Chapter II: Book I (2)

It has been necessary to bear in mind these phases of practical civilization because much that we know of the purely scientific attainments of the Egyptians is based upon modern observation of their pyramids and temples. It was early observed, for example, that the pyramids are obviously oriented as regards the direction in which they face, in strict accordance with some astronomical principle. Early in the nineteenth century the Frenchman Biot made interesting studies in regard to this subject, and a hundred years later, in our own time, Sir Joseph Norman Lockyer, following up the work of various intermediary observers, has given the subject much attention, making it the central theme of his work on The Dawn of Astronomy.(1) Lockyer's researches make it clear that in the main the temples of Egypt were oriented with reference to the point at which the sun rises on the day of the summer solstice. The time of the solstice had peculiar interest for the Egyptians, because it corresponded rather closely with the time of the rising of the Nile. The floods of that river appear with very great regularity; the on-rushing tide reaches the region of Heliopolis and Memphis almost precisely on the day of the summer solstice. The time varies at different stages of the river's course, but as the civilization of the early dynasties centred at Memphis, observations made at this place had widest vogue.

Considering the all-essential character of the Nile floods-without which civilization would be impossible in Egypt--it is not strange that the time of their appearance should be taken as marking the beginning of a new year. The fact that their coming coincides with the solstice makes such a division of the calendar perfectly natural. In point of fact, from the earliest periods of which records have come down to us, the new year of the Egyptians dates from the summer solstice. It is certain that from the earliest historical periods the Egyptians were aware of the approximate length of the year. It would be strange were it otherwise, considering the ease with which a record of days could be kept from Nile flood to Nile flood, or from solstice to solstice. But this, of course, applies only to an approximate count. There is some reason to believe that in the earliest period the Egyptians made this count only 360 days. The fact that their year was divided into twelve months of thirty days each lends color to this belief; but, in any event, the mistake was discovered in due time and a partial remedy was applied through the interpolation of a "little month" of five days between the end of the twelfth month and the new year. This nearly but not quite remedied the matter. What it obviously failed to do was to take account of that additional quarter of a day which really rounds out the actual year.

It would have been a vastly convenient thing for humanity had it chanced that the earth had so accommodated its rotary motion with its speed of transit about the sun as to make its annual flight in precisely 360 days. Twelve lunar months of thirty days each would then have coincided exactly with the solar year, and most of the complexities of the calendar, which have so puzzled historical students, would have been avoided; but, on the other hand, perhaps this very simplicity would have proved detrimental to astronomical science by preventing men from searching the heavens as carefully as they have done. Be that as it may, the complexity exists. The actual year of three hundred and sixty-five and (about) one-quarter days cannot be divided evenly into months, and some such expedient as the intercalation of days here and there is essential, else the calendar will become absolutely out of harmony with the seasons.

In the case of the Egyptians, the attempt at adjustment was made, as just noted, by the introduction of the five days, constituting what the Egyptians themselves termed "the five days over and above the year." These so-called epagomenal days were undoubtedly introduced at a very early period. Maspero holds that they were in use before the first Thinite dynasty, citing in evidence the fact that the legend of Osiris explains these days as having been created by the god Thot in order to permit Nuit to give birth to all her children; this expedient being necessary to overcome a ban which had been pronounced against Nuit, according to which she could not give birth to children on any day of the year. But, of course, the five additional days do not suffice fully to rectify the calendar. There remains the additional quarter of a day to be accounted for. This, of course, amounts to a full day every fourth year. We shall see that later Alexandrian science hit upon the expedient of adding a day to every fourth year; an expedient which the Julian calendar adopted and which still gives us our familiar leap-year. But, unfortunately, the ancient Egyptian failed to recognize the need of this additional day, or if he did recognize it he failed to act on his knowledge, and so it happened that, starting somewhere back in the remote past with a new year's day that coincided with the inundation of the Nile, there was a constantly shifting maladjustment of calendar and seasons as time went on.

The Egyptian seasons, it should be explained, were three in number: the season of the inundation, the season of the seed-time, and the season of the harvest; each season being, of course, four months in extent. Originally, as just mentioned, the season of the inundations began and coincided with the actual time of inundation. The more precise fixing of new year's day was accomplished through observation of the time of the so-called heliacal rising of the dog-star, Sirius, which bore the Egyptian name Sothis. It chances that, as viewed from about the region of Heliopolis, the sun at the time of the summer solstice occupies an apparent position in the heavens close to the dog-star. Now, as is well known, the Egyptians, seeing divinity back of almost every phenomenon of nature, very naturally paid particular reverence to so obviously influential a personage as the sun-god. In particular they thought it fitting to do homage to him just as he was starting out on his tour of Egypt in the morning; and that they might know the precise moment of his coming, the Egyptian astronomer priests, perched on the hill-tops near their temples, were wont to scan the eastern horizon with reference to some star which had been observed to precede the solar luminary. Of course the precession of the equinoxes, due to that axial wobble in which our clumsy earth indulges, would change the apparent position of the fixed stars in reference to the sun, so that the same star could not do service as heliacal messenger indefinitely; but, on the other hand, these changes are so slow that observations by many generations of astronomers would be required to detect the shifting. It is believed by Lockyer, though the evidence is not quite demonstrative, that the astronomical observations of the Egyptians date back to a period when Sothis, the dog-star, was not in close association with the sun on the morning of the summer solstice. Yet, according to the calculations of Biot, the heliacal rising of Sothis at the solstice was noted as early as the year 3285 B.C., and it is certain that this star continued throughout subsequent centuries to keep this position of peculiar prestige. Hence it was that Sothis came to be associated with Isis, one of the most important divinities of Egypt, and that the day in which Sothis was first visible in the morning sky marked the beginning of the new year; that day coinciding, as already noted, with the summer solstice and with the beginning of the Nile flow.

