Power of concentration is a very valuable quality, which few people acquire except through education. It is true that it grows naturally, to a considerable extent, as young people get older; very young infants seldom think of any one thing for more than a few minutes, but with every year that passes their attention grows less volatile until they are adult. Nevertheless, they are hardly likely to acquire enough concentration without a long period of intellectual education. There are three qualities which distinguish perfect concentration: it should be intense, prolonged, and voluntary. Intensity is illustrated by the story of Archimedes, who is said to have never noticed when the Romans captured Syracuse and came to kill him, because he was absorbed in a mathematical problem. To be able to concentrate on the same matter for a considerable time is essential to difficult achievement, and even to the understanding of any complicated or abstruse subject. A profound spontaneous interest brings this about naturally, so far as the object of interest is concerned. Most people can concentrate on a mechanical puzzle for a long time; but this is not in itself very useful. To be really valuable, the concentration must also be within the control of the will. By this I mean that, even where some piece of knowledge is uninteresting in itself, a man can force himself to acquire it if he has an adequate motive for doing so. I think it is above all the control of attention by the will that is conferred by higher education. In this one respect, an old-fashioned education is admirable; I doubt whether modern methods are as successful in teaching a man to endure voluntary boredom. However, if this defect does exist in modern educational practice, it is by no means irremediable. The matter is one to which I shall return later. Patience and industry ought to result from a good education. It was formerly thought that they could only be secured, in most cases, by the enforcement of good habits imposed by external authority. Undoubtedly this method has some success, as may be seen when a horse is broken in. But I think it is better to stimulate the ambition required for overcoming difficulties, which can be done by grading the difficulties so that the pleasure of success may at first be won fairly easily. This gives experience of the rewards of persistence, and gradually the amount of persistence required can be increased. Exactly similar remarks apply to the belief that knowledge is difficult but not impossible, which is best generated by inducing the pupil to solve a series of carefully graded problems.