken of as the moon's evection. This consists of periodical
aberrations from the moon's regular motion in its orbit, which,
as we now know, are due to the gravitation pull of the sun, but
which remained unexplained until the time of Newton. Ptolemy also
made original observations as to the motions of the planets. He
is, therefore, entitled to a respectable place as an observing
astronomer; but his chief fame rests on his writings.

His great works have to do with geography and astronomy. In the
former field he makes an advance upon Strabo, citing the latitude
of no fewer than five thousand places. In the field of astronomy,
his great service was to have made known to the world the labors
of Hipparchus. Ptolemy has been accused of taking the star-chart
of his great predecessor without due credit, and indeed it seems
difficult to clear him of this charge. Yet it is at least open to
doubt whether be intended any impropriety, inasmuch as be all
along is sedulous in his references to his predecessor. Indeed,
his work might almost be called an exposition of the astronomical
doctrines of Hipparchus. No one pretends that Ptolemy is to be
compared with the Rhodesian observer as an original investigator,
but as a popular expounder his superiority is evidenced in the
fact that the writings of Ptolemy became practically the sole
astronomical text-book of the Middle Ages both in the East and in
the West, while the writings of Hipparchus were allowed to
perish.

The most noted of all the writings of Ptolemy is the work which
became famous under the Arabic name of Almagest. This word is
curiously derived from the Greek title ,
"the greatest construction," a name given the book to distinguish
it from a work on astrology in four books by the same author. For
convenience of reference it came to be spoken of merely as megisth>, from which the Arabs form the title Tabair al Magisthi,
under which title the book was published in the year 827. From
this it derived the word Almagest, by which Ptolemy's work
continued to be known among the Arabs, and subsequently among
Europeans when the book again became known in the West. Ptolemy's
book, as has been said, is virtually an elaboration of the
doctrines of Hipparchus. It assumes that the earth is the fixed
centre of the solar system, and that the stars and planets
revolve about it in twenty-four hours, the earth being, of
course, spherical. It was not to be expected that Ptolemy should
have adopted the heliocentric idea of Aristarchus. Yet it is much
to be regretted that he failed to do so, since the deference
which was accorded his authority throughout the Middle Ages would
doubtless have been extended in some measure at least to this
theory as well, had he championed it. Contrariwise, his
unqualified acceptance of the geocentric doctrine sufficed to
place that doctrine beyond the range of challenge.

The Almagest treats of all manner of astronomical problems, but
the feature of it which gained it widest celebrity was perhaps
that which has to do with eccentrics and epicycles. This theory
was, of course, but an elaboration of the ideas of Hipparchus;
but, owing to the celebrity of the expositor, it has come to be
spoken of as the theory of Ptolemy. We have sufficiently detailed
the theory in speaking of Hipparchus. It should be explained,
however, that, with both Hipparchus and Ptolemy, the theory of
epicycles would appear to have been held rather as a working
hypothesis than as a certainty, so far as the actuality of the
minor spheres or epicycles is concerned. That is to say, these
astronomers probably did not conceive either the epicycles or the
greater spheres as constituting actual solid substances.
Subsequent generations, however, put this interpretation upon the
theory, conceiving the various spheres as actual crystalline
bodies. It is difficult to imagine just how the various epicycles
were supposed to revolve without interfering with the major
spheres, but perhaps this is no greater difficulty than is
presented by the alleged properties of the ether, which
physicists of to-day accept as at least a working hypothesis. We
shall see later on how firmly the conception of concentric
crystalline spheres was held to, and that no real challenge was
ever given that theory until the discovery was made that comets
have an orbit that must necessarily intersect the spheres of the
various planets.

Ptolemy's system of geography in eight books, founded on that of
Marinus of Tyre, was scarcely less celebrated throughout the
Middle Ages than the Almagest. It contained little, however, that
need concern us here, being rather an elaboration of the
doctrines to which we have already sufficiently referred. None of
Ptolemy's original manuscripts has come down to us, but there is
an alleged fifth-century manuscript attributed to Agathadamon of
Alexandria which has peculiar interest because it contains a
series of twenty-seven elaborately colored maps that are supposed
to be derived from maps drawn up by Ptolemy himself. In these
maps the sea is colored green, the mountains red or dark yellow,
and the land white. Ptolemy assumed that a degree at the equator
was 500 stadia instead of 604 stadia in length. We are not
informed as to the grounds on which this assumption was made, but
it has been suggested that the error was at least partially
instrumental in leading to one very curious result. "Taking the
parallel of Rhodes," says Donaldson,[5] "he calculated the
longitudes from the Fortunate Islands to Cattigara or the west
coast of Borneo at 180 degrees, conceiving this to be one-half
the circumference of the globe. The real distance is only 125
degrees or 127 degrees, so that his measurement is wrong by one
third of the whole, one-sixth for the error in the measurement of
a degree and one-sixth for the errors in measuring the distance
geometrically. These errors, owing to the authority attributed to
the geography of Ptolemy in the Middle Ages, produced a
consequence of the greatest importance. They really led to the
discovery of America. For the design of Columbus to sail from the
west of Europe to the east of Asia was founded on the supposition
that the distance was less by one third than it really was." This
view is perhaps a trifle fanciful, since there is nothing to
suggest that the courage of Columbus would have balked at the
greater distance, and since the protests of the sailors, which
nearly thwarted his efforts, were made long before the distance
as estimated by Ptolemy had been covered; nevertheless it is
interesting to recall that the great geographical doctrines, upon
which Columbus must chiefly have based his arguments, had been
before the world in an authoritative form practically unheeded
for more than twelve hundred years, awaiting a champion with
courage enough to put them to the test.