But now for the difficulties introduced by that unreckoned quarter of a day. Obviously with a calendar of 365 days only, at the end of four years, the calendar year, or vague year, as the Egyptians came to call it, had gained by one full day upon the actual solar year--that is to say, the heliacal rising of Sothis, the dog-star, would not occur on new year's day of the faulty calendar, but a day later. And with each succeeding period of four years the day of heliacal rising, which marked the true beginning of the year--and which still, of course, coincided with the inundation--would have fallen another day behind the calendar. In the course of 120 years an entire month would be lost; and in 480 years so great would become the shifting that the seasons would be altogether misplaced; the actual time of inundations corresponding with what the calendar registered as the seed-time, and the actual seed-time in turn corresponding with the harvest-time of the calendar.

At first thought this seems very awkward and confusing, but in all probability the effects were by no means so much so in actual practice. We need go no farther than to our own experience to know that the names of seasons, as of months and days, come to have in the minds of most of us a purely conventional significance. Few of us stop to give a thought to the meaning of the words January, February, etc., except as they connote certain climatic conditions. If, then, our own calendar were so defective that in the course of 120 years the month of February had shifted back to occupy the position of the original January, the change would have been so gradual, covering the period of two life-times or of four or five average generations, that it might well escape general observation.

Each succeeding generation of Egyptians, then, may not improbably have associated the names of the seasons with the contemporary climatic conditions, troubling themselves little with the thought that in an earlier age the climatic conditions for each period of the calendar were quite different. We cannot well suppose, however, that the astronomer priests were oblivious to the true state of things. Upon them devolved the duty of predicting the time of the Nile flood; a duty they were enabled to perform without difficulty through observation of the rising of the solstitial sun and its Sothic messenger. To these observers it must finally have been apparent that the shifting of the seasons was at the rate of one day in four years; this known, it required no great mathematical skill to compute that this shifting would finally effect a complete circuit of the calendar, so that after (4 X 365 =) 1460 years the first day of the calendar year would again coincide with the heliacal rising of Sothis and with the coming of the Nile flood. In other words, 1461 vague years or Egyptian calendar years Of 365 days each correspond to 1460 actual solar years of 365 1/4 days each. This period, measured thus by the heliacal rising of Sothis, is spoken of as the Sothic cycle.

To us who are trained from childhood to understand that the year consists of (approximately) 365 1/4 days, and to know that the calendar may be regulated approximately by the introduction of an extra day every fourth year, this recognition of the Sothic cycle seems simple enough. Yet if the average man of us will reflect how little he knows, of his own knowledge, of the exact length of the year, it will soon become evident that the appreciation of the faults of the calendar and the knowledge of its periodical adjustment constituted a relatively high development of scientific knowledge on the part of the Egyptian astronomer. It may be added that various efforts to reform the calendar were made by the ancient Egyptians, but that they cannot be credited with a satisfactory solution of the problem; for, of course, the Alexandrian scientists of the Ptolemaic period (whose work we shall have occasion to review presently) were not Egyptians in any proper sense of the word, but Greeks.

Since so much of the time of the astronomer priests was devoted to observation of the heavenly bodies, it is not surprising that they should have mapped out the apparent course of the moon and the visible planets in their nightly tour of the heavens, and that they should have divided the stars of the firmament into more or less arbitrary groups or constellations. That they did so is evidenced by various sculptured representations of constellations corresponding to signs of the zodiac which still ornament the ceilings of various ancient temples. Unfortunately the decorative sense, which was always predominant with the Egyptian sculptor, led him to take various liberties with the distribution of figures in these representations of the constellations, so that the inferences drawn from them as to the exact map of the heavens as the Egyptians conceived it cannot be fully relied upon. It appears, however, that the Egyptian astronomer divided the zodiac into twenty-four decani, or constellations. The arbitrary groupings of figures, with the aid of which these are delineated, bear a close resemblance to the equally arbitrary outlines which we are still accustomed to use for the same purpose.

