We have seen that Primary Education in Hellas consisted of letters and music, with a contemporary training in gymnastics; to which triple course was added, late in the fourth century, drawing and painting. How the day was divided between mental and physical training is unknown—probably, like everything else, this varied with the taste of the individual—but the following sketch from Lucian,[207] although it belongs to a much later date, may perhaps give some idea of a schoolboy’s day:—

“He gets up at dawn, washes the sleep from his eyes, and puts on his cloak. Then he goes out from his father’s house, with his eyes fixed upon the ground, not looking at any one who meets him. Behind him follow attendants and paidagogoi, bearing in their hands the implements of virtue, writing-tablets or books containing the great deeds of old, or, if he is going to a music-school, his well-tuned lyre.

“When he has laboured diligently at intellectual studies, and his mind is sated with the benefits of the school curriculum, he exercises his body in liberal pursuits, riding or hurling the javelin or spear. Then the wrestling-school with its sleek, oiled pupils, labours under the mid-day sun, and sweats in the regular athletic contests. Then a bath, not too prolonged; then a meal, not too large, in view of afternoon school. For the schoolmasters are waiting for him again, and the books which openly or by allegory teach him who was a great hero, who was a lover of justice and purity. With the contemplation of such virtues he waters the garden of his young soul. When evening sets a limit to his work, he pays the necessary tribute to his stomach and retires to rest, to sleep sweetly after his busy day.”

The school hours were naturally arranged to suit the times of Hellenic meals, for which the boys returned home. The ordinary arrangement was a light breakfast at daybreak, a solid meal at mid-day, and supper at sunset. So the schools opened at sunrise.[208] Solon enacted that they should not open earlier. They closed in time to allow the boys to return home to lunch,[209] opened again in the afternoon, and closed before sunset.[210] How many of the intermediate hours were spent in work,[211] and what intervals there were, is unknown. There was, of course, no weekly rest on Sundays; but festivals, which were whole holidays, were numerous throughout Hellas, and, in Alexandria at any rate, on the 7th and 20th of every month the schools were closed, these days being sacred to Apollo.[212] There were also special school festivals, such as that of the Muses, and holidays in commemoration of benefactors; thus Anaxagoras left a bequest to Klazomenai, on condition that the day of his death should be celebrated annually by a holiday in the schools.[213] It must also be remembered that one of the three branches of Primary Education in Hellas would be called play in England: an afternoon spent in running races, jumping, wrestling, or riding would not be regarded as work by an English schoolboy. Music, too, is usually learned during play-hours in an English school. Even Letters, when the elementary stage was past, meant reciting, reading, or learning by heart the literature of the boy’s own language, and most of it not stiff literature by any means, but such fascinating fairy-tales as are found in Homer. There is little trace of Hellenic boys creeping unwillingly to school: their lessons were made eminently attractive.

Of the fees which were paid to schoolmasters little is known. An amusing passage in Lucian,[214] dealing with the under-world, describes those who had been kings or satraps upon earth as reduced in the future state “to beggary, and compelled by poverty either to sell kippers or to teach the elements of reading and writing.” From this it may be inferred that elementary schoolmasters did not make much money by their fees. This inference is supported by the fact that even the poorest Athenians managed to send their sons to such schools. Plato in the Laws reserves the profession for foreigners, thus suggesting that it was neither well paid nor highly esteemed. To call a man a schoolmaster was almost an insult; Demosthenes, abusing Aischines, says, “You taught letters, I went to school.”[215] The weakness of the masters’ position may be seen too from the extreme contempt with which their pupils seem to have treated them. The boys bring their pets—cats and dogs and leopards—into school, and play with them under the master’s chair. Theophrastos,[216] in describing the characteristics of the mean man, says that “he does not send his children to school all the month of Anthesterion” (that is, from the middle of February to the middle of March) “on account of the number of feasts.” The school-bills were paid by the month, and, since boys did not go to school on the great festivals, and Anthesterion contained many such days, the mean parent thought he would not get his money’s worth for this particular month, and so withdrew his boys while it lasted.