GALEN--THE LAST GREAT ALEXANDRIAN

There is one other field of scientific investigation to which we
must give brief attention before leaving the antique world. This
is the field of physiology and medicine. In considering it we
shall have to do with the very last great scientist of the
Alexandrian school. This was Claudius Galenus, commonly known as
Galen, a man whose fame was destined to eclipse that of all other
physicians of antiquity except Hippocrates, and whose doctrines
were to have the same force in their field throughout the Middle
Ages that the doctrines of Aristotle had for physical science.
But before we take up Galen's specific labors, it will be well to
inquire briefly as to the state of medical art and science in the
Roman world at the time when the last great physician of
antiquity came upon the scene.

The Romans, it would appear, had done little in the way of
scientific discoveries in the field of medicine, but,
nevertheless, with their practicality of mind, they had turned to
better account many more of the scientific discoveries of the
Greeks than did the discoverers themselves. The practising
physicians in early Rome were mostly men of Greek origin, who
came to the capital after the overthrow of the Greeks by the
Romans. Many of them were slaves, as earning money by either
bodily or mental labor was considered beneath the dignity of a
Roman citizen. The wealthy Romans, who owned large estates and
numerous slaves, were in the habit of purchasing some of these
slave doctors, and thus saving medical fees by having them attend
to the health of their families.

By the beginning of the Christian era medicine as a profession
had sadly degenerated, and in place of a class of physicians who
practised medicine along rational or legitimate lines, in the
footsteps of the great Hippocrates, there appeared great numbers
of "specialists," most of them charlatans, who pretended to
possess supernatural insight in the methods of treating certain
forms of disease. These physicians rightly earned the contempt of
the better class of Romans, and were made the object of many
attacks by the satirists of the time. Such specialists travelled
about from place to place in much the same manner as the
itinerant "Indian doctors" and "lightning tooth-extractors" do
to-day. Eye-doctors seem to have been particularly numerous, and
these were divided into two classes, eye-surgeons and eye-doctors
proper. The eye-surgeon performed such operations as cauterizing
for ingrowing eyelashes and operating upon growths about the
eyes; while the eye-doctors depended entirely upon salves and
lotions. These eye-salves were frequently stamped with the seal
of the physician who compounded them, something like two hundred
of these seals being still in existence. There were besides these
quacks, however, reputable eye-doctors who must have possessed
considerable skill in the treatment of certain ophthalmias. Among
some Roman surgical instruments discovered at Rheims were found
also some drugs employed by ophthalmic surgeons, and an analysis
of these show that they contained, among other ingredients, some
that are still employed in the treatment of certain affections of
the eye.

One of the first steps taken in recognition of the services of
physicians was by Julius Caesar, who granted citizenship to all
physicians practising in Rome. This was about fifty years before
the Christian era, and from that time on there was a gradual
improvement in the attitude of the Romans towards the members of
the medical profession. As the Romans degenerated from a race of
sturdy warriors and became more and more depraved physically, the
necessity for physicians made itself more evident. Court
physicians, and physicians-in-ordinary, were created by the
emperors, as were also city and district physicians. In the year
133 A.D. Hadrian granted immunity from taxes and military service
to physicians in recognition of their public services.

The city and district physicians, known as the archiatri
populaires, treated and cared for the poor without remuneration,
having a position and salary fixed by law and paid them
semi-annually. These were honorable positions, and the archiatri
were obliged to give instruction in medicine, without pay, to the
poor students. They were allowed to receive fees and donations
from their patients, but not, however, until the danger from the
malady was past. Special laws were enacted to protect them, and
any person subjecting them to an insult was liable to a fine "not
exceeding one thousand pounds."