IDEAS OF COSMOLOGY

In viewing this astronomical system of the Egyptians one cannot avoid the question as to just what interpretation was placed upon it as regards the actual mechanical structure of the universe. A proximal answer to the question is supplied us with a good deal of clearness. It appears that the Egyptian conceived the sky as a sort of tangible or material roof placed above the world, and supported at each of its four corners by a column or pillar, which was later on conceived as a great mountain. The earth itself was conceived to be a rectangular box, longer from north to south than from east to west; the upper surface of this box, upon which man lived, being slightly concave and having, of course, the valley of the Nile as its centre. The pillars of support were situated at the points of the compass; the northern one being located beyond the Mediterranean Sea; the southern one away beyond the habitable regions towards the source of the Nile, and the eastern and western ones in equally inaccessible regions. Circling about the southern side of the world was a great river suspended in mid-air on something comparable to mountain cliffs; on which river the sun-god made his daily course in a boat, fighting day by day his ever-recurring battle against Set, the demon of darkness. The wide channel of this river enabled the sun-god to alter his course from time to time, as he is observed to do; in winter directing his bark towards the farther bank of the channel; in summer gliding close to the nearer bank. As to the stars, they were similar lights, suspended from the vault of the heaven; but just how their observed motion of translation across the heavens was explained is not apparent. It is more than probable that no one explanation was, universally accepted.

In explaining the origin of this mechanism of the heavens, the Egyptian imagination ran riot. Each separate part of Egypt had its own hierarchy of gods, and more or less its own explanations of cosmogony. There does not appear to have been any one central story of creation that found universal acceptance, any more than there was one specific deity everywhere recognized as supreme among the gods. Perhaps the most interesting of the cosmogonic myths was that which conceived that Nuit, the goddess of night, had been torn from the arms of her husband, Sibu the earth-god, and elevated to the sky despite her protests and her husband's struggles, there to remain supported by her four limbs, which became metamorphosed into the pillars, or mountains, already mentioned. The forcible elevation of Nuit had been effected on the day of creation by a new god, Shu, who came forth from the primeval waters. A painting on the mummy case of one Betuhamon, now in the Turin Museum, illustrates, in the graphic manner so characteristic of the Egyptians, this act of creation. As Maspero(2) points out, the struggle of Sibu resulted in contorted attitudes to which the irregularities of the earth's surface are to be ascribed.

In contemplating such a scheme of celestial mechanics as that just outlined, one cannot avoid raising the question as to just the degree of literalness which the Egyptians themselves put upon it. We know how essentially eye-minded the Egyptian was, to use a modern psychological phrase--that is to say, how essential to him it seemed that all his conceptions should be visualized. The evidences of this are everywhere: all his gods were made tangible; he believed in the immortality of the soul, yet he could not conceive of such immortality except in association with an immortal body; he must mummify the body of the dead, else, as he firmly believed, the dissolution of the spirit would take place along with the dissolution of the body itself. His world was peopled everywhere with spirits, but they were spirits associated always with corporeal bodies; his gods found lodgment in sun and moon and stars; in earth and water; in the bodies of reptiles and birds and mammals. He worshipped all of these things: the sun, the moon, water, earth, the spirit of the Nile, the ibis, the cat, the ram, and apis the bull; but, so far as we can judge, his imagination did not reach to the idea of an absolutely incorporeal deity. Similarly his conception of the mechanism of the heavens must be a tangibly mechanical one. He must think of the starry firmament as a substantial entity which could not defy the law of gravitation, and which, therefore, must have the same manner of support as is required by the roof of a house or temple. We know that this idea of the materiality of the firmament found elaborate expression in those later cosmological guesses which were to dominate the thought of Europe until the time of Newton. We need not doubt, therefore, that for the Egyptian this solid vault of the heavens had a very real existence. If now and then some dreamer conceived the great bodies of the firmament as floating in a less material plenum--and such iconoclastic dreamers there are in all ages--no record of his musings has come down to us, and we must freely admit that if such thoughts existed they were alien to the character of the Egyptian mind as a whole.

While the Egyptians conceived the heavenly bodies as the abiding-place of various of their deities, it does not appear that they practised astrology in the later acceptance of that word. This is the more remarkable since the conception of lucky and unlucky days was carried by the Egyptians to the extremes of absurdity. "One day was lucky or unlucky," says Erman,(3) "according as a good or bad mythological incident took place on that day. For instance, the 1st of Mechir, on which day the sky was raised, and the 27th of Athyr, when Horus and, Set concluded peace together and divided the world between them, were lucky days; on the other hand, the 14th of Tybi, on which Isis and Nephthys mourned for Osiris, was an unlucky day. With the unlucky days, which, fortunately, were less in number than the lucky days, they distinguished different degrees of ill-luck. Some were very unlucky, others only threatened ill-luck, and many, like the 17th and the 27th Choiakh, were partly good and partly bad according to the time of day. Lucky days might, as a rule, be disregarded. At most it might be as well to visit some specially renowned temple, or to 'celebrate a joyful day at home,' but no particular precautions were really necessary; and, above all, it was said, 'what thou also seest on the day is lucky.' It was quite otherwise with the unlucky and dangerous days, which imposed so many and such great limitations on people that those who wished to be prudent were always obliged to bear them in mind when determining on any course of action. Certain conditions were easy to carry out. Music and singing were to be avoided on the 14th Tybi, the day of the mourning of Osiris, and no one was allowed to wash on the 16th Tybi; whilst the name of Set might not be pronounced on the 24th of Pharmuthi. Fish was forbidden on certain days; and what was still more difficult in a country so rich in mice, on the 12th of Tybi no mouse might be seen. The most tiresome prohibitions, however, were those which occurred not infrequently, namely, those concerning work and going out: for instance, four times in Paophi the people had to 'do nothing at all,' and five times to sit the whole day or half the day in the house; and the same rule had to be observed each month. It was impossible to rejoice if a child was born on the 23d of Thoth; the parents knew it could not live. Those born on the 20th of Choiakh would become blind, and those born on the 3d of Choiakh, deaf."

