practise, I shall take no account of it; but a properly constructed definition should have mathematical rigor; this rigor is lacking. What I say of weight would evidently apply to the force of the resiliency of a dynamometer, which the temperature and a multitude of circumstances may cause to vary.
This is not all; we can not say the weight of the body P may be applied to the body C and directly balance the force F. What is applied to the body C is the action A of the body P on the body C; the body P is submitted on its part, on the one hand, to its weight; on the other hand, to the reaction R of the body C on P. Finally, the force F is equal to the force A, since it balances it; the force A is equal to R, in virtue of the principle of the equality of action and reaction; lastly, the force R is equal to the weight of P, since it balances it. It is from these three equalities we deduce as consequence the equality of F and the weight of P.
We are therefore obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.
For recognizing the equality of two forces here, we are then in possession of two rules: equality of two forces which balance; equality of action and reaction. But, as we have seen above, these two rules are insufficient; we are obliged to have recourse to a third rule and to assume that certain forces, as, for instance, the weight of a body, are constant in magnitude and direction. But this third rule, as I have said, is an experimental law; it is only approximately true; it is a bad definition.
We are therefore reduced to Kirchhoff's definition; force is equal to the mass multiplied by the acceleration. This 'law of Newton' in its turn ceases to be regarded as an experimental law, it is now only a definition. But this