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 he intended any impropriety, inasmuch as he 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 (gr h megisth suntazis), "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 (gr h 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.