CHARMS AND INCANTATIONS

Where such conceptions as these pertained, it goes without saying that charms and incantations intended to break the spell of the unlucky omens were equally prevalent. Such incantations consisted usually of the recitation of certain phrases based originally, it would appear, upon incidents in the history of the gods. The words which the god had spoken in connection with some lucky incident would, it was thought, prove effective now in bringing good luck to the human supplicant--that is to say, the magician hoped through repeating the words of the god to exercise the magic power of the god. It was even possible, with the aid of the magical observances, partly to balk fate itself. Thus the person predestined through birth on an unlucky day to die of a serpent bite might postpone the time of this fateful visitation to extreme old age. The like uncertainty attached to those spells which one person was supposed to be able to exercise over another. It was held, for example, that if something belonging to an individual, such as a lock of hair or a paring of the nails, could be secured and incorporated in a waxen figure, this figure would be intimately associated with the personality of that individual. An enemy might thus secure occult power over one; any indignity practised upon the waxen figure would result in like injury to its human prototype. If the figure were bruised or beaten, some accident would overtake its double; if the image were placed over a fire, the human being would fall into a fever, and so on. But, of course, such mysterious evils as these would be met and combated by equally mysterious processes; and so it was that the entire art of medicine was closely linked with magical practices. It was not, indeed, held, according to Maspero, that the magical spells of enemies were the sole sources of human ailments, but one could never be sure to what extent such spells entered into the affliction; and so closely were the human activities associated in the mind of the Egyptian with one form or another of occult influences that purely physical conditions were at a discount. In the later times, at any rate, the physician was usually a priest, and there was a close association between the material and spiritual phases of therapeutics. Erman(4) tells us that the following formula had to be recited at the preparation of all medicaments: "That Isis might make free, make free. That Isis might make Horus free from all evil that his brother Set had done to him when he slew his father, Osiris. O Isis, great enchantress, free me, release me from all evil red things, from the fever of the god, and the fever of the goddess, from death and death from pain, and the pain which comes over me; as thou hast freed, as thou hast released thy son Horus, whilst I enter into the fire and come forth from the water," etc. Again, when the invalid took the medicine, an incantation had to be said which began thus: "Come remedy, come drive it out of my heart, out of these limbs strong in magic power with the remedy." He adds: "There may have been a few rationalists amongst the Egyptian doctors, for the number of magic formulae varies much in the different books. The book that we have specially taken for a foundation for this account of Egyptian medicine--the great papyrus of the eighteenth dynasty edited by Ebers(5)--contains, for instance, far fewer exorcisms than some later writings with similar contents, probably because the doctor who compiled this book of recipes from older sources had very little liking for magic."

It must be understood, however--indeed, what has just been said implies as much--that the physician by no means relied upon incantations alone; on the contrary, he equipped himself with an astonishing variety of medicaments. He had a particular fondness for what the modern physician speaks of as a "shot-gun" prescription--one containing a great variety of ingredients. Not only did herbs of many kinds enter into this, but such substances as lizard's blood, the teeth of swine, putrid meat, the moisture from pigs' ears, boiled horn, and numerous other even more repellent ingredients. Whoever is familiar with the formulae employed by European physicians even so recently as the eighteenth century will note a striking similarity here. Erman points out that the modern Egyptian even of this day holds closely to many of the practices of his remote ancestor. In particular, the efficacy of the beetle as a medicinal agent has stood the test of ages of practice. "Against all kinds of witchcraft," says an ancient formula, "a great scarabaeus beetle; cut off his head and wings, boil him; put him in oil and lay him out; then cook his head and wings, put them in snake fat, boil, and let the patient drink the mixture." The modern Egyptian, says Erman, uses almost precisely the same recipe, except that the snake fat is replaced by modern oil.

In evidence of the importance which was attached to practical medicine in the Egypt of an early day, the names of several physicians have come down to us from an age which has preserved very few names indeed, save those of kings. In reference to this Erman says(6): "We still know the names of some of the early body physicians of this time; Sechmetna'eonch, 'chief physician of the Pharaoh,' and Nesmenan his chief, the 'superintendent of the physicians of the Pharaoh.' The priests also of the lioness-headed goddess Sechmet seem to have been famed for their medical wisdom, whilst the son of this goddess, the demi-god Imhotep, was in later times considered to be the creator of medical knowledge. These ancient doctors of the New Empire do not seem to have improved upon the older conceptions about the construction of the human body."

