104 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



we have seen to be equivalent to Newton's doctrine asserts that 

 the ratio of the numbers Vi and v\ (if the particles be supposed to 

 start from rest at Piand^i as in the ideal experiment described 

 on p. 100) characterises the behaviour of the two particles 

 throughout the " transaction " ; so that if when the particles are 

 at any other pair of points, P and p, the velocities are V and v, 

 the ratio of the changes in the values of the velocities, i.e., the 

 ratio (V Vi)/(^ ^i) will preserve the value which we have 

 already defined as the inverse ratio of the masses of the particles. 

 It follows from the well-known relations between the velocity of a 

 point, the time it is in movement and the distance through which 

 it passes, that the distances PiP 2 and p\p% will be again in this 

 characteristic ratio ; though their actual values will depend upon 

 the " law " which gives the velocity of one of the points at different 

 distances from the other. It will be clear, in fact, that in 

 general a given pair of these second positions will imply a 

 definite law of this kind ; so that when we have determined 

 two pairs of positions of the particles, such as PI, ?2, and p\ t p 2 , 

 we have the data (namely, the mass ratio and the " law of 

 distance " involved) which are alone necessary to determine the 

 subsequent movements of the particles. Generalizing this 

 result, we reach the conclusion that whenever a particle takes 

 up at a definite moment a definite new point of space its 

 occupation of this point may be regarded as a " taking note " of 

 any two previous configurations of all the points of the universe, 

 including itself, and, therefore, a taking note of all such con- 

 figurations. 



46. 



In view of the fact that we have ascribed only psychological 

 value to the concepts of momentum and force, regarding them 

 merely as instruments for the " economic description " of 

 Objective facts, suspicion may arise that this view of the 

 " causal law " which governs the behaviour of a mass-particle 

 is conventional also, so that if another set of descriptive 



