IX GREEK SCIENCE OF THE ALEXANDRIAN OR HELLENISTIC PERIOD A History of Science: in Five Volumes. Volume I: The Beginnings of Science | ||
9. IX
GREEK SCIENCE OF THE ALEXANDRIAN OR
HELLENISTIC PERIOD
WE are entering now upon the most important scientific epoch of antiquity. When Aristotle and Theophrastus passed from the scene, Athens ceased to be in any sense the scientific centre of the world. That city still retained its reminiscent glory, and cannot be ignored in the history of culture, but no great scientific leader was ever again to be born or to take up his permanent abode within the confines of Greece proper. With almost cataclysmic suddenness, a new intellectual centre appeared on the south shore of the Mediterranean. This was the city of Alexandria, a city which Alexander the Great had founded during his brief visit to Egypt, and which became the capital of Ptolemy Soter when he chose Egypt as his portion of the dismembered empire of the great Macedonian. Ptolemy had been with his master in the East, and was with him in Babylonia when he died. He had therefore come personally in contact with Babylonian civilization, and we cannot doubt that this had a most important influence upon his life, and through him upon the new civilization of the West. In point of culture, Alexandria must be regarded as the successor of Babylon, scarcely less directly than of Greece. Following the
Athens in the day of her prime had known nothing quite like this. Such private citizens as Aristotle are known to have had libraries, but there were no great public collections of books in Athens, or in any other part of the Greek domain, until Ptolemy founded his famous library. As is well known, such libraries had existed in Babylonia for thousands of years. The character which the Ptolemaic epoch took on was no doubt due to Babylonian influence, but quite as much to the personal experience of Ptolemy himself as an explorer in the Far East. The marvellous conquering journey of Alexander had enormously widened the horizon of the Greek geographer, and stimulated the imagination of all ranks of the people, It was but natural, then, that geography and its parent science astronomy should occupy the attention of the best minds in this succeeding epoch. In point of fact, such a company of star-gazers and earth-measurers came upon the scene in this third century B.C. as had never before existed anywhere in the world. The whole trend of the time was towards mechanics. It was as if the greatest thinkers had squarely faced about from the attitude of the mystical philosophers of the preceding century, and had set themselves the task of solving all the mechanical riddles of the universe,
The wonderful company of men who performed the feats that are about to be recorded did not all find their home in Alexandria, to be sure; but they all came more or less under the Alexandrian influence. We shall see that there are two other important centres; one out in Sicily, almost at the confines of the Greek territory in the west; the other in Asia Minor, notably on the island of Samos—the island which, it will be recalled, was at an earlier day the birthplace of Pythagoras. But whereas in the previous century colonists from the confines of the civilized world came to Athens, now all eyes turned towards Alexandria, and so improved were the facilities for communication that no doubt the discoveries of one coterie of workers were known to all the others much more quickly than had ever been possible before. We learn, for example, that the studies of Aristarchus of Samos were definitely known to Archimedes of Syracuse, out in Sicily. Indeed, as we shall see, it is through a chance reference preserved in one of the writings of Archimedes that one of the most important speculations of Aristarchus is made known to us. This illustrates sufficiently the intercommunication through which the thought of the
Notwithstanding the number of great workers who were not properly Alexandrians, none the less the epoch is with propriety termed Alexandrian. Not merely in the third century B.C., but throughout the lapse of at least four succeeding centuries, the city of Alexander and the Ptolemies continued to hold its place as the undisputed culture-centre of the world. During that period Rome rose to its pinnacle of glory and began to decline, without ever challenging the intellectual supremacy of the Egyptian city. We shall see, in a later chapter, that the Alexandrian influences were passed on to the Mohammedan conquerors, and every one is aware that when Alexandria was finally overthrown its place was taken by another Greek city, Byzantium or Constantinople. But that transfer did not occur until Alexandria had enjoyed a longer period of supremacy as an intellectual centre than had perhaps ever before been granted to any city, with the possible exception of Babylon.
