338 Scientific Proceedings, Royal Dublin Society. 



This may be seen otherwise, by comparing with this equation 



that of the area A, of a plane curve, viz, : A = jydx, which is 



precisely analogous as to its form, and the abstract relations of 

 its constituents. Now, no matter how we interpret the symbols in 

 this latter equation, we cannot say that the y therein is the cause 

 of the area. If y and x be regarded as actual co-ordinates, or 

 right lines, and A as the actual area, y will certainly describe 

 the area, if x increases continuously, carrying y at its end all the 

 while ; but y will be utterly inefficacious otherwise. It is impor- 

 tantly concerned in the description of the area, but that is all. 

 If the equation be interpreted as purely numerical, it is equally 

 impossible to regard y as being in any true sense the cause of A. 



Otherwise thus : — From the very idea of (efficient) cause, it 

 must be regarded as proportional to its effect, if this admit of 

 quantity, " causa wquat effectum." Consequently, if the quanti- 

 tative effect be increasing, the cause must be conceived of as 

 expending itself at the very rate at which the effect increases. 

 Now, the dynamical affair which is expended proportionally 

 with the production of the motion, or momentum, is the imjmlse 

 and not the force concerned. (The force is not expended at all, 

 as we shall see in the next section.) 



(2.) It is the notion that force is the cause of motion which 

 gives rise to the expression, " expenditure of force," so frequently 

 used by dynamicists and physicists. We are told by the highest 

 and latest authority that " force is wholly expended in the 

 Action it produces." But if we reflect upon what we mean by 

 force, as simple pressure or tension, we shall find that it is not 

 capable of being expended; for it cannot be thought of as having 

 quantity, though it has amount, which may be diminished. 

 Again, suppose that a given statical pressure has been exerted 

 by a spring for ten minutes, at the end of that period it is 

 precisely the same as it was at the beginning. It has not been 

 expended in any proper sense of that word. This is equally true 

 whether elastic force depend upon molecular kinetics or not; 

 and it would be true even if there were expenditure of molecular 

 ability, in order to keep up that force, which, it would seem, no 

 one contemplates. 



Similarly with the force or pressure concerned in the produc- 

 tion of motion or momentum. Suppose it to be a constant force 