Mean parents also deducted from the fees in proportion, if their sons were absent from school owing to ill-health for a day or two;[217] but this was not usually done. The bills were paid on the 30th of each month.[218] Schoolmasters apparently had some difficulty in getting their bills paid at all; according to Demosthenes’ statement, his bills were never paid, owing to the fraudulent behaviour of his guardian Aphobos.[219]

No doubt the fees varied according to the merits of the school, for the schools at Athens seem to have differed greatly. Demosthenes, when boasting of his career, in his speech On the Crown, says that he went as a boy to the respectable schools;[220] the quality and quantity of the teaching must have been varied to suit the parent’s pocket. For the poor there would probably be schools where only the elements of reading and writing were taught. In the higher class of school these elements would be taught by under-masters, frequently slaves; but free citizens might also be reduced by poverty to take such a post. This may be seen from the case of the father of Aischines, the orator.[221] Impoverished and exiled like many democrats by the Thirty Tyrants, he returned with the Restoration a ruined man. To earn his living, he became an usher at the school of one Elpias, close to the Theseion, and taught letters: his son Aischines seems to have begun his life by assisting his father in this occupation. His opponent, Demosthenes, takes advantage of the contempt with which these ushers were regarded to declare that the father was a slave of Elpias,[222] “wearing big fetters and a collar,” and the son was employed in “grinding the ink and sponging the forms and sweeping out the schoolroom (παιδαγωγεῖον), the work of a servant, not of a free boy.”

No doubt letters and music were often taught at the same school, in different rooms. Such an arrangement would be natural and convenient. The vases suggest it, but their evidence is uncertain. The school buildings seem often to have been surrounded by playgrounds. A passage in Aelian[223] shows us the boys, just let out of school, playing at tug-of-war. No doubt in these places they played with their hoops and tops, and amused themselves with pick-a-back and the stone- and dice-games which corresponded to our marbles. In villages these playgrounds probably did duty as palaistrai.

The headmaster of the school sat on a chair with a high back; under-masters and boys had stools without backs, but cushions were provided. For lessons in class there were benches.[224] There was a high reading-desk for recitations. Round the walls hung writing-tablets, rulers, and baskets or cases containing manuscript rolls labelled with the author’s name, composing the school library; the rolls might also hang by themselves.[225] Masters were expected to possess at any rate a copy of Homer—Alkibiades thrashed one who did not. Sometimes they emended their edition themselves.[226] In the music-schools hung lyres and flutes and flute-cases. The (παιδαγωγειον) mentioned by Demosthenes may have been an anteroom where the paidagogoi sat, but more probably the word is only a rhetorical variant for “schoolroom.” There were often busts of the Muses round the walls,[227] which were also decorated with vases, serving for domestic purposes, and, perhaps, illustrating with their pictures the books which the boys were reading. At a later date, at any rate, a series of cartoons, illustrating scenes in the Iliad and Odyssey, were sometimes hung upon the walls: the “Tabula Iliaca,” now in the Capitoline Museum, has been recognised as a fragment of such a series.

The first stage was to learn to read and write. Instead of a slate, boys in Hellas had tablets of wax, usually made in two halves, so as to fold on a hinge in the middle, the waxen surfaces coming inwards and so being protected. Sometimes there were three pieces, forming a triptych, or even more. For pencil, they had an instrument with a sharp point at one end, suitable for making marks on the wax, and a flat surface at the other, which was used to erase what had been written, and so make the tablets ready for future use. These tablets are shown in the school-scenes on the fifth-century vases.[228] At a later period, when parchment and papyrus became more common, these materials were used in the schools. Lines could be ruled with a lump of lead, and writing done either with ink and a reed pen or with lead; for erasures a sponge was employed.

