362 RELATIVE MOTION AND UNIVERSAL GRAVITATION. [CH. XIII. 



body would exert no force on the second, and the acceleration 

 of the second body relative to the frame would not be produced 

 by a force arising from interactions between parts of a system. 

 It is one of our Postulates that all accelerations are so produced, 

 and it thus appears that this Postulate implies a restriction upon 

 the position of the origin of the frame of reference. 



To take the same example as before: If the origin of the 

 frame of reference were fixed in the Earth, then any other body 

 would exert zero force on the Earth, and the Earth consequently 

 would not act on the body. The " acceleration due to gravity " 

 could not be regarded as produced by forces exerted by the parts 

 of the Earth on the parts of a falling body. 



We have so far explained and illustrated the relativity of 

 force by showing that, unless the frame of reference is properly 

 chosen, bodies will not have definite masses, and action and re- 

 action will not be equal and opposite. 



We may evade these difficulties by taking the origin at the 

 centre of inertia of a system so remote from all other bodies 

 that it may be considered to be independent of them. Thus 

 for the motion of a body near the Earth's surface it will be 

 sufficient to consider the body and the Earth as such a system ; 

 for the motions of the planets it will be sufficient to consider 

 the solar system as such a system. When however the origin 

 of the frame of reference is taken at the centre of inertia of a 

 system the system must be regarded as independent ; in other 

 words, no meaning could be attached to the phrase "action of 

 external bodies on the system." For example, so long as the 

 origin of the frame of reference is the centre of inertia of the 

 solar system no meaning could be attached to the phrase " force 

 exerted on the Sun by a star." 



*287. Choice of lines of reference. We have seen that a 

 frame of reference is determined by the origin, a line through 

 the origin, and a plane through the line ; and we have recorded, 

 by way of examples and otherwise, a number of theorems re- 

 lating to changes introduced into the descriptions of particular 

 motions by changing the frame of reference. Thus in Example 4, 

 p. 52, and Example 2, p. 186, we noticed a transformation from 

 uniform rectilinear motion to motion with a central acceleration 