As to the actual scientific attainments of the Egyptian physician, it is difficult to speak with precision. Despite the cumbersome formulae and the grotesque incantations, we need not doubt that a certain practical value attended his therapeutics. He practised almost pure empiricism, however, and certainly it must have been almost impossible to determine which ones, if any, of the numerous ingredients of the prescription had real efficacy.

The practical anatomical knowledge of the physician, there is every reason to believe, was extremely limited. At first thought it might seem that the practice of embalming would have led to the custom of dissecting human bodies, and that the Egyptians, as a result of this, would have excelled in the knowledge of anatomy. But the actual results were rather the reverse of this. Embalming the dead, it must be recalled, was a purely religious observance. It took place under the superintendence of the priests, but so great was the reverence for the human body that the priests themselves were not permitted to make the abdominal incision which was a necessary preliminary of the process. This incision, as we are informed by both Herodotus(7) and Diodorus(8), was made by a special officer, whose status, if we may believe the explicit statement of Diodorus, was quite comparable to that of the modern hangman. The paraschistas, as he was called, having performed his necessary but obnoxious function, with the aid of a sharp Ethiopian stone, retired hastily, leaving the remaining processes to the priests. These, however, confined their observations to the abdominal viscera; under no consideration did they make other incisions in the body. It follows, therefore, that their opportunity for anatomical observations was most limited.

Since even the necessary mutilation inflicted on the corpse was regarded with such horror, it follows that anything in the way of dissection for a less sacred purpose was absolutely prohibited. Probably the same prohibition extended to a large number of animals, since most of these were held sacred in one part of Egypt or another. Moreover, there is nothing in what we know of the Egyptian mind to suggest the probability that any Egyptian physician would make extensive anatomical observations for the love of pure knowledge. All Egyptian science is eminently practical. If we think of the Egyptian as mysterious, it is because of the superstitious observances that we everywhere associate with his daily acts; but these, as we have already tried to make clear, were really based on scientific observations of a kind, and the attempt at true inferences from these observations. But whether or not the Egyptian physician desired anatomical knowledge, the results of his inquiries were certainly most meagre. The essentials of his system had to do with a series of vessels, alleged to be twenty-two or twenty-four in number, which penetrated the head and were distributed in pairs to the various members of the body, and which were vaguely thought of as carriers of water, air, excretory fluids, etc. Yet back of this vagueness, as must not be overlooked, there was an all-essential recognition of the heart as the central vascular organ. The heart is called the beginning of all the members. Its vessels, we are told, "lead to all the members; whether the doctor lays his finger on the forehead, on the back of the head, on the hands, on the place of the stomach (?), on the arms, or on the feet, everywhere he meets with the heart, because its vessels lead to all the members."(9) This recognition of the pulse must be credited to the Egyptian physician as a piece of practical knowledge, in some measure off-setting the vagueness of his anatomical theories.

ABSTRACT SCIENCE

But, indeed, practical knowledge was, as has been said over and over, the essential characteristic of Egyptian science. Yet another illustration of this is furnished us if we turn to the more abstract departments of thought and inquire what were the Egyptian attempts in such a field as mathematics. The answer does not tend greatly to increase our admiration for the Egyptian mind. We are led to see, indeed, that the Egyptian merchant was able to perform all the computations necessary to his craft, but we are forced to conclude that the knowledge of numbers scarcely extended beyond this, and that even here the methods of reckoning were tedious and cumbersome. Our knowledge of the subject rests largely upon the so-called papyrus Rhind,(10) which is a sort of mythological hand-book of the ancient Egyptians. Analyzing this document, Professor Erman concludes that the knowledge of the Egyptians was adequate to all practical requirements. Their mathematics taught them "how in the exchange of bread for beer the respective value was to be determined when converted into a quantity of corn; how to reckon the size of a field; how to determine how a given quantity of corn would go into a granary of a certain size," and like every-day problems. Yet they were obliged to make some of their simple computations in a very roundabout way. It would appear, for example, that their mental arithmetic did not enable them to multiply by a number larger than two, and that they did not reach a clear conception of complex fractional numbers. They did, indeed, recognize that each part of an object divided into 10 pieces became 1/10 of that object; they even grasped the idea of 2/3 this being a conception easily visualized; but they apparently did not visualize such a conception as 3/10 except in the crude form of 1/10 plus 1/10 plus 1/10. Their entire idea of division seems defective. They viewed the subject from the more elementary stand-point of multiplication. Thus, in order to find out how many times 7 is contained in 77, an existing example shows that the numbers representing 1 times 7, 2 times 7, 4 times 7, 8 times 7 were set down successively and various experimental additions made to find out which sets of these numbers aggregated 77.

