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



reference which fulfils a certain condition but that we do not 

 know where its origin is or how its axes point. This is very like 

 saying that there is an absolute space in which bodies move, or 

 that bodies have absolute positions, but that we never can know 

 what those absolute positions are. It is equivalent to denying 

 the relativity of motion. 



Now if we content ourselves with a statement of the Law of 

 Gravitation as an abstract formula representing observed facts, 

 it will take the form given to it in Article 97, viz.: &quot;If the 

 frame of reference has its origin at the centre of inertia of the 

 Solar System, and its lines of reference determined by stars so 

 remote as to have no observable annual parallax, the force between 

 two particles within the system is ymm /r*, where m and m are 

 the masses of the particles and r is their distance.&quot; 



The law thus applies to forces within a particular system 

 which can be treated as independent (Article 286). The similarity 

 of chemical constitution of the bodies outside the solar system 

 and of those within it suggests that the law probably has an 

 application to such bodies as well. It is thus suggested that, for 

 any system of bodies which can be treated as isolated, the force 

 between two particles is expressed by the law of gravitation when 

 their motions are referred to a frame whose origin is at the centre 

 of inertia of the system and whose axes point to bodies external 

 to the system and at sufficiently great distances. 



With the understanding referred to in Article 97, that the law 

 applies only to particles at measurable distances, the above is 

 probably the most general statement that we can rnake. The law 

 as extended to bodies outside the solar system is not proved to be 

 an expression of facts of observation. For example, in the motions 

 of double stars, the relative paths are oval curves, but they are 

 not proved to be ellipses, nor is there any evidence to show that 

 one component star occupies a focus of the path of the other 

 relative to itf. On the other hand there are no facts of observa 

 tion in this department of Astronomy which conflict with the 

 proposed extension of the law to bodies outside the solar system. 



*290. Measurement of Time. Relatively to the stars the 

 Earth rotates about its polar axis as we have explained in 



t See Tisserand, Mecanique Celeste, Tome i., Chapter 1. Paris, 1889. 