EUCLID (ABOUT 300 B.C.)
Our present concern is with that first wonderful development of scientific activity which began under the first Ptolemy, and which presents, in the course of
HEROPHILUS AND ERASISTRATUS
The catholicity of Ptolemy's tastes led him, naturally enough, to cultivate the biological no less than the physical sciences. In particular his influence permitted an epochal advance in the field of medicine. Two anatomists became famous through the investigations they were permitted to make under the patronage of the enlightened ruler. These earliest of really scientific investigators of the mechanism of the human body were named Herophilus and Erasistratus. These two anatomists gained their knowledge by the dissection of human bodies (theirs are the first records that we have of such practices), and King Ptolemy himself is said to have been present at some of these dissections. They were the first to discover that the nerve-trunks have their origin in the brain and spinal cord, and they are credited also with the discovery that these nerve-trunks are of two different kinds—one to convey motor, and the other sensory impulses. They discovered, described, and named the coverings of the brain. The name of Herophilus is still applied by anatomists, in honor of the discoverer, to one of the sinuses or large canals that convey the venous blood from the head. Herophilus also noticed and described four cavities or ventricles in the brain, and reached the conclusion that one of these ventricles was the seat of the soul—a belief shared until comparatively recent times by many physiologists. He made also a careful
With the increased knowledge of anatomy came also corresponding advances in surgery, and many experimental operations are said to have been performed upon condemned criminals who were handed over to the surgeons by the Ptolemies. While many modern writers have attempted to discredit these assertions, it is not improbable that such operations were performed. In an age when human life was held so cheap, and among a people accustomed to torturing condemned prisoners for comparatively slight offences, it is not unlikely that the surgeons were allowed to inflict perhaps less painful tortures in the cause of science. Furthermore, we know that condemned criminals were sometimes handed over to the medical profession to be "operated upon and killed in whatever way they thought best'' even as late as the sixteenth century. Tertullian [67] probably exaggerates, however, when he puts the number of such victims in Alexandria at six hundred.
Had Herophilus and Erasistratus been as happy in their deductions as to the functions of the organs as they were in their knowledge of anatomy, the science of medicine would have been placed upon a very high plane even in their time. Unfortunately, however, they not only drew erroneous inferences as to the functions of the organs, but also disagreed radically as to what functions certain organs performed, and how diseases should be treated, even when agreeing perfectly on the subject of anatomy itself. Their contribution to the knowledge of the scientific treatment of diseases
Half a century after the time of Herophilus there appeared a Greek physician, Heraclides, whose reputation in the use of drugs far surpasses that of the anatomists of the Alexandrian school. His reputation has been handed down through the centuries as that of a physician, rather than a surgeon, although in his own time he was considered one of the great surgeons of the period. Heraclides belonged to the "Empiric'' school, which rejected anatomy as useless, depending entirely on the use of drugs. He is thought to have been the first physician to point out the value of opium in certain painful diseases. His prescription of this drug for certain cases of "sleeplessness, spasm, cholera, and colic,'' shows that his use of it was not unlike that of the modern physician in certain cases; and his treatment of fevers, by keeping the patient's head cool and facilitating the secretions of the body, is still recognized as "good practice.'' He advocated a free use of liquids in quenching the fever patient's thirst—a recognized therapeutic measure to-day, but one that was widely condemned a century ago.
