23. The term _transmission_ or _communication_ of motion, which is so much used in physical science, expresses something real so long as limited to the phenomenon which is under calculation; but it would be an absurdity, if it meant that the _same_ motion which was in one body has _passed_ to another. The sum of the quantities of motion is the same in elastic bodies after impact as before it; the velocity being divided between them, and the one gaining what the other loses. This is proved by calculation, and confirmed by experience. But it is evident that one body does not impart the _same_ individual velocity which it contained to the other body; for not only can the velocity not be separated from the body and pass from one subject to another; but it cannot even be conceived except as a relation, the idea of which includes the ideas of a body moved, of space, and of time. It is true that Q representing the quantity of the motion before impact, the value of Q remains the same after impact; but this only expresses the phenomenon in relation to its effects, as subject to calculation; not that the velocity in the second member of the equation is composed of the parts of the first. Let A and B represent two bodies, the individual masses of which are expressed by these two letters; and V, _v_ their respective velocities before impact. The quantity of motion will be Q = A × V + B × _v_. After impact there will be a new velocity which we may call _w_, and the quantity of motion will be Q = A × _w_ + B × _u_. Mathematically speaking, the value of Q will be the same; but this only means that if the results of the motion be expressed in lines or numbers, we shall have the same after impact as before it; it does not and cannot mean that in the velocity _u_, considered as united to the subject, there is a portion of velocity which has been detached from V to be joined to _v_. 24. Hence, we do not conceive the accidents of bodies as possible without a subject in which they are inherent; and that substances are not inherent in another being, but are conceived and really exist without this inherence. A figure cannot exist without a thing figured, but the thing figured may still exist, through all other things are destroyed. The analysis of the nature of substance shows that its existence supposes the existence of another being which produced it; but relation between them is that of cause and effect, not of inherence, or that of the subject and its modification.