ῥίμφα ἑ γοῦνα φέρει μετά τ’ ἤθεα καὶ νόμον ἵππων.

For this adaptation of metre to sense in connection with the movement of horses, we may take another example. To describe Agamemnon dealing destruction among the routed Trojans on foot, we have a line and a half of somewhat accelerated but by no means very rapid movement[765];

ὣς ἄρ’ ὑπ’ Ἀτρείδῃ Ἀγαμέμνονι πῖπτε κάρηνα
Τρώων φευγόντων.

But when he comes to the Trojan horses in their flight, we have two lines, dactylic to the utmost extent that the metre will allow, except in one half-foot;

πολλοὶ δ’ ἐριαύχενες ἵπποι
κείν’ ὄχεα κροτάλιζον ἀνὰ πτολέμοιο γεφύρας,
ἡνιόχους ποθέοντες ἀμύμονας.

Then, coming back to the dead charioteers, he visibly slackens again;

οἱ δ’ ἐπὶ γαίῃ
κείατο, γύπεσσιν πολὺ φίλτεροι ἢ ἀλόχοισιν.

To exhibit numerically the relative distribution of times in these members of the sentence, we have these three very different proportions;

In the first, 13 long syllables to 8 short.

In the second, 16 long syllables to 22 short.

In the third, 11 long syllables to 10 short.

He has imparted much of the same glowing movement to the speech, which in the Nineteenth Iliad is assigned to the Immortal horses of Achilles; though the subject includes a reference to the death of their master[766]. In nearly every line, throughout the passage, that relates to their own motion, the number of dactyls is at the maximum, and in the ten lines there are eighty-six short syllables to sixty long ones; a proportion, which I doubt our finding elsewhere in Homer, except it be among the similes, to which Homer seems in many cases to give a peculiarly elastic prosodial movement.

Rhesus, king of the Thracians, who arrives at Troy after the commencement of the Wrath, becomes sufficiently distinguished for the central point of interest in the Doloneia, by virtue chiefly of his horses. They are the most beautiful, says Dolon, and the largest that I have ever seen[767];

λευκότεροι χιόνος, θείειν δ’ ἀνέμοισιν ὁμοῖοι.

The justice of this panegyric is corroborated by the emphatic expression of Nestor, who pronounces them,

αἰνῶς ἀκτίνεσσιν ἐοικότες ἠελίοιο·

and their unparalleled excellence forms the subject of the speech of the old king, on the return of Ulysses and Diomed to the camp[768].

It is not only, however, in elaborate pictures that Homer shows his feeling for horses, but also, and not less markedly, in minor touches. Does he not speak with the manifest feeling of a skilled admirer of the animal, when he describes the pair driven by Eumelus, rapid as birds, the same in shade of colour, the same in years, the same to a hair’s breadth in height across their backs[769]?

ποδώκεας, ὄρνιθας ὣς,
ὄτριχας, οἰέτεας, σταφύλῃ ἐπὶ νῶτον ἐΐσας.

Again, we are met by the same feeling which, in a bolder flight, made the horses of Rhesus weep, when Pandarus falls headlong from the chariot of Æneas, and his arms rattle over him in death. The horses, instead of plunging or starting off, with a finer feeling tremble by the corpse[770];

παρέτρεσσαν δέ οἱ ἵπποι
ὠκύποδες.

We may trace the same disposition, under a lighter and more amusing form, in what had already passed between Æneas and Pandarus. Pandarus had excused himself for not having brought a chariot and horses to Troy, on account of his fears about finding forage for them where such crowds were to be gathered into a small space; at the same time describing, rather boastfully, his father Lycaon’s eleven carriages with a pair for each. (Il. v. 192-203.) Æneas replies by inviting him into his chariot when he will see what Trojan horses are like. Then, he continues, do you fight, and I will drive; or, as you may choose, do you drive, and I will fight. Pandarus immediately replies, that Æneas had better by all means be the driver of his own horses.

Then again, Homer will have the utmost care taken of them; and, so to speak, he looks to it himself. When he describes them as unemployed, he specifies their food; those of Achilles during the Wrath stand[771],

λωτὸν ἐρεπτόμενοι ἐλεόθρεπτόν τε σέλινον.

But those of Lycaon, which had remained at home, were[772]

κρῖ λευκὸν ἐρεπτόμενοι καὶ ὀλύρας.