The early stages of learning to write are described in the Protagoras of Plato.[229] “When a boy is not yet clever at writing, the masters first draw lines, and then give him the tablet and make him write as the lines direct.” The passage has been variously interpreted. Some regard the master as merely writing a series of letters which the boy is to copy underneath. The word used in Greek for the master’s writing is ὑπογράψαντες, and it is significant that the word for a “copy” in this sense is a derivative of this word, ὑπογραμμός. Such a copy, corresponding to the phrases like “England exports engines” or “Germany grows grapes,” which are employed in English schools for this purpose, is extant.[230] It is a nonsense sentence designed to contain all the letters of the alphabet μάρπτε σφὶγξ κλὼψ ζβυχθηδόν. If this rendering is correct, the master wrote a sentence of this sort on the tablets, and the boy copied it underneath. Others interpret the lines which the master draws on the tablet as parallel straight lines, within which the boy had to write. Just such a device is often employed in English copy-books. The word used for “lines,” γραμμαί, usually means “straight lines,” which supports this interpretation. But ὑπογραφή, on the other hand, a derivative of ὑπογράφειν, is used for irregular traces, e.g. a footstep,[231] and ὑπογράφειν itself is a technical term in Hellenic art for “sketching in” what is afterwards to be finished in detail. Consequently a third rendering of the passage makes the master draw a faint, rough outline of the various letters, and the boy has to go over them with his pen, marking the grooves in the wax deeper and filling in the details. For example, in England, the master might draw |·| and the boy go over the two vertical lines and draw in the other two, M. Thus all three interpretations are sensible and rest on good authority. But surely the master may be regarded as adopting all three processes, according to the intelligence of the pupils. For the beginner he would outline the whole letter, and leave him only the task of going over it again. Then he would gradually give less and less help, till the boy was capable of writing the letters with the assistance of the parallel lines alone. Finally these would be withdrawn, and the boy would be left to write his imitation of the copy without assistance. The phrase in Plato is purposely vague, and will include the whole of this process.

The letters were written in lines horizontal and vertical, so that they fell beneath one another. No stops or accents were inserted, and no spaces were left between words. The writing-master probably ruled both the horizontal and the vertical lines on the tablet for his pupil. On the Vase of Douris,[232] an under-master is represented as writing with his pen on a wax tablet, while a boy stands in front of him. He is probably meant either to be writing a copy or else correcting his pupil’s exercise. Over his head hangs a ruler, for marking out the guiding lines on the tablet. Behind the boy sits a bearded man with a staff, who is probably the paidagogos. The boys in the class are clearly coming up one by one to receive their copies or have their exercises corrected, while the rest are doing their writing. It will be noticed that there is no desk or table: the Hellenes wrote with their tablets on their knees.

As soon as the boy had acquired a certain facility in writing, he entered the dictation class. The master read out something, and the boys wrote it down.[233] At first, of course, very simple words would be dictated, and there would not be much to write. But, later on, the boys would write at his dictation passages of the poets and other authors. For this purpose, ink and parchment may sometimes have been employed: Aischines seems to have “ground ink”[234] for a writing-school. Various “elaborations in the way of speed and beauty” of writing seem to have been customary in the case of more advanced pupils.[235] Possibly they learnt to make flourishes and ornamental letters. Speed would naturally be taught, for it was usual to take notes at the lectures of Sophists and Philosophers, and speed is required for this purpose. This must have involved the use of the cursive letters, which otherwise were not needed, for the Hellene had not very much writing to do, unless he became a clerk to a public body.

Learning to read must have been a difficult business in Hellas, for books were written in capitals at this time. There were no spaces between the words, and no stops were inserted. Thus, the reader had to exercise much ingenuity before he could arrive at the meaning of a sentence. Still more difficult for the boys to grasp was the Attic accent, upon which the masters set a great importance. So difficult was it, that few foreigners ever acquired it, and a born Athenian, if he went abroad for a few years, often lost the power of speaking with the Attic intonation. The first step in learning to read is to acquire the alphabet. The Hellenes, wishing, as usual, to make learning as easy as possible, seem to have put the alphabet into verse. A metrical alphabet, ascribed to Kallias, a contemporary of Perikles, is still extant, but in a mutilated form, which has been restored in several not very convincing ways. Probably it has been adapted to suit different alphabets, for there were several current in different parts of Hellas. The following is a conjectural restoration:—

This complete alphabet of twenty-four letters, which appears in modern Greek Grammars, was not adopted for official purposes at Athens till 403 B.C., “but it is clear that it was in ordinary use at Athens considerably earlier.”[237]

