It is this definition we try to materialize, so to speak, when we measure a force with a dynamometer, or in balancing it with a weight. Two forces _F_ and _F'_, which for simplicity I will suppose vertical and directed upward, are applied respectively to two bodies _C_ and _C'_; I suspend the same heavy body _P_ first to the body _C_, then to the body _C'_; if equilibrium is produced in both cases, I shall conclude that the two forces _F_ and _F'_ are equal to one another, since they are each equal to the weight of the body _P_. But am I sure the body _P_ has retained the same weight when I have transported it from the first body to the second? Far from it; _I am sure of the contrary_; I know the intensity of gravity varies from one point to another, and that it is stronger, for instance, at the pole than at the equator. No doubt the difference is very slight and, in 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_.