FOKCE 677 



the second, as required by the law of inertia) . We know that by intro- 

 ducing 3n variable auxiliaries, a system of 3n equations of the fourth 

 order may be reduced to a system of 6n equations of the second order. 

 If, then, we suppose that the 3n auxiliary variables represent the co- 

 ordinates of n invisible molecules, the result is again conformable to 

 the law of inertia. To sum up, this law, verified experimentally in 

 some particular cases, may be extended fearlessly to the most general 

 cases; for we know that in these general cases it can neither be con- 

 firmed nor contradicted by experiment. 



The Law of Acceleration. The acceleration of a body is equal to 

 the force which acts on it divided by its mass. 



Can this law be verified by experiment? If so, we have to measure 

 the three magnitudes mentioned in the enunciation : acceleration, force, 

 and mass. I admit that acceleration may be measured, because I pass 

 over the difficulty arising from the measurement of time. But how 

 are we to measure force and mass? We do not even know what they 

 are. What is mass ? Newton replies : " The product of the volume 

 and the density." " It were better to say," answer Thomson and Tait, 

 " that density is the quotient of the mass by the volume." What is 

 force ? " It is," replies Lagrange, " that which moves or tends to 

 move a body." " It is," according to Kirchoff, " the product of the 

 mass and the acceleration." Then why not say that mass is the quo- 

 tient of the force by the acceleration? These difficulties are insur- 

 mountable. 



When we say force is the cause of motion, we are talking metaphy- 

 sics ; and this definition, if we had to be content with it, would be 

 absolutely fruitless, would lead to absolutely nothing. For a defini- 

 tion to be of any use it must tell us how to measure force; and that 

 is quite sufiicient, for it is by no means necessary to tell what force 

 is in itself, nor whether it is the cause or the effect of motion. We 

 must therefore first define what is meant by the equality of two 

 forces. When are two forces equal? We are told that it is when they 

 give the same acceleration to the same mass, or when acting in oppo- 

 site directions they are in equilibrium. This definition is a sham. A 

 force applied to a body cannot be uncoupled and applied to another 

 body as an engine is uncoupled from one train and coupled to an- 

 other. It is therefore impossible to say what acceleration such a force, 

 applied to such a body, would give to another body if it were applied 

 to it. It is impossible to tell how two forces which are not acting in 

 exactly opposite directions would behave if they were acting in oppo- 

 site directions. It is this definition which we try to materialize, as 

 it were, when we measure a force with a dynamometer or with a bal- 

 ance. Two forces, F and F', which I suppose, for simplicity, to be 

 acting vertically upwards, are respectively applied to two bodies, C 

 and f '. T attach a body weighing P first to C and then to C'; if 