This metrical alphabet formed the prologue to what may be called a spelling-drama, in which the whole process of learning to spell was expressed either in iambic lines or in choral songs. Since its author, Kallias, is coupled with Strattis, the comic poet,[238] it may be inferred that the play was a comedy, not a tragedy; the chorus would then be twenty-four in number. Each member of the chorus represented one of the twenty-four letters. In the first choric song the letters were put together in pairs, in the fashion of a spelling class. The first strophé runs as follows:—

In the corresponding antistrophé Gamma was similarly coupled with the seven vowels, and so on apparently through the alphabet. During the song, which was set to excellent music, the members of the chorus, dressed to represent the letters quite clearly, and no doubt posturing in the right attitude, would form themselves into the required pairs. Thus, during the first line Beta and Alpha would come together, during the second Beta and Ei, and so on. After this song came a lecture on the vowels, in iambic verse, the chorus being told to repeat them one by one after the speaker. There seems to have been a plot of some sort in this extraordinary drama, but the main interest was, no doubt, the spelling. Opportunities were also taken for describing the shapes of the letters, the audience having to guess what letter was intended. This kind of alphabetical puzzle seems to have caught the popular fancy at Athens, for Euripides, Agathon, and Theodektes all employed it. In each case the concealed word was “Theseus.”

In the same spirit, Sophocles, in his satyric drama Amphiaraos, introduced an actor who represented the shapes of the letters by his dancing.[240] Periclean Athens seems to have taken a very keen interest in matters of spelling: the audience must all have known their letters, or such devices could never have become so popular.

Kallias’ play is the ancestor of such books as Reading without Tears. His dramatic presentation of the process of spelling must have caught the imagination and impressed the memory of many Athenian boys. It may even be suspected that his method was adopted in enterprising schools, and spelling lessons were conducted to a tune, perhaps even accompanied by dancing.[241] The tunes of Kallias were highly praised, and were, no doubt, very different from the monotonous drone which announces to the outside world the presence of a Board School.

To return to more prosaic methods. Plato gives an interesting sketch[242] of a reading class. “When boys have just learnt their letters, they recognise any of them readily enough in the shortest and easiest syllables, and are able to give a correct answer about them. But in the longer and more difficult syllables they are not certain, but form a wrong opinion and answer wrongly. Then the best way is to take them back to the syllables in which they recognise the same letters and then compare them with those in which they made mistakes, and, putting them side by side, show that in both combinations the same letters have the same meaning.”

Take an English example. The master writes SCRAPE on the blackboard and asks the boys to tell him what letters it contains. The class fail to recognise the letters: the word is too long and difficult. The master then writes beside it consecutively APE, RAPE, CAPE, in all of which the boys recognise the letters correctly. Then CRAPE and SCRAP. From these he passes on to SCRAPE, which they now recognise by analogy from the words which they know already. “Finally, they learn always to give the same name to the same letter whenever it comes.”[243]

The methods by which boys learn to spell are the same in all ages. “When boys come together to learn their letters, they are asked what letters there are in some word or other.”[244] A certain amount of mental arithmetic seems to have been included in this stage of spelling: the pupils were asked how many letters there were in a word, as well as the order in which they were arranged.[245] But this will be discussed later.

While the boys were still unable to read, and often afterwards owing to the comparative scarcity of books, the master dictated to them the poetry which he intended them to learn by heart, and they repeated it after him.

The Kulix of Douris gives an interesting picture of either a reading or a repetition lesson.[246] On a high-backed chair sits an elderly master, holding a roll in his hand. On it is inscribed what is clearly meant to be an hexameter line from some epic poet, but Douris was not very well educated, and so the line is misspelt and will not scan. In front of the master stands a boy, behind whom sits an elderly man who is probably, as in the writing scene, a paidagogos. The master may be dictating the poem while the boy learns it by heart after him, or he may be hearing him say it. But very possibly the scene represents a reading-lesson. The attitudes of boy and master are not very convenient, if both are reading out of the same book; but this was unavoidable, for, owing to the canons of vase-painting, the figures could only be full-faced or in profile, and the front of the manuscript had to be turned in such a way as to be legible.