--1 7
--2 14
--4 28
--8 56

A line before the first, second, and fourth of these numbers indicated that it is necessary to multiply 7 by 1 plus 2 plus 8--that is, by 11, in order to obtain 77; that is to say, 7 goes 11 times in 77. All this seems very cumbersome indeed, yet we must not overlook the fact that the process which goes on in our own minds in performing such a problem as this is precisely similar, except that we have learned to slur over certain of the intermediate steps with the aid of a memorized multiplication table. In the last analysis, division is only the obverse side of multiplication, and any one who has not learned his multiplication table is reduced to some such expedient as that of the Egyptian. Indeed, whenever we pass beyond the range of our memorized multiplication table-which for most of us ends with the twelves--the experimental character of the trial multiplication through which division is finally effected does not so greatly differ from the experimental efforts which the Egyptian was obliged to apply to smaller numbers.

Despite his defective comprehension of fractions, the Egyptian was able to work out problems of relative complexity; for example, he could determine the answer of such a problem as this: a number together with its fifth part makes 21; what is the number? The process by which the Egyptian solved this problem seems very cumbersome to any one for whom a rudimentary knowledge of algebra makes it simple, yet the method which we employ differs only in that we are enabled, thanks to our hypothetical x, to make a short cut, and the essential fact must not be overlooked that the Egyptian reached a correct solution of the problem. With all due desire to give credit, however, the fact remains that the Egyptian was but a crude mathematician. Here, as elsewhere, it is impossible to admire him for any high development of theoretical science. First, last, and all the time, he was practical, and there is nothing to show that the thought of science for its own sake, for the mere love of knowing, ever entered his head.

In general, then, we must admit that the Egyptian had not progressed far in the hard way of abstract thinking. He worshipped everything about him because he feared the result of failing to do so. He embalmed the dead lest the spirit of the neglected one might come to torment him. Eye-minded as he was, he came to have an artistic sense, to love decorative effects. But he let these always take precedence over his sense of truth; as, for example, when he modified his lists of kings at Abydos to fit the space which the architect had left to be filled; he had no historical sense to show to him that truth should take precedence over mere decoration. And everywhere he lived in the same happy-go-lucky way. He loved personal ease, the pleasures of the table, the luxuries of life, games, recreations, festivals. He took no heed for the morrow, except as the morrow might minister to his personal needs. Essentially a sensual being, he scarcely conceived the meaning of the intellectual life in the modern sense of the term. He had perforce learned some things about astronomy, because these were necessary to his worship of the gods; about practical medicine, because this ministered to his material needs; about practical arithmetic, because this aided him in every-day affairs. The bare rudiments of an historical science may be said to be crudely outlined in his defective lists of kings. But beyond this he did not go. Science as science, and for its own sake, was unknown to him. He had gods for all material functions, and festivals in honor of every god; but there was no goddess of mere wisdom in his pantheon. The conception of Minerva was reserved for the creative genius of another people.

III. SCIENCE OF BABYLONIA AND ASSYRIA

Throughout classical antiquity Egyptian science was famous. We know that Plato spent some years in Egypt in the hope of penetrating the alleged mysteries of its fabled learning; and the story of the Egyptian priest who patronizingly assured Solon that the Greeks were but babes was quoted everywhere without disapproval. Even so late as the time of Augustus, we find Diodorus, the Sicilian, looking back with veneration upon the Oriental learning, to which Pliny also refers with unbounded respect. From what we have seen of Egyptian science, all this furnishes us with a somewhat striking commentary upon the attainments of the Greeks and Romans themselves. To refer at length to this would be to anticipate our purpose; what now concerns us is to recall that all along there was another nation, or group of nations, that disputed the palm for scientific attainments. This group of nations found a home in the valley of the Tigris and Euphrates. Their land was named Mesopotamia by the Greeks, because a large part of it lay between the two rivers just mentioned. The peoples themselves are familiar to every one as the Babylonians and the Assyrians. These peoples were of Semitic stock--allied, therefore, to the ancient Hebrews and Phoenicians and of the same racial stem with the Arameans and Arabs.

The great capital of the Babylonians during the later period of their history was the famed city of Babylon itself; the most famous capital of the Assyrians was Nineveh, that city to which, as every Bible-student will recall, the prophet Jonah was journeying when he had a much-exploited experience, the record of which forms no part of scientific annals. It was the kings of Assyria, issuing from their palaces in Nineveh, who dominated the civilization of Western Asia during the heyday of Hebrew history, and whose deeds are so frequently mentioned in the Hebrew chronicles. Later on, in the year 606 B.C., Nineveh was overthrown by the Medes(1) and Babylonians. The famous city was completely destroyed, never to be rebuilt. Babylon, however, though conquered subsequently by Cyrus and held in subjection by Darius,(2) the Persian kings, continued to hold sway as a great world-capital for some centuries. The last great historical event that occurred within its walls was the death of Alexander the Great, which took place there in the year 322 B.C.