To each he gives the appropriate provender: to the former, in an encampment, what the grassy marsh by its side afforded: to the latter, in a king’s palace, the grain, or hard food, of their proper home.

And so in the night-adventure of the Tenth Book, when Ulysses drags away the bodies of those Thracians whom Diomed has slain, it is to make a clear path for the horses of Rhesus which were to be carried off, that they may not take fright from treading on corpses[773];

νεκροῖς ἀμβαίνοντες· ἀήθεσσον γὰρ ἔτ’ αὐτῶν.

Throughout the chariot-race, in the Twenty-third Book, we find them uppermost in the Poet’s mind, though the drivers, being his prime heroes, are not wholly forgotten.

Even as to colour, of which Homer’s perceptions appear to have been so vague, it may be remarked, that he employs it somewhat more freely with reference to horses, than to other objects having definite form or powers of locomotion.

But his liveliest conceptions of them are with respect to motion, form, and feelings: and I suppose there is no poem like the Iliad for characteristic touches in respect to any of the three.

Beauty in inanimate nature.

It has been much debated whether the ancients generally, and whether Homer in particular, had any distinct idea of beauty in landscape.

It may be admitted, even in respect to Homer, that his similes, to which one would naturally look for proof, less commonly refer to the eye than to other faculties. They commonly turn upon sound, motion, force, or multitude: rarely, in comparison, upon colour, or even upon form; still more rarely upon colour or form in such combinations as to constitute what we call the picturesque.

It seems to me, that we may draw the best materials of a demonstration in this case from comparing his descriptions of the form of scenery by means of the outlines of countries, with his use of other epithets which he employs to denote beauty.

The country of Lacedæmon was mountainous, and it is hence termed by Homer in the Odyssey and in the Catalogue, κοιλή. (Il. ii. 581, Od. iv. 1.)

But it is also termed by him ἐρατεινὴ (Il. iii. 239), and this, it may be observed, in a speech of Helen’s; to whom, while she was at Troy, the image of it in memory could hardly, perhaps, be agreeable from any moral association. We are, therefore, led to refer it to the physical conformation or beauty of the district.

Next, we have pretty clear proof that in Homer’s mind the epithet ἐρατεινὴ was one proper to describe beauty in the strictest sense. For he says of Helen, with regard to her daughter Hermione[774]:

ἐγείνατο παῖδ’ ἐρατεινὴν,
Ἑρμιόνην, ἣ εἶδος ἔχε χρυσῆς Ἀφροδίτης.

‘She had a lovely (ἐρατεινὴν) daughter, endowed with the beauty of golden Aphrodite.’ And I observe but few passages in Homer, perhaps only one (Od. xxiii. 300), when ἐρατεινὸς does not naturally and properly bear this sense. A sense etymologically analogous to our own use of the word lovely, which we employ to indicate not only beauty, but a high degree of it.

It therefore appears to be clear that Homer called Lacedæmon ἐρατεινὴ, because it was shaped in mountain and valley, and because countries so formed present a beautiful appearance to the eye, as compared with countries of other forms less marked. It is applied to Emathia (Il. xiv. 225) and to Scheria (Od. vii. 79), both mountainous; to the city Ilios, (Il. v. 210), which stood on ground high and partially abrupt near the roots of Ida; and I do not find it in any place of the poems associated with flat lands.

The other instance which I shall cite seems to present the argument in a complete form, within the compass of a single line.

When describing Ithaca in the Odyssey, Telemachus says it is[775],

αἰγίβοτος, καὶ μᾶλλον ἐπήρατος ἱπποβότοιο.

Here we may assume that by αἰγίβοτος, goat-feeding, he means mountainous, and even sharp and rocky; moreover consequently, in comparison, barren, so that it could not be agreeable in the sense of being profitable. On the other hand, the horse is an animal ill-suited to range among rocks; and by ἱππόβοτος Homer always means a district or country sufficiently open and plain to be suitable for feeding horses in numbers. Now, in saying that Arran is more ἐπήρατος than southern Lancashire, we should leave no doubt upon the mind of any reader as to the meaning; which must surely be that it offers more beauty to the eye. Just such a comparison does Homer make of the scenery of Ithaca as it was with what it would have been, if the island had been flat.

