en. I.] MATTER, MOTION, AND FORCE. 283 



namely, energy and velocity. That in each case the force- 

 element is primordial, is shown by the facts that what we 

 cannot conceive as diminished by the compression of matter 

 is not its extension but its power of resistance ; what we 

 cannot conceive as diminished by the retardation of motion is 

 not its velocity but its energy. 



Therefore, in asserting that matter is indestructible and 

 that motion is continuous, we assert, by implication, that 

 force is persistent. Our two fundamental theorems are thus 

 seen to derive their validity from a yet deeper theorem, — the 

 proposition that the force manifested in the knowable uni- 

 verse is constant, can neither be increased nor diminished. 



To this result, which we have here obtained through a 

 general consideration of the problems treated by the abstract- 

 concrete sciences, we shall be equally led by any special ques- 

 tion of molar physics, molecular physics, or chemistry which 

 we may choose to analyze. When we say that the curve 

 described by a cascade in leaping from a projecting ledge of 

 rock is a parabola of which the coordinates express respec- 

 tively the momentum of the water and the intensity of 

 gravity at the verge of the ledge ; or when we say that the 

 line followed by any solid body, drawn by two differently 

 situated forces, is the diagonal of a parallelogram of which 

 the sides express the respective intensities of the forces ; the 

 validity of our assertion depends entirely upon the postulate 

 that the forces in question are constant in amount. Annihi- 

 late a single unit of force, and our proposition is hopelessly 

 falsified. Similarly in molecular physics, when we enunciate 

 the formula by means of which Joseph Fourier founded the 

 mathematical theory of heat — namely, the formula that, in 

 all cases of radiation and conduction, the therm ological action 

 between two bodies is proportional to the difference of their 

 temperatures — we imply that action and reaction are always 

 equal between the systems of molecules which compose the 

 two bodies. And the equality of action and reaction between 