ARCHIMEDES OF SYRACUSE AND THE FOUNDATION OF
MECHANICS
We do not know just when Euclid died, but as he was at the height of his fame in the time of Ptolemy I., whose reign ended in the year 285 B.C., it is hardly probable that he was still living when a young man named Archimedes came to Alexandria to study. Archimedes was born in the Greek colony of Syracuse,
Archimedes was primarily a mathematician. Left to his own devices, he would probably have devoted his entire time to the study of geometrical problems. But King Hiero had discovered that his protégé had wonderful mechanical ingenuity, and he made good use of this discovery. Under stress of the king's urgings, the philosopher was led to invent a great variety of mechanical contrivances, some of them most curious ones. Antiquity credited him with the invention of more than forty machines, and it is these, rather than his purely mathematical discoveries, that gave his name popular vogue both among his contemporaries and with posterity. Every one has heard of the screw of Archimedes, through which the paradoxical effect was produced of making water seem to flow up hill. The best idea of this curious mechanism is obtained if one will take in hand an ordinary corkscrew, and imagine this instrument to be changed into a hollow tube, retaining precisely the same shape but increased to some feet in length and to a proportionate diameter. If one will hold the corkscrew in a slanting direction and turn it slowly to the right, supposing that the point dips up a portion of water each time it revolves,
Some other of the mechanisms of Archimedes have been made known to successive generations of readers through the pages of Polybius and Plutarch. These are the devices through which Archimedes aided King Hiero to ward off the attacks of the Roman general Marcellus, who in the course of the second Punic war laid siege to Syracuse.
Plutarch, in his life of Marcellus, describes the Roman's attack and Archimedes' defence in much detail. Incidentally he tells us also how Archimedes came to make the devices that rendered the siege so famous:
ARCHIMEDES
(From an old Print.)
[Description:
Early modern print or Archimedes using a protractor over
a picture of a building, lying on a desk in front of him.
]
"But Archimedes having told King Hiero, his kinsman and friend, that it was possible to remove as great a weight as he would, with as little strength as he listed to put to it: and boasting himself thus (as they report of him) and trusting to the force of his reasons, wherewith he proved this conclusion, that if there were another globe of earth, he was able to remove this of ours, and pass it over to the other: King Hiero wondering to hear him, required him to put his device in execution, and to make him see by experience, some great or heavy weight removed, by little force. So Archimedes caught hold with a book of one of the greatest carects, or hulks of the king (that to draw it to the shore out of the water required a marvellous number of people to go about it, and was hardly to be done so) and put a great number of men more into her, than her ordinary burden: and he himself sitting alone at his ease far off, without any straining at all, drawing the end of an engine with many wheels and pulleys, fair and softly with his hand, made it come as gently and smoothly to him, as it had floated in the sea. The king wondering to see the sight, and knowing by proof the greatness of his art; be prayed him to make him some engines, both to assault and defend, in all manner of sieges and assaults. So Archimedes made him many engines, but King Hiero never occupied any of them, because he reigned the most part of his time in peace without any wars. But this provision and munition of engines, served the Syracusan's turn
Polybius describes what was perhaps the most important of these contrivances, which was, he tells us,
"Marcellus was in no small degree embarrassed,'' Polybius continues, "when he found himself encountered in every attempt by such resistance. He perceived that all his efforts were defeated with loss; and were even derided by the enemy. But, amidst all the anxiety that he suffered, he could not help jesting upon the inventions of Archimedes. This man, said he, employs our ships as buckets to draw water: and boxing about our sackbuts, as if they were unworthy to be associated with him, drives them from his company with disgrace. Such was the success of the siege on the side of the sea.''
Subsequently, however, Marcellus took the city by strategy, and Archimedes was killed, contrary, it is said, to the express orders of Marcellus. "Syracuse being taken,'' says Plutarch,
We are further indebted to Plutarch for a summary of the character and influence of Archimedes, and for an interesting suggestion as to the estimate which the great philosopher put upon the relative importance of his own discoveries. "Notwithstanding Archimedes had such a great mind, and was so profoundly learned, having hidden in him the only treasure and secrets of geometrical inventions: as be would never set forth
It should be observed that neither Polybius nor Plutarch mentions the use of burning-glasses in connection with the siege of Syracuse, nor indeed are these referred to by any other ancient writer of authority. Nevertheless, a story gained credence down to a late day to the effect that Archimedes had set fire to the fleet of the enemy with the aid of concave mirrors. An experiment was made by Sir Isaac Newton to show the possibility of a phenomenon so well in accord with the genius of Archimedes, but the silence of all
It will be observed that the chief principle involved in all these mechanisms was a capacity to transmit great power through levers and pulleys, and this brings us to the most important field of the Syracusan philosopher's activity. It was as a student of the lever and the pulley that Archimedes was led to some of his greatest mechanical discoveries. He is even credited with being the discoverer of the compound pulley. More likely he was its developer only, since the principle of the pulley was known to the old Babylonians, as their sculptures testify. But there is no reason to doubt the general outlines of the story that Archimedes astounded King Hiero by proving that, with the aid of multiple pulleys, the strength of one man could suffice to drag the largest ship from its moorings.