On the walls of the school hang a manuscript rolled up and tied with a string, and an ornamental basket. These baskets were used as bookcases, to hold the manuscript rolls. They may sometimes be seen on vases suspended over the heads of reading figures, as in the British Museum vase,[247] which represents a woman reading a scroll. The paidagogos, we may notice, is revealing his humble origin by crossing his feet, a serious offence against good manners in Hellas.

“When the boys knew their letters and were beginning to understand what was written, the masters put beside them on the benches the works of good poets for them to read, and made them learn them by heart. They chose for this purpose poets that contained many moral precepts, and narratives and praises of the heroes of old, in order that the boy might admire them and imitate them and desire to become such a man himself.”[248] It is noteworthy that Hellenic boys began at once with the very best literature to be found in their language: there was no preliminary course of childish tales. Grammar, when invented, was taught at a later stage: the boys plunged straight into literature.

The schoolmasters at Athens differed as to which was the best way of introducing boys to their national literature. The great majority held that a properly educated boy ought to be saturated in all poetry, comic and serious, hearing much of it in the reading class, and learning much of it—in fact, whole poets—by heart.[249] A minority would pick out the leading passages,[250] the “purple patches,” and certain whole speeches,[251] and put them together and have them committed to memory. Plato argued in favour of expurgated editions of passages carefully selected according to a very strict standard, since much in literature was good and much bad.[252]

Homer, of course, played the largest part in these literary studies; from early times “he was given an honourable place in the teaching of the young.”[253] Vast quantities of the Iliad and Odyssey were learnt by heart. Nikeratos, in Xenophon,[254] says: “My father, wishing me to grow up into a good man, made me learn all the lines of Homer; and now I can repeat the whole of the Iliad and Odyssey from memory.” Such prodigious feats were, no doubt, assisted by the rhapsodes, who could be heard at Athens declaiming Homer “nearly every day.”[255] The Hellenes did not let their greatest poet lie neglected, to be “revived” at long intervals. Homer was supposed to teach everything, especially soldiering and good morals. “I suppose you know,” continues Nikeratos,[256] “that Homer, the wisest of men, has written about all human matters. So whoever of you wishes to excel as a householder or public speaker or general, or desires to become like Achilles or Aias or Nestor or Odusseus, let him come to me.” Then he proceeds to show how, for example, the poet gives full directions about the proper way to drive a chariot in a race. Aristophanes[257] makes the shade of Aeschylus say, “Whence did divine Homer win his honour and renown, save from this, that he taught drill, courage, the arming of troops? Many a man of valour he trained, and our own dead hero, Lamachos. I took my print from him, and represented many deeds of valour done by a Patroklos or lion-hearted Teukros, to rouse my countrymen to model themselves upon such men, when they heard the trumpet sound.”

The great poet does not seem to have been taught pedantically; the attention of the boys was not concentrated simply on the difficulties of the Homeric vocabulary. In fact, probably they were little troubled with such points; the sense, the rhythm, and the beauty of the original do not depend upon an exact understanding of every word, as many a modern reader has discovered. In a fragment of Aristophanes,[258] a father asks his son the meaning of some hard words in Homer, such as ἀμένηνα κάρηνα and κόρυμβα; the son is quite unable to translate them, at any rate when separated from their context, and can only retort by asking his father to interpret some archaic phrases in Solon’s laws. A later comic poet[259] introduced a cook who insisted on using Homeric language, just as a modern chef writes his menu in French; the man who has hired him is ludicrously unable to understand his phrases, and has to go in search of a commentary.

Explanations and interpretations of supposed moral allegories in Homer, and lessons drawn from a close study of his characters, were very popular in Hellas, and no doubt figured in the schools.

