286-288] RELATIVITY OF FORCE. 363 



varying inversely as the cube of the distance ; in Article 198 

 we noticed a transformation from one law of central acceleration 

 to another. 



Now it is one of our Postulates that accelerations are 

 produced by interactions between bodies, and the choice of the 

 frame of reference is restricted by the condition that the accelera- 

 tions of the parts of a system must be such as reduce to com- 

 ponents in the lines joining the particles. This condition is 

 however in general extremely difficult of application, and we 

 make use of the possibility of changing the acceleration by 

 changing the frame of reference to* simplify the description of 

 motions. 



We refer the motion to be described to such a frame among 

 possible frames that the description of the observed motion may 

 be more easily brought under such general principles as the Law 

 of Gravitation and the Conservation of Energy than it would be 

 for others. 



To see how this might have been done in a particular case, let 

 us imagine what might have been the course of history in respect 

 of the theory of the motion of falling bodies. Let us suppose 

 that after Galilei's experiments on falling bodies the next con- 

 siderable step was Foucault's pendulum experiment. It would 

 have been known (1) that bodies tend to fall with uniform accele- 

 ration in a vertical direction, (2) that this statement is not exact, 

 but, at any rate in one case there is, for a supported body, a 

 westerly component acceleration as well as a vertical component 

 (Example 7, p. 360). Further, if the fact of the eastward deviation 

 of a falling body (Article 281) had been observed, it would have 

 been known that for another case there was, for an unsupported 

 body, an easterly component as well as a vertical component. It 

 is also perfectly possible that it might have been found that, 

 relative to lines of reference pointing to fixed stars, the accelera- 

 tion in all such cases was simply directed to the Earth's centre. 

 It would then have appeared much simpler to choose such lines of 

 reference for the description of the motion in terms of acceleration 

 than to choose axes fixed in the Earth. 



*288. Relativity of Force and Conservation of Momen- 

 tum. The theory of the relativity of force makes it necessary 