The property of the lever, from its fundamental principle, was studied by him, beginning with the self-evident fact that "equal bodies at the ends of the equal arms of a rod, supported on its middle point, will balance each other''; or, what amounts to the same thing stated in another way, a regular cylinder of uniform matter will balance at its middle point. From this starting-point he elaborated the subject on such clear and satisfactory principles that they stand to-day practically unchanged and with few additions. From all his studies and experiments he finally formulated the principle that "bodies will be in equilibrio when their distance from the fulcrum or point of support is inversely as their weight.'' He is credited with having summed up his estimate of the capabilities of the
But perhaps the feat of all others that most appealed to the imagination of his contemporaries, and possibly also the one that had the greatest bearing upon the position of Archimedes as a scientific discoverer, was the one made familiar through the tale of the crown of Hiero. This crown, so the story goes, was supposed to be made of solid gold, but King Hiero for some reason suspected the honesty of the jeweller, and desired to know if Archimedes could devise a way of testing the question without injuring the crown. Greek imagination seldom spoiled a story in the telling, and in this case the tale was allowed to take on the most picturesque of phases. The philosopher, we are assured, pondered the problem for a long time without succeeding, but one day as he stepped into a bath, his attention was attracted by the overflow of water. A new train of ideas was started in his ever-receptive brain. Wild with enthusiasm he sprang from the bath, and, forgetting his robe, dashed along the streets of Syracuse, shouting: "Eureka! Eureka!'' (I have found it!) The thought that had come into his mind was this: That any heavy substance must have a bulk proportionate to its weight; that gold and silver differ in weight, bulk for bulk, and that the way to test the bulk of such an irregular object as a crown was to immerse it in water. The experiment was made. A lump of pure gold of the weight of the crown was immersed in a certain receptacle filled with water, and the overflow noted. Then a lump of pure silver of the
Whatever the truth of this picturesque narrative, the fact remains that some, such experiments as these must have paved the way for perhaps the greatest of all the studies of Archimedes—those that relate to the buoyancy of water. Leaving the field of fable, we must now examine these with some precision. Fortunately, the writings of Archimedes himself are still extant, in which the results of his remarkable experiments are related, so we may present the results in the words of the discoverer.
Here they are: "First: The surface of every coherent liquid in a state of rest is spherical, and the centre of the sphere coincides with the centre of the earth. Second: A solid body which, bulk for bulk, is of the same weight as a liquid, if immersed in the liquid will sink so that the surface of the body is even with the surface of the liquid, but will not sink deeper. Third: Any solid body which is lighter, bulk for bulk, than a liquid, if placed in the liquid will sink so deep as to displace the mass of liquid equal in weight to another body. Fourth: If a body which is lighter than a liquid is forcibly immersed in the liquid, it will be pressed upward with a force corresponding to the weight of a like volume of water, less the weight of the body itself. Fifth: Solid bodies which, bulk for bulk, are heavier than a liquid, when immersed in the liquid
Curiously enough, the discovery which Archimedes himself is said to have considered the most important of all his innovations is one that seems much less striking. It is the answer to the question, What is the relation in bulk between a sphere and its circumscribing cylinder? Archimedes finds that the ratio is simply two to three. We are not informed as to how he reached his conclusion, but an obvious method would be to immerse a ball in a cylindrical cup. The experiment is one which any one can make for himself, with approximate accuracy, with the aid of a tumbler and a solid rubber ball or a billiard-ball of just the right size. Another geometrical problem which Archimedes solved was the problem as to the size of a triangle which has equal area with a circle; the answer being, a triangle having for its base the circumference of the circle and for its altitude the radius. Archimedes solved also the problem of the relation of the diameter of the circle to its circumference; his answer being a close approximation to the familiar 3.1416, which every tyro in geometry will recall as the equivalent of π.
