cations. A year is found amply sufficient for this, the more so because intricate calculations are, for the most part, performed by the aid of machines. The same economy of effort is observed throughout the other branches of pure mathematics, and all sciences worthy of the name are now but branches of mixed mathematics.
"The acquaintance with the tools of knowledge is usually obtained by the age of fifteen. At this age the boy,—I say boy, as I shall first speak of his further training; though up to this point boys and girls receive the same training,—the boy, I say, is expected to have a fair mastery of language as an instrument of expression, and a slight knowledge of literature. I say a slight knowledge, because he has hitherto been carefully kept from indiscriminate reading. A thorough knowledge of a few books is thought of more value than a skimming over many. He is expected also to possess all the mathematical knowledge required for his further studies. In addition to drawing, photography, and similar aids, he has acquired the management of the most important tools, and has had practice in the working of metals and other materials. His handicraft is now chosen for him."
"Can he not choose for himself?" I inquired.
"The matter is arranged somewhat as follows: if my son, for example, wishes to follow my pursuit, he may do so; since there are many evident advantages in so doing, But if, as is often the case, he does not wish to do so, he adopts the line of work assigned to him. A great part of the misery of ancient times arose from waste of various kinds. Not the least of these was the waste of misdirected effort, resulting in the overcrowding of callings.