An example of Roman practicality is shown in the method of
treating hemorrhage, as described by Aulus Cornelius Celsus (53
B.C. to 7 A.D.). Hippocrates and Hippocratic writers treated
hemorrhage by application of cold, pressure, styptics, and
sometimes by actual cauterizing; but they knew nothing of the
simple method of stopping a hemorrhage by a ligature tied around
the bleeding vessel. Celsus not only recommended tying the end of
the injured vessel, but describes the method of applying two
ligatures before the artery is divided by the surgeon--a common
practice among surgeons at the present time. The cut is made
between these two, and thus hemorrhage is avoided from either end
of the divided vessel.

Another Roman surgeon, Heliodorus, not only describes the use of
the ligature in stopping hemorrhage, but also the practice of
torsion--twisting smaller vessels, which causes their lining
membrane to contract in a manner that produces coagulation and
stops hemorrhage. It is remarkable that so simple and practical a
method as the use of the ligature in stopping hemorrhage could
have gone out of use, once it had been discovered; but during the
Middle Ages it was almost entirely lost sight of, and was not
reintroduced until the time of Ambroise Pare, in the sixteenth
century.

Even at a very early period the Romans recognized the advantage
of surgical methods on the field of battle. Each soldier was
supplied with bandages, and was probably instructed in applying
them, something in the same manner as is done now in all modern
armies. The Romans also made use of military hospitals and had
established a rude but very practical field-ambulance service.
"In every troop or bandon of two or four hundred men, eight or
ten stout fellows were deputed to ride immediately behind the
fighting-line to pick up and rescue the wounded, for which
purpose their saddles had two stirrups on the left side, while
they themselves were provided with water-flasks, and perhaps
applied temporary bandages. They were encouraged by a reward of a
piece of gold for each man they rescued. 'Noscomi' were male
nurses attached to the military hospitals, but not inscribed 'on
strength' of the legions, and were probably for the most part of
the servile class."[6]

From the time of the early Alexandrians, Herophilus and
Erasistratus, whose work we have already examined, there had been
various anatomists of some importance in the Alexandrian school,
though none quite equal to these earlier workers. The best-known
names are those of Celsus (of whom we have already spoken), who
continued the work of anatomical investigation, and Marinus, who
lived during the reign of Nero, and Rufus of Ephesus. Probably
all of these would have been better remembered by succeeding
generations had their efforts not been eclipsed by those of
Galen. This greatest of ancient anatomists was born at Pergamus
of Greek parents. His father, Nicon, was an architect and a man
of considerable ability. Until his fifteenth year the youthful
Galen was instructed at home, chiefly by his father; but after
that time he was placed under suitable teachers for instruction
in the philosophical systems in vogue at that period. Shortly
after this, however, the superstitious Nicon, following the
interpretations of a dream, decided that his son should take up
the study of medicine, and placed him under the instruction of
several learned physicians.

Galen was a tireless worker, making long tours into Asia Minor
and Palestine to improve himself in pharmacology, and studying
anatomy for some time at Alexandria. He appears to have been full
of the superstitions of the age, however, and early in his career
made an extended tour into western Asia in search of the
chimerical "jet-stone"--a stone possessing the peculiar qualities
of "burning with a bituminous odor and supposed to possess great
potency in curing such diseases as epilepsy, hysteria, and gout."

By the time he had reached his twenty-eighth year he had
perfected his education in medicine and returned to his home in
Pergamus. Even at that time he had acquired considerable fame as
a surgeon, and his fellow-citizens showed their confidence in his
ability by choosing him as surgeon to the wounded gladiators
shortly after his return to his native city. In these duties his
knowledge of anatomy aided him greatly, and he is said to have
healed certain kinds of wounds that had previously baffled the
surgeons.

In the time of Galen dissections of the human body were forbidden
by law, and he was obliged to confine himself to dissections of
the lower animals. He had the advantage, however, of the
anatomical works of Herophilus and Erasistratus, and he must have
depended upon them in perfecting his comparison between the
anatomy of men and the lower animals. It is possible that he did
make human dissections surreptitiously, but of this we have no
proof.

He was familiar with the complicated structure of the bones of
the cranium. He described the vertebrae clearly, divided them
into groups, and named them after the manner of anatomists of
to-day. He was less accurate in his description of the muscles,
although a large number of these were described by him. Like all
anatomists before the time of Harvey, he had a very erroneous
conception of the circulation, although he understood that the
heart was an organ for the propulsion of blood, and he showed
that the arteries of the living animals did not contain air
alone, as was taught by many anatomists. He knew, also, that the
heart was made up of layers of fibres that ran in certain fixed
directions--that is, longitudinal, transverse, and oblique; but
he did not recognize the heart as a muscular organ. In proof of
this he pointed out that all muscles require rest, and as the
heart did not rest it could not be composed of muscular tissue.

