If it were so, we could nevertheless, by observation of the _relative_ motions of the heavenly bodies, measure the masses of these bodies. But have we the right to admit the hypothesis of central forces? Is this hypothesis rigorously exact? Is it certain it will never be contradicted by experiment? Who would dare affirm that? And if we must abandon this hypothesis, the whole edifice so laboriously erected will crumble. We have no longer the right to speak of the component of the acceleration of _A_ due to the action of _B_. We have no means of distinguishing it from that due to the action of _C_ or of another body. The rule for the measurement of masses becomes inapplicable. What remains then of the principle of the equality of action and reaction? If the hypothesis of central forces is rejected, this principle should evidently be enunciated thus: the geometric resultant of all the forces applied to the various bodies of a system isolated from all external action will be null. Or, in other words, _the motion of the center of gravity of this system will be rectilinear and uniform_. There it seems we have a means of defining mass; the position of the center of gravity evidently depends on the values attributed to the masses; it will be necessary to dispose of these values in such a way that the motion of the center of gravity may be rectilinear and uniform; this will always be possible if Newton's third law is true, and possible in general only in a single way. But there exists no system isolated from all external action; all the parts of the universe are subject more or less to the action of all the other parts. _The law of the motion of the center of gravity is rigorously true only if applied to the entire universe._ But then, to get from it the values of the masses, it would be necessary to observe the motion of the center of gravity of the universe. The absurdity of this consequence is manifest; we know only relative motions; the motion of the center of gravity of the universe will remain for us eternally unknown. Therefore nothing remains and our efforts have been fruitless; we are driven to the following definition, which is only an avowal of powerlessness: _masses are coefficients it is convenient to introduce into calculations_. We could reconstruct all mechanics by attributing different values to all the masses. This new mechanics would not be in contradiction either with experience or with the general principles of dynamics (principle of inertia, proportionality of forces to masses and to accelerations, equality of action and reaction, rectilinear and uniform motion of the center of gravity, principle of areas).