The investigation of the relations which subsist amongst various physical quantities, and which are exemplified in the different transformations of energy, is one of the most interesting investigations in the whole range of physics. On the other hand, the mathematical methods which are usually employed for this purpose are of such a nature as to be unavailable to any who are unacquainted with higher mathematical methods. It is one of the objects of the present note to point out how these relations may be worked out by means of the most elementary methods. For the notation of the calculus, though used below as a matter of convenience, is quite unnecessary, since we might use, e.g., small and capital type of the same letter to denote quantities of the same kind of different magnitudes.