I ought however to notice the very forced interpretation of Damm, which is this: μᾶλλον ἐπήρατος, sc. ἐμοὶ, nam est patria mea; et ad μᾶλλον subintelligit τοῦ σοῦ Ἄργεος φίλη μοι ἔστι.

Homer was better versed in the art of wedding words to thought, than such an interpretation supposes. For, according to it, the thought of Homer was this; ‘Though you rule over broad and open Argos, my mountainous Ithaca is dearer to me, because it is my country.’ So that he has left out the point of the sentence, without the faintest trace to guide his reader. The idea of the sentence, which is prolonged through many verses, turns entirely on the difference between an open and a steep rocky country as such, and not in the least on native attachments. And Telemachus, who is lauding the richness and fertility of Argos, and apologizing for the barrenness of Ithaca, not ungracefully, in passing, throws in, by way of compensation, the element of beauty, as one possessed by Ithaca, and as one which it must miss if it were flat.

Indeed, we here trace the usual refinement of Homer in this, that Telemachus does not say, True, your Argos is rich, but my Ithaca is picturesque: but, after commending the fertility of broad Argos, he says, ‘In Ithaca we have no broad runs[776], and nothing like a meadow: it will feed nothing but goats, yet it is more picturesque than if it, a little speck of that kind, were flat and open.’

The word ἐπήρατος is less frequently used in Homer than ἐρατεινός; but we have it in six places besides this. There is only one of them where it is capable of meaning dear, in connection with the idea of country[777]. In another it means enjoyable or splendid, being applied to the banquet[778]. In the other places it is applied to a town on the Shield, a cavern in Ithaca (twice), and the garments put upon Venus in Cyprus; and in those four places it can only mean fair or beautiful.

We are not, then, justified in limiting Homer’s sense of natural beauty to what was associated with utility[779]. On the contrary, it appears plainly to extend to beauty proper, and even to that kind of beauty in nature which we of the present day most love.

I have dealt thus far with the most doubtful part of the question, and have ventured to dissent from Mr. Ruskin, whose authority I admit, and of whose superior insight, as well as of his extraordinary powers of expression, I am fully conscious.

Germ of feeling for the picturesque.

Mr. Ruskin thinks[780] that ‘Homer has no trace of feeling for what we call the picturesque’; that Telemachus apologizes for the scenery of Ithaca; and that rocks are never loved but as caves. I think that the expressions I have produced from the text show that these propositions cannot be sustained. At the same time I admit that the feeling with Homer is one in the bud only: as, indeed, until within a very few generations, it has lain undeveloped among ourselves. Homer may have been the father of this sentiment for his nation, as he was of so much besides. But the plant did not grow up kindly among those who followed him.

I assent entirely, on the other hand, to what Mr. Ruskin has said respecting his sense of orderly beauty in common nature. The garden of Alcinous is truly Dutch in its quadrangular conceptions; but it is plain that the Poet means us to regard it as truly beautiful[781]. Symmetry, serenity, regularity, adopted from the forms of living beauty which were before him, enter largely into Homer’s conceptions of one form, at least, of inanimate beauty.

The scenery of the cave of Calypso[782] is less restrained in its cast, than is the garden in Scheria; but even here Homer introduces four fountains, which compose a regular figure, and are evidently meant to supply an element of form which was required by the fashionable standard.

Another element of landscape, as we understand it, is, that the natural objects which it represents should be in rather extensive combination; and our established traditions would also require that the view of them should be modified by the rendering of the atmosphere, especially with reference to the scale of distances.

It is very difficult to find instances of extended landscape in Homer. But I think that we have at least one, in the famed simile, where he compares the Trojan watchfires on the plain to the calm night, which by the light of moon and stars exhibits a breadth of prospect to the rejoicing shepherd’s eye. Here are certainly tranquillity and order; but with them we seem also to have both extent and atmosphere; to which even bold and even broken outline must be added by those who, like myself, are not prepared to surrender to the destroying ὄβελος the line[783]

ἔκ τ’ ἔφανεν πᾶσαι σκοπιαὶ, καὶ πρώονες ἄκροι.

Upon the whole, considering Homer’s early date, and the very late development among the moderns of a taste for scenery of the picturesque and romantic order, I do not know that we are entitled even at first sight to challenge him as inferior to any modern of analogous date in this province. Yet we may fairly pronounce that he is inferior to himself; that is to say, he appears to have a sense of beauty, in the region of inanimate nature, certainly less keen in proportion than that, with which he looked upon the animated creation.

