Temperature and Molecular Attraction. 99 



of gravitation shows how this total force is distributed among 

 various masses. In considering the problem of two bodies 

 it will greatly shorten the necessary discussion to consider 

 that they are governed by the gravitational law of force, 

 since the consequences of both laws, so far as they concern 

 the point under discussion, are identical. The problem of two 

 bodies under the influence of the gravitational attraction has 

 of course been completely solved, and the relations pointed 

 out below are therefore not new. But certain of the appli- 

 cations made of these recognized mechanical consequences 

 are new so far as I am aware. At any rate it is certain that 

 the idea that molecular attraction is affected by temperature 

 is so widespread, and has been considered sucli a necessary 

 deduction from so many facts, that every precaution must 

 be taken to set forth clearly their true relationship. For 

 this reason I state the various steps involved, though leaving 

 the reader to obtain the proof of the more fundamental 

 statements from any suitable work on analytical or celestial 

 mechanics. 



It will be assumed that the two bodies are spheres and 

 homogeneous in concentric layers. It will also be assumed 

 that the two bodies, and every particle of the two bodies, are 

 subject to the action of a force /, which obeys the law of 

 gravitation as proposed by Newton : 



f=-k^p, (3) 



where m-^ and m 2 are the masses of the two attracting particles, 

 s is their distance apart, and k is a constant. It can then be 

 shown that : — 



1. The attraction of the two bodies will act as though it 

 proceeded from the centres of the spheres, and will be pro- 

 portional to the respective masses of the spheres, and will 

 vary inversely as the square of their distance apart. 



2. Whatever the relative motion of the two spheres may 

 become, the centre of mass of the two spheres will retain its 

 original condition, remaining either at rest or moving in a 

 straight line with constant speed. 



3. The force of attraction will cause the two bodies to 

 describe similar conies around their common centre of 

 gravity. 



4. The motion of one body with respect to the other is in 

 a plane passing through the centre of the other. 



5. The mass mj will move with reference to the centre of 

 mass m 2 preciselv as if its mass had been added to the mass 



H2 