In the time of Herodotus the fame of Babylon was at its height, and the father of history has left us a most entertaining account of what he saw when he visited the wonderful capital. Unfortunately, Herodotus was not a scholar in the proper acceptance of the term. He probably had no inkling of the Babylonian language, so the voluminous records of its literature were entirely shut off from his observation. He therefore enlightens us but little regarding the science of the Babylonians, though his observations on their practical civilization give us incidental references of no small importance. Somewhat more detailed references to the scientific attainments of the Babylonians are found in the fragments that have come down to us of the writings of the great Babylonian historian, Berosus,(3) who was born in Babylon about 330 B.C., and who was, therefore, a contemporary of Alexander the Great. But the writings of Berosus also, or at least such parts of them as have come down to us, leave very much to be desired in point of explicitness. They give some glimpses of Babylonian history, and they detail at some length the strange mythical tales of creation that entered into the Babylonian conception of cosmogony--details which find their counterpart in the allied recitals of the Hebrews. But taken all in all, the glimpses of the actual state of Chaldean(4) learning, as it was commonly called, amounted to scarcely more than vague wonder-tales. No one really knew just what interpretation to put upon these tales until the explorers of the nineteenth century had excavated the ruins of the Babylonian and Assyrian cities, bringing to light the relics of their wonderful civilization. But these relics fortunately included vast numbers of written documents, inscribed on tablets, prisms, and cylinders of terra-cotta. When nineteenth-century scholarship had penetrated the mysteries of the strange script, and ferreted out the secrets of an unknown tongue, the world at last was in possession of authentic records by which the traditions regarding the Babylonians and Assyrians could be tested. Thanks to these materials, a new science commonly spoken of as Assyriology came into being, and a most important chapter of human history was brought to light. It became apparent that the Greek ideas concerning Mesopotamia, though vague in the extreme, were founded on fact. No one any longer questions that the Mesopotamian civilization was fully on a par with that of Egypt; indeed, it is rather held that superiority lay with the Asiatics. Certainly, in point of purely scientific attainments, the Babylonians passed somewhat beyond their Egyptian competitors. All the evidence seems to suggest also that the Babylonian civilization was even more ancient than that of Egypt. The precise dates are here in dispute; nor for our present purpose need they greatly concern us. But the Assyrio-Babylonian records have much greater historical accuracy as regards matters of chronology than have the Egyptian, and it is believed that our knowledge of the early Babylonian history is carried back, with some certainty, to King Sargon of Agade,(5) for whom the date 3800 B.C. is generally accepted; while somewhat vaguer records give us glimpses of periods as remote as the sixth, perhaps even the seventh or eighth millenniums before our era.

At a very early period Babylon itself was not a capital and Nineveh had not come into existence. The important cities, such as Nippur and Shirpurla, were situated farther to the south. It is on the site of these cities that the recent excavations have been made, such as those of the University of Pennsylvania expeditions at Nippur,(6) which are giving us glimpses into remoter recesses of the historical period.

Even if we disregard the more problematical early dates, we are still concerned with the records of a civilization extending unbroken throughout a period of about four thousand years; the actual period is in all probability twice or thrice that. Naturally enough, the current of history is not an unbroken stream throughout this long epoch. It appears that at least two utterly different ethnic elements are involved. A preponderance of evidence seems to show that the earliest civilized inhabitants of Mesopotamia were not Semitic, but an alien race, which is now commonly spoken of as Sumerian. This people, of whom we catch glimpses chiefly through the records of its successors, appears to have been subjugated or overthrown by Semitic invaders, who, coming perhaps from Arabia (their origin is in dispute), took possession of the region of the Tigris and Euphrates, learned from the Sumerians many of the useful arts, and, partly perhaps because of their mixed lineage, were enabled to develop the most wonderful civilization of antiquity. Could we analyze the details of this civilization from its earliest to its latest period we should of course find the same changes which always attend racial progress and decay. We should then be able, no doubt, to speak of certain golden epochs and their periods of decline. To a certain meagre extent we are able to do this now. We know, for example, that King Khammurabi, who lived about 2200 B.C., was a great law-giver, the ancient prototype of Justinian; and the epochs of such Assyrian kings as Sargon II., Asshurnazirpal, Sennacherib, and Asshurbanapal stand out with much distinctness. Yet, as a whole, the record does not enable us to trace with clearness the progress of scientific thought. At best we can gain fewer glimpses in this direction than in almost any other, for it is the record of war and conquest rather than of the peaceful arts that commanded the attention of the ancient scribe. So in dealing with the scientific achievements of these peoples, we shall perforce consider their varied civilizations as a unity, and attempt, as best we may, to summarize their achievements as a whole. For the most part, we shall not attempt to discriminate as to what share in the final product was due to Sumerian, what to Babylonian, and what to Assyrian. We shall speak of Babylonian science as including all these elements; and drawing our information chiefly from the relatively late Assyrian and Babylonian sources, which, therefore, represent the culminating achievements of all these ages of effort, we shall attempt to discover what was the actual status of Mesopotamian science at its climax. In so far as we succeed, we shall be able to judge what scientific heritage Europe received from the Orient; for in the records of Babylonian science we have to do with the Eastern mind at its best. Let us turn to the specific inquiry as to the achievements of the Chaldean scientist whose fame so dazzled the eyes of his contemporaries of the classic world.

