or downwards, or round and round.  The legislator should impress on his citizens the value of arithmetic.  No instrument of education has so much power; nothing more tends to sharpen and inspire the dull intellect.  But the legislator must be careful to instil a noble and generous spirit into the students, or they will tend to become cunning rather than wise.  This may be proved by the example of the Egyptians and Phoenicians, who, notwithstanding their knowledge of arithmetic, are degraded in their general character; whether this defect in them is due to some natural cause or to a bad legislator.  For it is clear that there are great differences in the power of regions to produce good men:  heat and cold, and water and food, have great effects both on body and soul; and those spots are peculiarly fortunate in which the air is holy, and the Gods are pleased to dwell.  To all this the legislator must attend, so far as in him lies.

Book vi.  And now we are about to consider (1) the appointment of magistrates; (2) the laws which they will have to administer must be determined.  I may observe by the way that laws, however good, are useless and even injurious unless the magistrates are capable of executing them.  And therefore (1) the intended rulers of our imaginary state should be tested from their youth upwards until the time of their election; and (2) those who are to elect them ought to be trained in habits of law, that they may form a right judgment of good and bad men.  But uneducated colonists, who are unacquainted with each other, will not be likely to choose well.  What, then, shall we do?  I will tell you:  The colony will have to be intrusted to the ten commissioners, of whom you are one, and I will help you and them, which is my reason for inventing this romance.  And I cannot bear that the tale should go wandering about the world without a head,—­it will be such an ugly monster.  ‘Very good.’  Yes; and I will be as good as my word, if God be gracious and old age permit.  But let us not forget what a courageously mad creation this our city is.  ’What makes you say so?’ Why, surely our courage is shown in imagining that the new colonists will quietly receive our laws?  For no man likes to receive laws when they are first imposed:  could we only wait until those who had been educated under them were grown up, and of an age to vote in the public elections, there would be far greater reason to expect permanence in our institutions.  ‘Very true.’  The Cnosian founders should take the utmost pains in the matter of the colony, and in the election of the higher officers, particularly of the guardians of the law.  The latter should be appointed in this way:  The Cnosians, who take the lead in the colony, together with the colonists, will choose thirty-seven persons, of whom nineteen will be colonists, and the remaining eighteen Cnosians—­you must be one of the eighteen yourself, and become a citizen of the new state.  ‘Why do not you