102 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



of transference of momentum is the complete expression of 

 the " notice " which one particle is taking, at the moment, of 

 the positional changes of the other. 



44. 



We have thus reached by a route partly historical, partly 

 hypothetical, the classical Newtonian position. The concept 

 of a special type of transaction ideally supposed to take place 

 between two mass-particles, is extended in the Newtonian 

 mechanics to account for all happenings in the material world. 

 But to "effect this extension it is necessary to think of the 

 behaviour of a given particle at a given time as an expression 

 of the fact that it is "taking note" of the behaviour of every 

 other particle in the universe. It is obvious that it cannot do 

 so in the simple way which alorie~has been contemplated "by us 

 up to the present the particle cannot exhibit at one and the 

 same time a rate of change of momentum directed along 

 each of the straight lines joining it to the other particles of 

 the universe, and equal in each case to the rate of change of 

 momentum exhibited simultaneously by the particle at the 

 other end of the straight line. "The distinct and general 

 formulation of the principle " by which (in modern terms) 

 the actual ra"be of change of momentum exhibited by 

 the particle is regarded as the " vector sum " of these 

 elementary rates, is one of the " chief advances " which 

 we owe to Newton.* But, as Mr. Eussell has, in effect, 

 pointed out in his penetrating criticism of the Newtonian 

 doctrine,f the acceptance of the vector law involves an important 

 widening of our concept of the way in which one material point 

 may " take note " of the behaviour of others ; for it is clearly 

 only by a convention that we can regard this rate of change of 

 momentum actually presented as the sum of rates of momentum 



* Mach, op. cit., p. 1 92. 

 t Op. cit. t Ch. LV. 



