3i8 



THE GRAMMAR OF SCIENCE 



C is introduced into the presence of A and B ? This prob- 

 lem may be put a little differently, thus : Suppose we 

 find when A and B are alone in the field that the accelera- 

 tion of A due to B is represented by the step b, and that 

 when A and C are alone in the field the acceleration of 

 A due to C is represented by the step c, then when both 

 B and C are in the field will these accelerations remain 

 the same, and consequently will the total accelerating 

 effect of B and C be represented, owing to the law we 

 have stated for combining accelerations (p. 236), by the 

 diagonal step d of the parallelogram, whose sides are b 

 and <:? Or, on the other hand, are we to conceive that 

 when B and C are both in the field the former accelera- 

 tion b due to B is altered to b' and the acceleration c due 



^^ 



Fig. 24. 



to C to d , so that the total acceleration of A is now the 

 diagonal d' ? Clearly if the latter statement be correct 

 the synthesis of motion becomes much more complex. 

 It will still be true that the acceleration of A is com- 

 pounded of the accelerations due to B and C, but these 

 accelerations will depend not on the respective positions 

 of B and C relative to A, but on the configuration of the 

 entire system A, B, C. It will thus be impossible to form 

 complex motions from the combination of simple ones, 

 until we have determined how the actions b and c of B 

 and C alone are modified into b' and ^ by being super- 

 posed. Now this question may also be looked at from 

 the standpoint of force. If m be the mass of A, then 

 m X b and m x c will be the forces of B and C on A, and 

 will be represented by steps in times the steps b and c in 



