336 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



may be called mass. For example, the mass of B with 

 respect to A is defined as the acceleration of A with respect 

 to B divided by the acceleration of B with respect to A, viz., 

 Q>ab! — clba = Mb A> The mass of A with respect to B is the 

 reciprocal of this. If the accelerations are equal the masses 

 are equal, and if they are unequal the masses are unequal. 

 By arbitrarily defining one of the bodies, say A, as a unit 

 body, the mass of B becomes a fixed number. By this method 

 numbers can be found which may be attached to all bodies. 

 These numbers constitute the measured values of masses, 

 and function accordingly in the equations of mechanics. 

 All that should be emphasized here is that mass does not, 

 according to this approach, refer descriptively to any 

 immediately given force-experience. A quotient of accelera- 

 tions is hardly one of the psychological simples of percep- 

 tion. Alternative definitions of mass, which are essentially 

 constructive like the one given, are the attempts of Lenzen l 

 and Broad 2 to define mass through certain constant prop- 

 erties of bodies as they behave under impact. 



In conclusion, then, the most significant feature of the 

 operational derivation of the concept of force is the invention 

 of a technique for measuring force. This requires the con- 

 struction (or the somewhat obscure discernment in the given) 

 of a property of bodies called "mass," which is capable of 

 measurement and affords the required technique. Force is 

 then measured by the product of mass and acceleration, 

 both of which are independently measurable. Many of the 

 complications of this technique have, of course, been omitted. 

 For example, the proportionality of mass to weight permits 

 one to substitute the direct measurement of the latter by 

 means of balances for the indirect measurement of the former. 

 But this method could not be employed as a definition of 

 mass, for then the difference between mass and weight would 

 be lost. Complications of this kind require more detailed 

 analysis than has been possible in this somewhat superficial 

 treatment. 



1 Physical Theory, pp. 107 el seq. 2 Scientific Thought, pp. 169 el seq. 