What is deficient in him with respect to landscape may however, in all likelihood, be more justly referred to positive than to negative causes.

Causes adverse to a more developed feeling.

It may be questioned whether the disposition to appreciate still nature, especially in large and elaborated combinations, may not in part depend upon conditions that were not to be found in the age of Homer. I should say, if the expression may be allowed, that we of this generation take landscape medicinally. Human life grows with the course of ages; and, especially in our age, it has grown to be excited and hurried. But nature has a reacting tendency towards repose; and, even in the case of the grosser stimulants, it seems to be their soothing power which most helps to recommend them. Besides the fact, however, that we have wants which the Greeks had not, this subject may be regarded in a broader view.

The mind of Homer and the mind of his age were not addicted even to contemplation, far less to introspection. Of ideas properly subjective there are very few indeed to be found in the poems. We have one such furnished by the passage where he equates thought to a wing, in a simile for the swift ships of the Phæacians,

ὡσεὶ πτέρον ἠὲ νόημα.

And another, the most remarkable that he supplies, when in more detail he uses the motion of a thought for an illustration of the rapid flight of Juno[784].

Even when it became speculative, the Greek mind did not give a subjective turn to its speculations. It was probably Christianity which, by the stimulus it applied to the general conscience, first gave mankind the introspective habit on a large scale; and mixed causes may often render the tendency excessive and morbid. But the tendency of the heroic age, standing at its maximum in Homer, was to pour life outward, nay almost to force it into every thing. The fountain from within overflowed; and its surplus went to make inanimate nature breathe. The profuse and easy fertility of Homer in simile surely of itself demonstrates a wonderful observation and appreciation of nature; but, as has been remarked, these similes are very rarely indeed still similes. They delight in sound, in multitude, above all in motion. The automatic chairs of Vulcan, the living theatre of the Shield of Achilles, that oldest mirror of our world, the bounding armour of the same hero, what are all these but the proofs of that redundant energy of life, whose first resistless impulse it was to carry the vital fire of Prometheus into every object that it encountered, and which, not yet having felt the palsying touch of exhaustion, lay under no necessity of curative provisions for repose? Therefore, while admitting the defect of Homer with respect to colour, and admitting also that landscape (if we are to understand by it the elaborate combination of natural objects reaching over considerable distances) is a great addition to the enjoyment and wealth of mankind, I think the capital explanation of the question raised is to be found, not in the want of any space, or of any faculty, in the mind of Homer, but in the fact that the space and the faculties were all occupied with more active and vivifying functions; that the beautiful forms in nature, which we see as beautiful forms only, were to him the hem of the garments, as it were, of that life with which all nature teemed. Accordingly, the general rule of the poems is, that where we should be passive, he is active; that which we think it much to contemplate with satisfaction, he is ever at work, with a bolder energy and a keener pleasure, to vivify. We deal with external nature, as it were unrifled; he saw in it only the residue which remained to it, after it had at every point thrown off its cream in supernatural formations. His uplifting and vitalizing process is everywhere at work. Animate nature is raised even to divinity; and inanimate nature is borne upward into life.

If, then, Homer sees less in the mere sensible forms of natural objects than we do, it probably is in a great degree because the genius of his people and his own genius had taught him to invest them with a soul, which drew up into itself the best of their attractions. Mr. Ruskin most justly tells us, with reference to the sea, that he cuts off from the material object the sense of something living, and fashions it into a great abstract image of a sea-power[785]. Yet it is not, I think, quite true, that the Poet leaves in the watery mass no element of life. On the contrary, I should say the key to his whole treatment of external nature is to be found in this one proposition: wheresoever we look for figure, he looks for life. His waves (as well as his fire) when they are stirred[786], shout, in the very word (ἰάχειν) that he gives to the Assembly of Achæans: when they break in foam, they put on the plume of the warrior’s helmet[787] (κορύσσεσθαι): when their lord drives over them, they open wide for joy[788]: and when he strides upon the field of battle, they, too, boil upon the shore, in an irrepressible sympathy with his effort and emotion[789].

SECT. III.
Homer’s perceptions and use of Number.