Numerous other of the studies of Archimedes having reference to conic sections, properties of curves and spirals, and the like, are too technical to be detailed
We need not follow Archimedes to the limits of his incomprehensible numbers of sand-grains. The calculation is chiefly remarkable because it was made before the introduction of the so-called Arabic numerals had simplified mathematical calculations. It will be recalled that the Greeks used letters for numerals, and, having no cipher, they soon found themselves in difficulties when large numbers were involved. The Roman system of numerals simplified the matter somewhat, but the beautiful simplicity of the decimal system did not come into vogue until the Middle Ages, as we shall see. Notwithstanding the difficulties, however, Archimedes followed out his calculations to the piling up of bewildering numbers, which the modern mathematician finds to be the
But it remains to notice the most interesting feature of this document in which the calculation of the sand-grains is contained. "It was known to me,'' says Archimedes, "that most astronomers understand by the expression `world' (universe) a ball of which the centre is the middle point of the earth, and of which the radius is a straight line between the centre of the earth and the sun.'' Archimedes himself appears to accept this opinion of the majority,—it at least serves as well as the contrary hypothesis for the purpose of his calculation,—but he goes on to say: "Aristarchus of Samos, in his writing against the astronomers, seeks to establish the fact that the world is really very different from this. He holds the opinion that the fixed stars and the sun are immovable and that the earth revolves in a circular line about the sun, the sun being at the centre of this circle.'' This remarkable bit of testimony establishes beyond question the position of Aristarchus of Samos as the Copernicus of antiquity. We must make further inquiry as to the teachings of the man who had gained such a remarkable insight into the true system of the heavens.
ARISTARCHUS OF SAMOS, THE COPERNICUS OF ANTIQUITY
It appears that Aristarchus was a contemporary of Archimedes, but the exact dates of his life are not known. He was actively engaged in making astronomical observations in Samos somewhat before the middle of the third century B.C.; in other words, just at the time when the activities of the Alexandrian
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
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
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,
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
DIAGRAM TO ILLUSTRATE ARISTARCHUS' MEASUREMENT OF THE
RELATIVE DISTANCES
FROM THE EARTH OF THE MOON AND THE SUN.
(For explanation of the diagram, see p. 218.)
[Description:
Figure of a right triangle, with a circle at each of the points;
the circle on the right angle in the upper left-hand corner is
labelled "M"; the circle on the angle on the right side is
labelled "S," and the circle on the lower left angle is labelled
"E."
]
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
It must be understood that in following out the, steps of reasoning by which we suppose Aristarchus
- "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.221
- "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
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
ERATOSTHENES, "THE SURVEYOR OF THE WORLD''
An altogether remarkable man was this native of Cyrene, who came to Alexandria from Athens to be
Nearly all the discoveries of Eratosthenes are associated with observations of the shadows cast by the
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° 42' 39'' of arc. One-half of this, or 23° 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
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
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
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
DIAGRAM TO ILLUSTRATE ERATOSTHENES' MEASUREMENT OF THE GLOBE
[Description: 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
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 Nicæa, 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
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
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
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
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
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
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,
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
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
Unfortunately, the pupil of Ctesibius, whatever his
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
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
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
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. See p. 248.)
[Description:
(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. See p. 248.)
]
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,
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
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. See p. 250.)
[Description:
(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. See p. 250.)
]
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
In recent times there has been a tendency to give to this steam-engine of Hero something more than
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. See p. 251.)
[Description:
(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. See p. 251.)
]
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,
Notes
IX GREEK SCIENCE OF THE ALEXANDRIAN OR HELLENISTIC PERIOD A History of Science: in Five Volumes. Volume I: The Beginnings of Science | ||