Such is the gift of the calculating boys who now and then make their appearance, who seem to have certain short-cuts to conclusions, which they cannot explain to themselves. Some are said to have been able to determine off-hand what numbers are prime,—numbers, I think, up to seven places. In a very different subject-matter, Napoleon supplies us with an instance of a parallel genius in reasoning, by which he was enabled to look at things in his own province, and to interpret them truly, apparently without any ratiocinative media. “By long experience,” says Alison, “joined to great natural quickness and precision of eye, he had acquired the power of judging, with extraordinary accuracy, both of the amount of the enemy’s force opposed to him in the field, and of the probable result of the movements, even the most complicated, going forward in the opposite armies.... He looked around him for a little while with his telescope, and immediately formed a clear conception of the position, forces, and intention of the whole hostile array. In this way he could, with surprising accuracy, calculate in a few minutes, according to what he could see of their formation and the extent of the ground which they occupied, the numerical force of armies of 60,000 or 80,000 men; and if their troops were at all scattered, he knew at once how long it would require for them to concentrate, and how many hours must elapse before they could make their attack.(27)” It is difficult to avoid calling such clear presentiments by the name of instinct; and I think they may so be called, if by instinct be understood, not a natural sense, one and the same in all, and incapable of cultivation, but a perception of facts without assignable media of perceiving. There are those who can tell at once what is conducive or injurious to their welfare, who are their friends, who their enemies, what is to happen to them, and how they are to meet it. Presence of mind, fathoming of motives, talent for repartee, are instances of this gift. As to that divination of personal danger which is found in the young and innocent, we find a description of it in one of Scott’s romances, in which the heroine, “without being able to discover what was wrong either in the scenes of unusual luxury with which she was surrounded, or in the manner of her hostess,” is said nevertheless to have felt “an instinctive apprehension that all was not right,—a feeling in the human mind,” the author proceeds to say, “allied perhaps to that sense of danger, which animals exhibit, when placed in the vicinity of the natural enemies of their race, and which makes birds cower when the hawk is in the air, and beasts tremble when the tiger is abroad in the desert.(28)”