While the faculties of Homer were in many respects both intense and refined in their action, beyond all ordinary, perhaps we might say beyond all modern, examples, there were other points in which they bear the marks of having been less developed than is now common even among the mass of many civilized nations. In the power of abstraction and distinct introspective contemplation, it is not improbable that he was inferior to the generality of educated men in the present day. In some other lower faculties, he is probably excelled by the majority of the population of this country, nay even by many of the children in its schools. I venture to specify, as examples of the last-named proposition, the faculties of number, and of colour. It may be true of one or both of these, that a certain indistinctness in the perception of them is incidental everywhere to the early stages of society. But yet it is surprising to find it where, as with Homer, it accompanies a remarkable quickness and maturity not only of great mental powers, but of certain other perceptions more akin to number and colour, such as those of motion, of sound, and of form. But let us proceed to examine, in the first place, the former of these two subjects.

It may be observed at the outset, that probably none of us are aware to how great an extent our aptitudes with respect to these matters are traditionary, and dependent therefore not upon ourselves, but upon the acquisitions made by the human race before our birth, and upon the degree in which those acquisitions have circulated, and have been as it were filtered through and through the community, so as to take their place among the elementary ideas, impressions, and habits of the population. For such parts of human knowledge, as have attained to this position, are usually gained by each successive generation through the medium of that insensible training, which begins from the very earliest infancy, and which precedes by a great interval all the systematic, and even all the conscious, processes of education. Nor am I for one prepared by any means to deny that there may be an actual ‘traducianism’ in the case: on the contrary, in full consistency with the teaching of experience, we may believe that the acquired aptitudes of one generation may become, in a greater or a less degree, the inherited and inborn aptitudes of another.

We must, therefore, reckon upon finding a set of marked differences in the relative degrees of advancement among different human faculties in different stages of society, which shall be simply referable to the source now pointed out, and distinct altogether from such variations as are referable to other causes. It is not difficult to admit this to be true in general: but the question, whether in the case before us it applies to number and colour, can of course only be decided by an examination of the Homeric text.

Yet, before we enter upon this examination, let us endeavour to throw some further light upon the general aspect of the proposition, which has just been laid down.

Of all visible things, colour is to our English eye the most striking. Of all ideas, as conceived by the English mind, number appears to be the most rigidly definite, so that we adopt it as a standard for reducing all other things to definiteness; as when we say that this field or this house is five, ten, or twenty times as large as that. Our merchants, and even our schoolchildren, are good calculators. So that there is a sense of something strikingly paradoxical, to us in particular, when we speak of Homer as having had only indeterminate ideas of these subjects.

Conceptions of Number not always definite.

There are however two practical instances, which may be cited to illustrate the position, that number is not a thing to be as matter of course definitely conceived in the mind. One of these is the case of very young children. To them the very lowest numbers are soon intelligible, but all beyond the lowest are not so, and only present a vague sense of multitude, that cannot be severed into its component parts. The distinctive mark of a clear arithmetical conception is, that the mind at one and the same time embraces the two ideas, first of the aggregate, secondly of each one of the units which make it up. This double operation of the brain becomes more arduous, as we ascend higher in the scale. I have heard a child, put to count beads or something of the sort, reckon them thus: ‘One, two, three, four, a hundred.’ The first words express his ideas, the last one his despair. Up to four, his mind could contain the joint ideas of unity and of severalty, but not beyond; so he then passed to an expression wholly general, and meant to express a sense like that of the word multitude.

But though the transition from number definitely conceived to number without bounds is like launching into a sea, yet the conception of multitude itself is in one sense susceptible of degree. We may have the idea of a limited, or of an unbounded, multitude. The essential distinction of the first is, that it might possibly be counted; the notion of the second is, that it is wholly beyond the power of numeration to overtake. Probably even the child, to whom the word ‘hundred’ expressed an indefinite idea, would have been faintly sensible of a difference in degree between ‘hundred’ and ‘million,’ and would have known that the latter expressed something larger than the former. The circumscribing outline of the idea apprehended is loose, but still there is such an outline. The clearness of the double conception is indeed effaced; the whole only, and not the whole together with each part, is contemplated by the mind; but still there is a certain clouded sense of a real difference in magnitude, as between one such whole and another.

