and on the Definitions of Physical Quantities. 91 



energy " and " potential energy," that which otherwise would be 

 a truism becomes a fact. 



13. A definition can neither be true nor false ; for it makes no 

 assertion, but says, " let such a word or phrase be used in such a 

 sense; w but it may be real or fantastic, according as the descrip- 

 tion contained in it corresponds or not to real objects and phe- 

 nomena; and when by the aid of experiment and observation a 

 set of definitions have been framed which possess reality, preci- 

 sion, and completeness, the investing of a physical fact with the 

 appearance of a truism is often an unavoidable consequence of 

 the use of the terms so defined. 



14. In the case of physical quantities in particular, the defini- 

 tion involves a rule for measuring the quantity; and the proof 

 of the reality of the definition is the fact that the application of 

 the rule to the same quantity under different circumstances gives 

 consistent results, which it would not do if the definition were 

 fantastic ; and hence the definitions of a set of physical quantities 

 necessarily involve mathematical relations amongst those quanti- 

 ties, which, when expressed as propositions and compared with 

 the definitions, wear the appearance of truisms and are at the 

 same time statements of fact. 



15. In illustration of the foregoing principles, it may be 

 pointed out that there is a certain set of definitions of the mea- 

 surement of time, force, and mass which reduces the laws of mo- 

 tion to the form of truisms: thus — 



I. Let " equal times " mean the times in which a moving body 

 under the influence of no force describes equal spaces. This defi- 

 nition is proved to be real by the fact that times which are equal 

 when compared by means of the free motion of one body, are 

 equal when compared by means of the free motion of any other 

 body. If the definition were fantastic, times might be equal as 

 measured by the free motion of one body, and unequal as mea- 

 sured by that of another. 



II. Let "force " mean a relation between a pair of bodies 

 such that their relative velocity changes or tends to change in 

 magnitude or direction, or both ; and let " equal forces " mean 

 those which act when equal changes of the relative velocity of a 

 given pair of bodies occur in equal times. This definition is 

 proved to be real by the fact that the comparative measurements 

 of forces made in different intervals of time are consistent with 

 each other, which would not be the case if the definition were 

 fantastic. 



III. Let the "mass" of a body mean a quantity inversely 

 proportional to the change of velocity impressed on that body in 

 a given time by a given force. This definition is proved to be 

 real by the fact that the ratio of the masses of two given bodies 



