100 Dr. J. E. Mills on the Relation of 



of m 2 , while itself had become a mere particle. This relative 

 orbit will in all respects be like the actual one around the 

 centre of gravity, only magnified in the proportion 



<y~ii . I,, ryv\ 



— = -. To reduce the relative orbit of m 1 to the true 



m 2 



orbit, the proportions of the relative orbit must therefore be 



multiplied by — . The velocity v* of 777,1 obtained at 



1 J m^+m 2 



any point of its relative orbit must be multiplied by the same 



factor in order to obtain its true velocity. In order to obtain 



the true energy Ej of m l its velocity squared at any point of 



its relative orbit must be multiplied by ^ 7 — 2 -.,. Similar 



relations hold for the motion of particle m 2 around the centre 

 of m v 



6. The force governing the motion of the two bodies can 

 therefore be regarded as proceeding from the centre of either 

 body, the other being reduced to a mere particle, and the 

 force would be measured by 



/= _*^ = - (4) 



€ is used to denote k{m 1 -\-m 2 ). Later in this article I speak 

 of this centre of force as the centre of mass. This is not, 

 strictly speaking, correct, but the transformation is easily 

 made as already described. 



7. Since energy — \f.ds, the energy changes involved in 

 bringing the particles from distance s 2 to distance s 1 is 



p>, m im2 (1 1\ 



1 A: — — . ds — km x m 2 1 — — — }. 



(5) 



If s 2 = co then this expression becomes — 1 — 2 . That is to 



say, the energy given out as two bodies approach each other, 

 multiplied by the distance apart of the bodies, is equal to a 

 constant which depends on the product of the masses of the 

 two bodies : 



E^ .s = hnim 2 (6) 



8. If we consider the mutual interaction of two bodies in 

 space we might consider that the force acting between these 

 bodies was of a mutual character, and that it acted con- 

 tinuously on both bodies. The question, Will the same 



