Page:System of Logic.djvu/477

 the proper definition of the _measure of force_. A principal question in the classification of minerals is, what is the definition of a mineral species. Physiologists have endeavored to throw light on their subject by defining organization, or some similar term." Questions of the same nature were long open and are not yet completely closed, respecting the definitions of Specific Heat, Latent Heat, Chemical Combination, and Solution.

"It is very important for us to observe, that these controversies have never been questions of insulated and arbitrary definitions, as men seem often tempted to imagine them to have been. In all cases there is a tacit assumption of some proposition which is to be expressed by means of the definition, and which gives it its importance. The dispute concerning the definition thus acquires a real value, and becomes a question concerning true and false. Thus, in the discussion of the question, What is a uniform force? it was taken for granted that gravity is a uniform force. In the debate of the vis viva, it was assumed that in the mutual action of bodies the whole effect of the force is unchanged. In the zoological definition of species (that it consists of individuals which have, or may have, sprung from the same parents), it is presumed that individuals so related resemble each other more than those which are excluded by such a definition; or, perhaps, that species so defined have permanent and definite differences. A definition of organization, or of some other term which was not employed to express some principle, would be of no value.

"The establishment, therefore, of a right definition of a term, may be a useful step in the explication of our conceptions; but this will be the case then only when we have under our consideration some proposition in which the term is employed. For then the question really is, how the conception shall be understood and defined in order that the proposition may be true.

"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 endeavor 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, "a 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 a 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. A 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 proposition it was deemed necessary to preserve, not from the motive (which operates in