That these natural aptitudes are carried to a very high degree and unusual extent, we have celebrated examples recorded in history, and frequently cited. We have Pascal, at twelve years old, discovering the greater portion of plane geometry, and without having been taught anything whatever of arithmetic, drawing all the figures of the first book of Euclid's geometry on the floor of his room, exactly estimating the mathematical relations of all these figures to each other; that is to say, constructing descriptive geometry for himself. We have the shepherd, Mangiamelo, calculating as an arithmetical machine, at five years old. We have Mozart executing a sonata with his four-years-old fingers, and composing an opera at eight. We have Theresa Milanollo playing the violin with such art and skill, at four years old, that Baillot said she must have played the violin before she was born. We have Rembrandt drawing like a master of the art, before he could read. Etc., etc. Every one remembers these examples, but it must be borne in mind that they do not constitute exceptions. They only represent a general fact, which in these particular cases was so prominent as to attract public attention. They are valuable as exponents to the public of a fundamental law of nature, the diversity of natural faculties and aptitudes, and the predominance of particular faculties among certain children. Children endowed with these extraordinary and precocious vocations are called _little prodigies_. This qualification is sometimes used in a depreciatory sense, for the little prodigies are accused of failing to carry out the promises of their childhood; it is observed that the brilliant abilities of their early years have not been guarantees of extraordinary success in their careers as grown men. A child, whose drawings were wonderful at four years old, has become a wretched dauber, as an established artist. A musician, who enchanted his audience at eight years old, has grown up a very mediocre performer. This remark is just, and the fact is explicable thus: If the little prodigies have not become great men, it is because they have not cultivated their faculties; because they have allowed sloth and disuse to extinguish their talents. It does not suffice to possess natural abilities for a science, or an art, work and study must strengthen and develop them. Little prodigies are outstripped in their career by hard workers, as is natural. They have come upon earth with remarkable faculties which they had acquired during a previous life, but they have done nothing to develop those faculties, which have remained as they were at the moment of terrestrial birth. The man of genius is the man who unceasingly cultivates and perfects such great natural aptitudes and faculties as he has been endowed with at his birth.