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 definition is still insufficient, for we do not know what mass is. It enables us doubtless to calculate the relation of two forces applied to the same body at different instants; it teaches us nothing about the relation of two forces applied to two different bodies. To complete it, it is necessary to go back anew to Newton's third law (equality of action and reaction), regarded again, not as an experimental law, but as a definition. Two bodies _A_ and _B_ act one upon the other; the acceleration of _A_ multiplied by the mass of _A_ is equal to the action of _B_ upon _A_; in the same way, the product of the acceleration of _B_ by its mass is equal to the reaction of _A_ upon _B_. As, by definition, action is equal to reaction, the masses of _A_ and _B_ are in the inverse ratio of their accelerations. Here we have the ratio of these two masses defined, and it is for experiment to verify that this ratio is constant. That would be all very well if the two bodies _A_ and _B_ alone were present and removed from the action of the rest of the world. This is not at all the case; the acceleration of _A_ is not due merely to the action of _B_, but to that of a multitude of other bodies _C_, _D_,... To apply the preceding rule, it is therefore necessary to separate the acceleration of _A_ into many components, and discern which of these components is due to the action of _B_. This separation would still be possible, if we _should assume_ that the action of _C_ upon _A_ is simply adjoined to that of _B_ upon _A_, without the presence of the body _C_ modifying the action of _B_ upon _A_; or the presence of _B_ modifying the action of _C_ upon _A_; if we should assume, consequently, that any two bodies attract each other, that their mutual action is along their join and depends only upon their distance apart; if, in a word, we assume _the hypothesis of central forces_. You know that to determine the masses of the celestial bodies we use a wholly different principle. The law of gravitation teaches us that the attraction of two bodies is proportional to their masses; if _r_ is their distance apart, _m_ and _m'_ their masses, _k_ a constant, their attraction will be _kmm'_/_r_^{2}. What we are measuring then is not mass, the ratio of force to acceleration, but the attracting mass; it is not the inertia of the body, but its attracting force. This is an indirect procedure, whose employment is not theoretically indispensable. It might very well have been that attraction was inversely proportional to the square of the distance without being proportional to the product of the masses, that it was equal to _f_/_r_^{2}, but without our having _f_ = _kmm'_.