"To unfold our conceptions by means of definitions has never been serviceable to science, except when it has been associated with an immediate use of the definitions. The endeavour to define a Uniform Force was combined with the assertion that gravity is a uniform force: the attempt to define Accelerating Force was immediately followed by the doctrine that accelerating forces may be compounded: the process of defining Momentum was connected with the principle that momenta gained and lost are equal: naturalists would have given in vain the definition of Species which we have quoted, if they had not also given the characters of species so separated.... Definition may be the best mode of explaining our conception, but that which alone makes it worth while to explain it in any mode, is the opportunity of using it in the expression of truth. When a definition is propounded to us as a useful step in knowledge, we are always entitled to ask what principle it serves to enunciate."
In giving, then, an exact connotation to the phrase, "an uniform force," the condition was understood, that the phrase should continue to denote gravity. The discussion, therefore, respecting the definition, resolved itself into this question, What is there of an uniform nature in the motions produced by gravity? By observations and comparisons, it was found, that what was uniform in those motions was the ratio of the velocity acquired to the time elapsed; equal velocities being added in equal times. An uniform force, therefore, was defined, a force which adds equal velocities in equal times. So, again, in defining momentum. It was already a received doctrine, that when two objects impinge upon one another, the momentum lost by the one is equal to that gained by the other. This proportion it was deemed necessary to preserve, not from the motive (which operates in many other cases) that it was firmly fixed in popular belief; for the proposition in question had never been heard of by any but the scientifically instructed. But it was felt to contain a truth: even a superficial observation of the phenomena left no doubt that in the propagation of motion from one body to another, there was something of which the one body gained precisely what the other lost; and the word momentum had been invented to express this unknown something. The settlement, therefore, of the definition of momentum, involved the determination of the question, What is that of which a body, when it sets another body in motion, loses exactly as much as it communicates? And when experiment had shown that this _something_ was the product of the velocity of the body by its mass, or quantity of matter, this became the definition of momentum.