If Homer occupied the first place in literary education, other leading authors were not neglected. All the great poets were made useful. “Orpheus taught ceremonial rites and abstinence from bloodshed, and Mousaios medicine and oracles, and Hesiod the tillage of land, the seasons of fruits and ploughing.”[260] Hesiod probably served more as a theological handbook than as a manual of agriculture; the moral precepts to Perses in the Works and Days probably also found favour with schoolmasters. The fourth-century comic poet Alexis gives an interesting catalogue of a school library.[261] Besides Orpheus, Hesiod, and Homer, who have been mentioned already, there are Epicharmos, Choirilos, the author of an epic poem on the Persian war, and what is called vaguely “tragedy,” probably meaning a selection from the great tragedians. We can see from Plato’s attacks that Aeschylus and Euripides must have been important in the schools, and we know that Athenian gentlemen were expected to be able to recite them at dinner-parties, and must therefore have learnt them by heart. The vague words “tragedy” and “comedy” are similarly used of the recitations of the boys at Teos. Various editions of moral precepts were also popular. Among these were The Precepts of Cheiron, or Cheironeia, supposed to have been given by the wise Centaur to his pupil Achilles and put into verse by Hesiod; on a vase at Berlin three boys are seen reading this work with apparent interest. The extant lines of Theognis are often supposed to represent a school edition of the poet’s works, containing the more improving portions. The lyric poets were taught at the lyre-school, and I shall discuss them later.

Alexis also mentions “all sorts of prose works” in the school library. The only one of these to which he gives a more definite name is a cookery-book by Simos. But that is only introduced for the sake of a joke; such a work would not, of course, figure in an Athenian school. Aesop may have been a prose work read in schools; it was considered the sign of an ignoramus “not to have thumbed Aesop,” or to be able to quote him.[262] Such moral works as Prodikos’ Choice of Herakles were probably popular in schools. The case of Lusis in Plato suggests that some of the old nature-philosophers may have been read. No doubt the school library varied according to the taste of the master, and his freedom of choice may have led to some curious selections. But on the whole prose works very rarely figured in the elementary schools, partly because they were usually too technical, still more because the artistic and literary sense of the Hellenes regarded poetry, if only because of its greater beauty and its imaginative value, as better for educational purposes than prose.

The schoolrooms were used as the scene of lectures, to which grown-up men were invited; probably the lectures would be given to the boys at a different time. The wandering teacher, Hippias of Elis, meeting Sokrates one day, invited him to such a lecture, which, from its subject, was clearly meant mainly for the young.[263] After the fall of Troy, according to the story which Hippias invented for the occasion, Neoptolemos asked the wise old Nestor what was good and honourable conduct and what manner of life would cause a young man to win renown. Given this convenient opening, Nestor replied by suggesting many excellent rules of conduct. Hippias had delivered this lecture at Sparta, where it had won great applause. He now proposes, he says, “to deliver it the day after to-morrow in the schoolroom of Pheidostratos, and to impart much other valuable information at the same time, at the request of Eudikos son of Apemantos. Mind you come and bring any friends who will be capable of appreciating what I say.” No doubt it was a very excellent little sermon on the duties of life, closely analogous to Prodikos’ famous Choice of Herakles, and most improving for the pupils of Pheidostratos, if they were allowed to attend.

One charming picture of two Athenian school friends,[264] in their sleeveless tunics, is extant. “I saw you, Sokrates,” says a guest at a dinner-party, “when you and Kritoboulos at the School of Letters were both looking for something in the same book, putting your head against his, and your bare shoulder against his shoulder.”

It is also recorded that the Athenians were great hands at nicknames:[265] it may be inferred that this peculiarity extended also to their schoolboys.

A vivid picture of school life has recently come to light in the third Mime of Herondas. It belongs to the Alexandrian period in point of date, but many of its details will, no doubt, suit the Athenian schools just as well; it is, however, quite inconceivable that gags and fetters were used as punishments at Athens in the schools.

A mother, Metrotimé, brings her truant boy, Kottalos, to his schoolmaster Lampriskos to receive a flogging.

The poor mother goes on to say that it is useless to scold the boy; for, if she does, he promptly runs away from home to sponge upon his grandmother, or sits up on the roof out of the way, like an ape, breaking the tiles, which is expensive for his parents.

