upwards without any effort on our part, and we shall certainly be doing no work by carrying it one or more metres in height—it will, in reality, help to pull us up, instead of requiring help from us to cause it to ascend. In fine, what we have said is meant to refer to the force of gravity alone, without taking into account a resisting medium such as the atmosphere, the existence of which need not be considered in our present calculations.
31. It should likewise be remembered, that while the energy of a moving body depends upon its velocity, it is independent of the direction in which the body is moving. We have supposed the body to be shot upwards with a given velocity, but it might be shot horizontally with the same velocity, when it would have precisely the same energy as before. A cannon ball, if fired vertically upwards, may either be made to spend its energy in raising itself, or in piercing through a series of deal boards. Now, if the same ball be fired horizontally with the same velocity it will pierce through the same number of deal boards.
In fine, direction of motion is of no consequence, and the only reason why we have chosen vertical motion is that, in this case, there is always the force of gravity steadily and constantly opposing the motion of the body, and enabling us to obtain an accurate measure of the work which it does by piercing its way upwards against this force.
32. But gravity is not the only force, and we might
