THE INTERNAL CONSTITUTION OF BODIES. 457 



By making the substitutions in the equation (4) we shall be able to 

 exhibit the result in the following form : 



{_ r [ dr"^ r" ' J i Y dr^ r- dr 



^2^(^-0^(1) 



= ^lL Q^^^ -t!LL ^Q'^^^ 



i d 

 The foregoing equation is satisfied by taking 



This equation is of the same form Avith that proposed (4), except 

 only that i is replaced by i — 1 . If therefore again, in the latter, we put 



r I— I dr 



we shall deduce from it another in terms of Q., in which i — 1 will be 

 replaced by ?' — 2; and by continuing these substitutions we shall finally 

 obtain the equation 



('■) 

 d'Qi (0 



which is integrable by the known methods, and gives 



where T- and V^ may be considered as two arbitrary functions of 9 and 



^ of the order i which satisfy the equation (3). 



(«■) 

 By adopting this value Q^, and by afterwards taking 



('■) 

 (i-i) 1 (0 dQ. 



Q =— Q. — -r-^ 



<-t J- "t( dr 



(i-I) 

 (.■-2) ^1 (f-1) 1 dQ. 



(,-2) 

 (i_3) ^ 1 (i_2) 1 d^ 



