MOTION, FORCE, MATTER 335 



means of mass, he can do so only by means of certain forces. 

 The humiliating outcome is that one can measure force only 

 by measuring force. 



The second attempt involves, if not a complete abandon- 

 ment of the empirical reference, at least the recognition 

 that mass may be a somewhat obscure and complex prop- 

 erty of events. From this point of view mass is considered 

 not to refer descriptively to any clearly given type of force- 

 experience. It is defined, rather, as a construct from the data, 

 and can be said to be given only in the sense that it is re- 

 quired to make certain experimental situations intelligible. 

 It is a property which "is ascribed to a body in order to 

 represent the results of experiments on the body. We are 

 acquainted with the phenomenon in the experiment, and 

 know the measure which we assign to the body, but we do not 

 appear to be acquainted with the property ascribed to the 

 body." 1 If the extreme conventionalism of Poincare's 

 position can, for the moment, be neglected, the view which 

 is here being maintained can be formulated in his words: 

 "Masses are coefficients it is convenient to introduce into calcula- 

 tions" 2 The fact of convenience prevents this from being a 

 purely nominal definition. It can be restated so as to elimi- 

 nate the tinge of arbitrariness by saying that masses are 

 coefficients determined by certain complicated experiments 

 on bodies, and by means of which other important prop- 

 erties may be demonstrated. The best example of this 

 attempt to define mass is that first given by Mach, 3 and 

 reproduced with some modifications by Lindsay and Mar- 

 genau. 4 In this approach mass is defined in terms of accelera- 

 tion, but in terms of a complicated function of the latter. 

 Given two bodies, A and B, each exhibiting an acceleration 

 toward the other, one may set up the function represented 

 by the quotient of these accelerations; experiment shows this 

 to be a constant, and it may therefore be presumed to be 

 some sort of property possessed by the bodies; this property 



1 V. F. Lenzen, Physical Theory, p. 111. 2 Foundations of Science, p. 102. 



3 Science of Mechanics (Chicago: Open Court, 1893), pp. 216-222. 



4 Foundations of Physics, pp. 91-94. 



