a maximum. There is a certain load which the ani, mal is barely able to support, but unable to move with any useful speed. On the other hand, there is a certain speed, at which the animal is barely able to move his own body, but unable to support any useful load. In both these cases, his useful effect as an agent of labour, vanishes; and between these limits, it varies according to different proportions. An empyrical formula, assigned by Euler, and quoted by numerous mechanical writers, comes perhaps sufficiently near the practical effects for our purposes.[1] Let us suppose that the greatest speed of which a horse is capable when unloaded, is fifteen miles an hour, and the greatest load which he is capable of bearing without moving with any useful speed, to be divided into 225 equal parts;—then the load which he is capable of bearing at fourteen miles an hour, will be one of these equal parts; that which he is capable of bearing at thirteen miles an hour will be four of these parts; at twelve miles an hour, nine of them, and so on; the load being expressed by the squares of the successive integer numbers increasing as the speed with which he moves is decreased. By multiplying the load by the speed, the useful effect is obtained; and by this mode of calculation, it would follow that the greatest effect of horse power is obtained when the animal moves at one third of that rate which is the greatest of which he is capable when unloaded; and that the load which he bears at that speed will be four-ninths of the greatest load which he is capable of bearing with any useful motion for two hours. From this we may infer generally, that in the use of animal
- ↑ Let L be the greatest load which the horse can bear without moving, and V his greatest speed without a load; then if x be any load, and y the corresponding speed, we shall have