BABYLONIAN ASTRONOMY

Our first concern naturally is astronomy, this being here, as in Egypt, the first-born and the most important of the sciences. The fame of the Chaldean astronomer was indeed what chiefly commanded the admiration of the Greeks, and it was through the results of astronomical observations that Babylonia transmitted her most important influences to the Western world. "Our division of time is of Babylonian origin," says Hornmel;(7) "to Babylonia we owe the week of seven days, with the names of the planets for the days of the week, and the division into hours and months." Hence the almost personal interest which we of to-day must needs feel in the efforts of the Babylonian star-gazer.

It must not be supposed, however, that the Chaldean astronomer had made any very extraordinary advances upon the knowledge of the Egyptian "watchers of the night." After all, it required patient observation rather than any peculiar genius in the observer to note in the course of time such broad astronomical conditions as the regularity of the moon's phases, and the relation of the lunar periods to the longer periodical oscillations of the sun. Nor could the curious wanderings of the planets escape the attention of even a moderately keen observer. The chief distinction between the Chaldean and Egyptian astronomers appears to have consisted in the relative importance they attached to various of the phenomena which they both observed. The Egyptian, as we have seen, centred his attention upon the sun. That luminary was the abode of one of his most important gods. His worship was essentially solar. The Babylonian, on the other hand, appears to have been peculiarly impressed with the importance of the moon. He could not, of course, overlook the attention-compelling fact of the solar year; but his unit of time was the lunar period of thirty days, and his year consisted of twelve lunar periods, or 360 days. He was perfectly aware, however, that this period did not coincide with the actual year; but the relative unimportance which he ascribed to the solar year is evidenced by the fact that he interpolated an added month to adjust the calendar only once in six years. Indeed, it would appear that the Babylonians and Assyrians did not adopt precisely the same method of adjusting the calendar, since the Babylonians had two intercular months called Elul and Adar, whereas the Assyrians had only a single such month, called the second Adar.(8) (The Ve'Adar of the Hebrews.) This diversity further emphasizes the fact that it was the lunar period which received chief attention, the adjustment of this period with the solar seasons being a necessary expedient of secondary importance. It is held that these lunar periods have often been made to do service for years in the Babylonian computations and in the allied computations of the early Hebrews. The lives of the Hebrew patriarchs, for example, as recorded in the Bible, are perhaps reckoned in lunar "years." Divided by twelve, the "years" of Methuselah accord fairly with the usual experience of mankind.

Yet, on the other hand, the convenience of the solar year in computing long periods of time was not unrecognized, since this period is utilized in reckoning the reigns of the Assyrian kings. It may be added that the reign of a king "was not reckoned from the day of his accession, but from the Assyrian new year's day, either before or after the day of accession. There does not appear to have been any fixed rule as to which new year's day should be chosen; but from the number of known cases, it appears to have been the general practice to count the reigning years from the new year's day nearest the accession, and to call the period between the accession day and the first new year's day 'the beginning of the reign,' when the year from the new year's day was called the first year, and the following ones were brought successively from it. Notwithstanding, in the dates of several Assyrian and Babylonian sovereigns there are cases of the year of accession being considered as the first year, thus giving two reckonings for the reigns of various monarchs, among others, Shalmaneser, Sennacherib, Nebuchadrezzar."(9) This uncertainty as to the years of reckoning again emphasizes the fact that the solar year did not have for the Assyrian chronology quite the same significance that it has for us.

The Assyrian month commenced on the evening when the new moon was first observed, or, in case the moon was not visible, the new month started thirty days after the last month. Since the actual lunar period is about twenty-nine and one-half days, a practical adjustment was required between the months themselves, and this was probably effected by counting alternate months as Only 29 days in length. Mr. R. Campbell Thompson(10) is led by his studies of the astrological tablets to emphasize this fact. He believes that "the object of the astrological reports which related to the appearance of the moon and sun was to help determine and foretell the length of the lunar month." Mr. Thompson believes also that there is evidence to show that the interculary month was added at a period less than six years. In point of fact, it does not appear to be quite clearly established as to precisely how the adjustment of days with the lunar months, and lunar months with the solar year, was effected. It is clear, however, according to Smith, "that the first 28 days of every month were divided into four weeks of seven days each; the seventh, fourteenth, twenty-first, twenty-eighth days respectively being Sabbaths, and that there was a general prohibition of work on these days." Here, of course, is the foundation of the Hebrew system of Sabbatical days which we have inherited. The sacredness of the number seven itself--the belief in which has not been quite shaken off even to this day--was deduced by the Assyrian astronomer from his observation of the seven planetary bodies--namely, Sin (the moon), Samas (the sun), Umunpawddu (Jupiter), Dilbat (Venus), Kaimanu (Saturn), Gudud (Mercury), Mustabarru-mutanu (Mars).(11) Twelve lunar periods, making up approximately the solar year, gave peculiar importance to the number twelve also. Thus the zodiac was divided into twelve signs which astronomers of all subsequent times have continued to recognize; and the duodecimal system of counting took precedence with the Babylonian mathematicians over the more primitive and, as it seems to us, more satisfactory decimal system.