The exact age at which arithmetic was taught to boys at Athens involves a somewhat complicated inquiry. The arrangements which Plato makes in the Republic and Laws defer this subject till the age of sixteen. In the Laws[268] he says: “It remains to discuss, first the question of Letters, and secondly that of the Lyre and practical arithmetic—by which I mean so much as is necessary for purposes of war and household management and the work of government.” His citizens will also require, he thinks, enough astronomy to make the calendar intelligible to them. In this passage he distinctly couples practical arithmetic with music; and when he proceeds to detail, he makes the study of the lyre last from thirteen to sixteen, and then deals with arithmetic, the weights and measures, and the astronomical calendar, studies which terminate with the seventeenth year. This course is designed for all the free boys in his State: it is to be noticed that it is eminently practical, elementary, and concrete. In the Republic he is educating a few picked boys: before they are eighteen they are to have gone through a course of abstract and theoretical mathematics, the Theory of Numbers, Plane and Solid Geometry, Kinetics and Harmonics. Thus he mentions two sorts of mathematics, the one practical and concrete, called by the Hellenes λογιστική,[269] whose object is mainly mercantile, and the other theoretical and abstract, which they called ἀριθμητική. Both sorts are to be learned in the period next before the eighteenth year.

But it must not be assumed that this was the case at Athens. The philosopher is dealing with an ideal State, where education can be arranged in the theoretically best way, not with the real Athens, where the boy might be called away to the counting-house or the farm at any moment, and many did not stay at school after they had once learned to read and write. Moreover Plato, as a good Pythagorean, saw a peculiar appropriateness in making numbers follow music, and his Dorian sympathies made him divide up education into clearly marked periods, in each of which only one subject was taught. This arrangement, I have already shown, did not find favour at Athens.

His system must, then, be received with caution. It is inherently far more probable that the simpler, practical arithmetic would be taught at the elementary schools of letters, which all citizens, including future tradesmen and artisans, attended, not at some later date in a separate school. But can any evidence be found for such an arrangement? Yes, Plato himself in the Laws[270] declares that the future builder ought to play with toy bricks and learn weights and measurements when he is a child. His builder, at any rate, cannot wait to learn arithmetic till he is sixteen. Then, in the same work, he quotes the instance of Egypt, where “a very large number of children learn practical arithmetic simultaneously with their letters,” and he goes on to commend the methods by which it was taught. Now Egypt in the Laws is represented as the home of ideal education, a sort of Utopia. Again, in Plato[271] Protagoras blames his brother Sophists for “leading their pupils back, much against their wish, and casting them again into the sciences from which they have escaped, practical arithmetic and astronomy and geometry and music.” How could the Sophists[272] be described as “leading them back and casting them again” into studies from which they had escaped? Where had they learnt these subjects before they were fourteen? It could only have been at school. But what the Sophists taught must have been new to the boys, or they would not have paid to learn it. It was new, because the Sophists taught the advanced and theoretical stages, which appear in the Republic, and the elementary schoolmasters taught the simpler and concrete elements of arithmetic, weights and measures, and the calendar, described in the Laws, which were necessary to every Athenian citizen. From all this it may be assumed that the Athenian boys, like Plato’s Egyptian boys, learnt simple arithmetic, weights and measures, and perhaps the calendar, “simultaneously with their letters.”

Now there are two passages in Xenophon which seem to suit this view. They are not conclusive in themselves, but they give a valuable hint. In the first[273] it is stated that any one who knows his letters could say how many letters there are in “Sokrates,” and in what order they occur. In the second,[274] in the course of an argument, two illustrations are used, in close connection with one another. The passage runs:—“Take the case of Letters. Suppose some one asks you how many letters there are in ‘Sokrates,’ and which are they?… Or take the case of Numbers. Suppose some one asks what is twice five?” These two quotations certainly make simple counting a part of learning letters, with which study the second passage also closely connects the multiplication table. It would seem that it was part of a spelling lesson to answer such questions as “How many letters in ‘Sokrates’?” Answer, “Eight.” “Where does R come?” Answer, “Fourth.” It may be noticed also that the symbols of the numerals in ancient Hellas were, with one or two exceptions, identical with the current alphabet. The games with cubic dice and knucklebones, to which the boys were much addicted, must also have needed some arithmetical skill. The natural conclusion is that simple arithmetic, with, probably, the weights and measures, and the outlines of the calendar, were taught by the letter-master: the practice of music by the music-master: while the theory of numbers, of astronomy, and of music were taught by the Sophists to μειράκια.