MOTION, FORCE, MATTER 331 



but the comparison may be presumed to hold only in case 

 there is no other factor of variation. However, there is just 

 such a factor. To refer a moment to the empirical level, 

 where there is contact with an observer and where forces 

 may therefore be felt, acceleration is not an accurate measure 

 of force. Greater force is exerted by a moving baseball than 

 by a moving tennis ball, though they have the same velocity; 

 and greater force is required to set an automobile in motion 

 than a bicycle. This further property of particles is called 

 mass, which Newton endeavored to clarify by calling it 

 "quantity of matter." Force, then, may be defined as 

 equivalent to the product of the mass by the acceleration, 

 f = m a. This is the basic equation of mechanics. 



In summary, then, force as it functions in science may be 

 described as a property of particles; its measured value is a 

 vector quantity, and it is universally correlated with (a) a 

 similar property, equal in intensity but opposite in direction, 

 and (b) two other properties known as mass and acceleration 

 by means of which it is measured. 



force: operational derivation 



The search for a definition of force which will meet the 

 needs of science has been the attempt to find a satisfactory 

 criterion for locating and measuring forces. However realistic 

 one may be in his attitude toward forces, he is compelled to 

 admit that their empirical definition in terms of pushes, 

 pulls, pressures, resistances, and the like — all of which imply 

 contact between an observer and an object — is both too 

 vague and too narrow to function adequately in science. Such 

 a definition is especially vague because it offers no technique 

 for measuring accurately the intensity and direction of 

 forces. But it is vague also because it confuses a large group 

 of "forces" all of which, to be sure, exhibit common features, 

 but which show also important differences and require 

 therefore to be distinguished. Furthermore, the definition is 

 too narrow because it implies, indirectly at least, that forces 

 can be known to be present only when the objects to which 



