a household; wherever measure is employed, men are more wide-awake in their dealings, and they get rid of their ridiculous ignorance. 'What do you mean?' I have observed this ignorance among my countrymen--they are like pigs--and I am heartily ashamed both on my own behalf and on that of all the Hellenes. 'In what respect?' Let me ask you a question. You know that there are such things as length, breadth, and depth? 'Yes.' And the Hellenes imagine that they are commensurable (1) with themselves, and (2) with each other; whereas they are only commensurable with themselves. But if this is true, then we are in an unfortunate case, and may well say to our compatriots that not to possess necessary knowledge is a disgrace, though to possess such knowledge is nothing very grand. 'Certainly.' The discussion of arithmetical problems is a much better amusement for old men than their favourite game of draughts. 'True.' Mathematics, then, will be one of the subjects in which youth should be trained. They may be regarded as an amusement, as well as a useful and innocent branch of knowledge;--I think that we may include them provisionally. 'Yes; that will be the way.' The next question is, whether astronomy shall be made a part of education. About the stars there is a strange notion prevalent. Men often suppose that it is impious to enquire into the nature of God and the world, whereas the very reverse is the truth. 'How do you mean?' What I am going to say may seem absurd and at variance with the usual language of age, and yet if true and advantageous to the state, and pleasing to God, ought not to be withheld. 'Let us hear.' My dear friend, how falsely do we and all the Hellenes speak about the sun and moon! 'In what respect?' We are always saying that they and certain of the other stars do not keep the same path, and we term them planets. 'Yes; and I have seen the morning and evening stars go all manner of ways, and the sun and moon doing what we know that they always do. But I wish that you would explain your meaning further.' You will easily understand what I have had no difficulty in understanding myself, though we are both of us past the time of learning. 'True; but what is this marvellous knowledge which youth are to acquire, and of which we are ignorant?' Men say that the sun, moon, and stars are planets or wanderers; but this is the reverse of the fact. Each of them moves in one orbit only, which is circular, and not in many; nor is the swiftest of them the slowest, as appears to human eyes. What an insult should we offer to Olympian runners if we were to put the first last and the last first! And if that is a ridiculous error in speaking of men, how much more in speaking of the Gods? They cannot be pleased at our telling falsehoods about them. 'They cannot.' Then people should at least learn so much about them as will enable them to avoid impiety.