And this leads me to the second of the two illustrations, to which reference has been made. That loss of definiteness in the conception of number, which the child in our day suffers before he has counted over his fingers, the grown man suffers also, though at a point commonly much higher in the scale. What point that may be, depends very much upon the particular habits and aptitudes of the individual. A student in a library of a thousand volumes, an officer before his regiment of a thousand men upon parade, may have a pretty clear idea of the units as well as of the totals; but when we come to a thousand times a thousand, or a thousand times a million, all view of the units, for most men, probably for every man, is lost: the million for the grown man is in a great degree like the hundred for the child. The numerical term has now become essentially a symbol; not only as every word is by its essence a symbol in reference to the idea it immediately denotes; but, in a further sense, it is a symbol of a symbol, for that idea which it denotes, is itself symbolical: it is a conventional representation of a certain vast number of units, far too great to be individually contemplated and apprehended. As we rise higher still from millions, say for example, into the class of billions, the vagueness increases. The million is now become a sort of new unit, and the relation of two millions to one million, is thus pretty clearly apprehended as being double; but this too becomes obscured as we mount, and even (for example) the relation of quantity between ten billions of wheat-corns, and an hundred billions of the same, is far less determinately conveyed to the mind, than the relation between ten wheat-corns and one. At this high level, the nouns of number approximate to the indefinite character of the class of algebraic symbols called known quantities.

In proportion as our conception of numbers is definite, the idea of them, instead of being suited for an address to the imagination, remains unsuited for poetic handling, and thrives within the sphere of the understanding only. But when we pass beyond the scale of determinate into that of practically indeterminate amounts, then the use of numbers becomes highly poetical. I would quote, as a very noble example of this use of number, a verse in the Revelations of St. John. ‘And I beheld, and I heard the voice of many angels round about the throne, and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands[790].’ As a proof of the power of this fine passage, I would observe, that the descent from ten thousand times ten thousand to thousands of thousands, though it is in fact numerically very great, has none of the chilling effect of anticlimax, because these numbers are not arithmetically conceived, and the last member of the sentence is simply, so to speak, the trail of light which the former draws behind it.

Now we must keep clearly before our minds the idea, that this poetical and figurative use of number among the Greeks at least preceded what I may call its calculative use. We shall find in Homer nothing that can strictly be called calculation. He repeatedly gives us what may be termed the factors of a sum in multiplication; but he never even partially combines them, even as they are combined for example in Cowper’s ballad,

John Gilpin’s spouse said to her dear,
Though wedded we have been
These twice ten tedious years, yet we
No holiday have seen.

Reference has been made to the convenience which we find in using number as a measure of quantity, and as a means of comparing things of every species in their own kind. But we never meet with this use of it in Homer. He has not even the words necessary to enable him to say, ‘This house is five times as large as that.’ If he had the idea to express, he would say, Five houses, each as large as that, would hardly be equal to this. The word τρὶς may be called an adverb of multiplication; but it is never used for these comparisons. Indeed, Damm observes, that in a large majority of instances it signifies an indefinite number, not a precise one. Τετράκις is found only once, and in a sense wholly indeterminate: the passage is[791] τρισμάκαρες Δαναοὶ καὶ τετράκις. Πεντάκις does not even exist. Ajax lifts a stone, not ‘twice as large as a mortal of to-day could raise’, but so large that it would require two such mortals to raise it. All Homer’s numerical expressions are in the most elementary forms; such forms, as are without composition, and refuse all further analysis.

Greek estimate of the discovery of Number.

His use of number appears to have been confined to simple addition: and it is probable that all the higher numbers which we find in the poems, were figurative and most vaguely conceived. If we are able to make good the proof of these propositions from the Homeric text, we shall then be well able to understand the manner in which Numeration, or the science of number, is spoken of by the Greeks of the historic age as a marvellous invention. It appears in Æschylus, as among the very greatest of the discoveries of Prometheus[792]:

καὶ μὴν ἀριθμὸν, ἔξοχον σοφισμάτων,
ἐξεῦρον αὐτοῖς·

he goes on to add,

γραμμάτων τε συνθέσεις.

So that the use of numbers by rule was to the Greek mind as much a discovery as the letters of the alphabet, and is even described here as a greater one: much as in later times men have viewed the use of logarithms, or of the method of fluxions or the calculus. In full conformity with this are the superlative terms, in which Plato speaks of number. Number, in fact, seems to be exhibited in great part of the Greek philosophy, as if it had actually been the guide of the human mind in its progress towards realizing all the great and cardinal ideas of order, measure, proportion, and relation.

