288, 289] RELATIVITY OF FORCE. 365 



The direction and sense of this unlocalised vector are fixed 

 relatively to the frame of reference, and might therefore be used 

 to determine one of the lines of reference. 



Thus an independent system presents a natural origin for a 

 frame of reference, viz., its centre of inertia, and one natural line 

 of reference, viz., the axis of resultant moment of momentum. 



The plane through the centre of inertia of an independent 

 system at right angles to the axis of resultant moment of momen- 

 tum is known as the invariable plane. 



This discussion and that in the' last Article show that there 

 are cases of practical importance in which it is possible to deter- 

 mine the frame of reference, at least partly, by dynamical conside- 

 rations. The rule is that among possible frames that one is to be 

 taken for which the field of force has the simplest expression. 



*289. Law of Gravitation. In connexion with the doc- 

 trine of the relativity of force, the matter which is of the greatest 

 importance is the statement of the Law of Gravitation in a 

 precise form. It is not sufficient to say, " The force between two 

 particles is the product of a constant, the masses of the particles, 

 and the reciprocal of the square of the distance between them," 

 for this is just the kind of statement which has no meaning until 

 the frame of reference is specified. 



We shall make some advance towards a more precise state- 

 ment if we say, " There is a frame of reference relative to which 

 the force between two particles of masses m, m' at distance r is 

 ymm'/r 2 " The objection to this statement is that we shall not be 

 able to say where that frame of reference is. Our statement will 

 imply forces between particles in the stars and particles in the 

 solar system, and we shall be unable at present f to fix the 

 position of either a possible origin or the directions of possible 

 axes relative to the sun and stars. Our statement then will 

 either involve a pretence of knowing something which we do not 

 know, or we shall be reduced to saying that there is a frame of 



t The objection needs qualification in view of the fact that it has been suggested 

 that the required frame of reference is presented in the undisturbed position of 

 parts of the luminiferous medium. If an Electrical and Optical Theory on the 

 basis of an ether "at rest" becomes established, it will perhaps be possible to free 

 the statement in the above form from the objection here urged. 



