330 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



nor in uniform motion in a straight line) exhibits force." 

 The law then states merely that force may be defined with 

 reference to something with which it is uniformly associated. 

 In other words, it is part of the meaning of force that it 

 should be associated with change of motion. 



But although this law tells one essentially what is meant 

 by force in terms of one of its important correlates, it does 

 not afford a means for measuring force. If the important 

 scientific statements about force are expressed in mathe- 

 matical equations, the notion must function in science not 

 as a quality but as a quantity. The quantitative character 

 of force is described in the second and third laws. These 

 state that force is capable of intensive variation, and that it 

 exhibits a directional feature. Hence force, as motion, is a 

 vector quantity. Forces then become numbers of certain 

 kinds and can be operated upon according to the laws of 

 vectoral calculation. 



Specifically, the second law is presumed to afford a tech- 

 nique for measuring force intensity in terms of change of 

 motion. Change of motion is capable of measurement 

 through meter rods and clocks, and does not require the 

 observer to be in contact with the moving object. Hence 

 precision can be achieved, and anthropomorphism avoided. 

 Change of motion is a somewhat more complicated function 

 of space and time than mere motion. Just as the latter is 

 the quotient of space over time, the former is the quotient 

 of this quotient over time, i.e., the time-rate of change of 

 velocity. This is called acceleration. The third law affords 

 no technique for measuring force. It does state, however, an 

 important fact about forces, viz., that they always occur in 

 pairs, not singly. Though these two forces are equal in 

 magnitude, they are opposite in direction; hence they are 

 different vectoral quantities. 



However, although the second law states a proportionality 

 between force and acceleration, it does not state an eguiva- 

 lence. It affords a means for comparing two forces through 

 the respective accelerations with which they are associated, 



