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inappropriateness in conceiving the soul under the figure of a line, or the pleasure of the tyrant as separated from the pleasure of the king by the numerical interval of 729. And in modern times we sometimes use metaphorically what Plato employed as a philosophical formula. 'It is not easy to estimate the loss of the tyrant, except perhaps in this way,' says Plato. So we might say, that although the life of a good man is not to be compared to that of a bad man, yet you may measure the difference between them by valuing one minute of the one at an hour of the other ('One day in thy courts is better than a thousand'), or you might say that 'there is an infinite difference.' But this is not so much as saying, in homely phrase, 'They are a thousand miles asunder.' And accordingly Plato finds the natural vehicle of his thoughts in a progression of numbers; this arithmetical formula he draws out with the utmost seriousness, and both here and in the number of generation seems to find an additional proof of the truth of his speculation in forming the number into a geometrical figure; just as persons in our own day are apt to fancy that a statement is verified when it has been only thrown into an abstract form. In speaking of the number 729 as proper to human life, he probably intended to intimate that one year of the tyrannical = 12 hours of the royal life.

The simple observation that the comparison of two similar solids is effected by the comparison of the cubes of their sides, is the mathematical groundwork of this fanciful expression. There is some difficulty in explaining the steps by which the number 729 is obtained; the oligarch is removed in the third degree from the royal and aristocratical, and the tyrant in the third degree from the oligarchical; but we have to arrange the terms as the sides of a square and to count the oligarch twice over, thus reckoning them not as = 5 but as = 9. The square of 9 is passed lightly over as only a step towards the cube.

3. Towards the close of the Republic, Plato seems to be more and more convinced of the ideal character of his own speculations. At the end of the 9th Book the pattern which is in heaven takes the place of the city of philosophers on earth. The vision which has received form and substance at his hands, is now discovered to be at a distance. And yet this distant kingdom is also the rule of man's life. ('Say not lo! here, or lo! there, for the kingdom of God is within you.') Thus a note is struck which prepares for the revelation of a future life in the following Book. But the future life is present still; the ideal of politics is to be realized in the individual.

BOOK X.

Many things pleased me in the order of our State, but there was nothing which I liked better than the regulation about poetry. The division of the soul throws a new light on our exclusion of imitation. I do not mind telling you in confidence that all poetry is an outrage on the understanding, unless the hearers have that balm of knowledge which heals error. I have loved Homer ever since I was a boy, and even now he appears to me to be the great master of tragic poetry. But much as I love the man, I love truth more, and therefore I must speak out: and first of all, will you explain what is imitation, for really I do not understand? 'How likely then that I should understand!' That might very well be, for the duller often sees better than the keener eye. 'True, but in your presence I can hardly venture to say what I think.' Then suppose that we begin in our old fashion, with the doctrine of universals. Let us assume the existence of beds and tables. There is one idea of a bed, or of a table, which the maker of each had in his mind when making them; he did not make the ideas of beds and tables, but he made beds and tables according to the ideas. And is there not a maker of the works of all workmen, who makes not only vessels but plants and animals, himself, the earth and heaven, and things in heaven and under the earth? He makes the Gods also. 'He must be a wizard indeed!' But do you not see that there