Up to what point human intelligence, in the time of Homer, was able to push the process of simple addition, we do not precisely know. It is not, however, hastily to be assumed that, in any one of his faculties, Homer was behind his age; and it is safer to believe that the poems, even in these points, represent it advantageously. Now, in one place at least, we have a primitive account of a process of addition. The passage is in the Fourth Odyssey, where Menelaus relates, how Proteus counted upon his fingers the number of his seals[793]. That it was a certain particular number is obvious, because when four of them had been killed by Eidothee, their skins were put upon Menelaus and his three comrades, and the four Greeks were then counted into the herd, so that the word ἀριθμὸς here evidently means a definite total. This addition by Proteus, however, was not addition in the proper arithmetical sense, and would be more properly called enumeration: it was probably effected simply by adding each unit singly, in succession, to the others, with the aid of the fingers, (proved through the word πεμπάσσεται,) but not by the aid of any scale or combination of units, either decimal or quinal. In the word δεκὰς we have, indeed, the first step towards a decimal scale; but we have not even that in the case of the number five, there being no πεντὰς or πεμπτάς. The meaning of πεμπάσσεται evidently is, not that he arranged the numeration in fives, but that, by means of the fingers of one hand, employed upon those of the other, he assisted the process of simple enumeration.

Highest numerals of the poems.

Homer’s highest numeral is μύριοι. He describes the Myrmidons as being μύριοι[794], though, if we assume a mean strength of about eighty-five for their crews, the force would but little have exceeded four thousand: and at the maximum of one hundred and twenty for each ship, it would only come to six thousand. Again, Homer uses the expression μύρια ᾔδη, to denote a person of instructed and accomplished mind[795].

Next to the μύρια, the highest numerals employed in the poems are those contained in the passage where the Poet says that the howl of Mars, on being wounded by Diomed, was as loud as the shout of an army of nine thousand or ten thousand men[796]:

ὅσσον τ’ ἐννεάχιλοι ἐπίαχον ἢ δεκάχιλοι
ἀνέρες ἐν πολέμῳ.

But it is clear that the expressions are purely poetical and figurative. For he never comes near the use of such high numbers elsewhere; and yet it obviously lay in his path to use these, and higher numbers still, when he was describing the strength of the Greek and Trojan armies.

The highest Homeric number, after those which have been named, is found in the three thousand horses of Erichthonius. This we must also consider poetical, because it is so far beyond the ordinary range of the poems, and in some degree likewise because of the obvious unlikelihood of his having possessed that particular number of mares[797].

Only thrice, besides the instances already quoted, does Homer use the fourth power of numbers; it is in the case of the single thousand. A thousand measures of wine were sent by Euneos as a present to Agamemnon and Menelaus. A thousand watch-fires were kindled by the Trojans on the plain. Iphidamas, having given an hundred oxen in order to obtain his wife, then promised a thousand goats and sheep out of his countless herds[798]. In all these three cases, it is more than doubtful whether the word thousand is not roughly and loosely used as a round number. The combination of the thousand sheep and goats with the hundred oxen, immediately awakens the recollection that even the Homeric hecatomb, though meaning etymologically an hundred oxen, practically meant nothing of the kind, but only what we should call a lot or batch of oxen. Again, it is so obviously improbable that the Trojans should in an hurried bivouac have lighted just a thousand fires, and placed just fifty men by each, that we may take this passage as plainly figurative, and as conveying no more than a very rude approximation, of such a kind as would be inadmissible where the practice of calculation is familiar. It is then most likely, that in the remaining one of the three passages, the Poet means only to convey that a large and liberal present of wine was sent by Euneus, as the consideration for his being allowed to trade with the army. There is certainly more of approximation to a definite use of the single thousand, than of the three, the nine, or the ten: but this difference in definiteness is in reality a main point in the evidence. Most of all does this become palpable, when we consider how strange is in itself the omission to state the numbers of the combatants on either side of this great struggle: an omission so strange, of what would be to ourselves a fact of such elementary and primary interest, that we can hardly account for it otherwise than by the admission, that to the Greeks of the Homeric age the totals of the armies, even if the Poet himself could have reckoned them, would have been unintelligible.

Among all the numbers found in Homer, the highest which he appears to use with a clearly determinate meaning, is that of the three hundred and sixty fat hogs under the care of Eumæus in Ithaca[799];