Many of his physiological experiments were conducted upon
scientific principles. Thus he proved that certain muscles were
under the control of definite sets of nerves by cutting these
nerves in living animals, and observing that the muscles supplied
by them were rendered useless. He pointed out also that nerves
have no power in themselves, but merely conduct impulses to and
from the brain and spinal-cord. He turned this peculiar knowledge
to account in the case of a celebrated sophist, Pausanias, who
had been under the treatment of various physicians for a numbness
in the fourth and fifth fingers of his left hand. These
physicians had been treating this condition by applications of
poultices to the hand itself. Galen, being called in
consultation, pointed out that the injury was probably not in the
hand itself, but in the ulner nerve, which controls sensation in
the fourth and fifth fingers. Surmising that the nerve must have
been injured in some way, he made careful inquiries of the
patient, who recalled that he had been thrown from his chariot
some time before, striking and injuring his back. Acting upon
this information, Galen applied stimulating remedies to the
source of the nerve itself--that is, to the bundle of
nerve-trunks known as the brachial plexus, in the shoulder. To
the surprise and confusion of his fellow-physicians, this method
of treatment proved effective and the patient recovered
completely in a short time.

Although the functions of the organs in the chest were not well
understood by Galen, he was well acquainted with their anatomy.
He knew that the lungs were covered by thin membrane, and that
the heart was surrounded by a sac of very similar tissue. He made
constant comparisons also between these organs in different
animals, as his dissections were performed upon beasts ranging in
size from a mouse to an elephant. The minuteness of his
observations is shown by the fact that he had noted and described
the ring of bone found in the hearts of certain animals, such as
the horse, although not found in the human heart or in most
animals.

His description of the abdominal organs was in general accurate.
He had noted that the abdominal cavity was lined with a peculiar
saclike membrane, the peritoneum, which also surrounded most of
the organs contained in the cavity, and he made special note that
this membrane also enveloped the liver in a peculiar manner. The
exactness of the last observation seems the more wonderful when
we reflect that even to-day the medical, student finds a correct
understanding of the position of the folds of the peritoneum one
of the most difficult subjects in anatomy.

As a practical physician he was held in the highest esteem by the
Romans. The Emperor Marcus Aurelius called him to Rome and
appointed him physician-inordinary to his son Commodus, and on
special occasions Marcus Aurelius himself called in Galen as his
medical adviser. On one occasion, the three army surgeons in
attendance upon the emperor declared that he was about to be
attacked by a fever. Galen relates how "on special command I felt
his pulse, and finding it quite normal, considering his age and
the time of day, I declared it was no fever but a digestive
disorder, due to the food he had eaten, which must be converted
into phlegm before being excreted. Then the emperor repeated
three times, 'That's the very thing,' and asked what was to be
done. I answered that I usually gave a glass of wine with pepper
sprinkled on it, but for you kings we only use the safest
remedies, and it will suffice to apply wool soaked in hot nard
ointment locally. The emperor ordered the wool, wine, etc., to be
brought, and I left the room. His feet were warmed by rubbing
with hot hands, and after drinking the peppered wine, he said to
Pitholaus (his son's tutor), 'We have only one doctor, and that
an honest one,' and went on to describe me as the first of
physicians and the only philosopher, for he had tried many before
who were not only lovers of money, but also contentious,
ambitious, envious, and malignant."[7]

It will be seen from this that Galen had a full appreciation of
his own abilities as a physician, but inasmuch as succeeding
generations for a thousand years concurred in the alleged
statement made by Marcus Aurelius as to his ability, he is
perhaps excusable for his open avowal of his belief in his
powers. His faith in his accuracy in diagnosis and prognosis was
shown when a colleague once said to him, "I have used the
prognostics of Hippocrates as well as you. Why can I not
prognosticate as well as you?" To this Galen replied, "By God's
help I have never been deceived in my prognosis."[8] It is
probable that this statement was made in the heat of argument,
and it is hardly to be supposed that he meant it literally.

His systems of treatment were far in advance of his theories
regarding the functions of organs, causes of disease, etc., and
some of them are still first principles with physicians. Like
Hippocrates, he laid great stress on correct diet, exercise, and
reliance upon nature. "Nature is the overseer by whom health is
supplied to the sick," he says. "Nature lends her aid on all
sides, she decides and cures diseases. No one can be saved unless
nature conquers the disease, and no one dies unless nature
succumbs."

From the picture thus drawn of Galen as an anatomist and
physician, one might infer that he should rank very high as a
scientific exponent of medicine, even in comparison with modern

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