454 



The author has next proceeded to examine the hypothesis 

 that the internal moments of the system may be represented 

 by the variation of a single function V. He finds that in this 

 case the number of constants in the equations of motion will 

 be reduced to thirty-six. This agrees with the result obtained 

 by Mr. Haughton. 



The author has also obtained this important result : 

 If F be a quadratic function of the nine quantities, 



dZd^d^dri^dvdridZdZdK 

 dx dy' dz dx' dy' dz dx' dy* d£ 



such that the internal moments of a system or body whose 

 particles act independently may be represented by 



\\\lVdxdydz, 



that part of the function which involves the products, 



d^dr, d^dK ^^^^ 

 dx' dy^ dx' dy^ 

 must be of the form 



\dx dy dy dx/ \dx dy dy dx) 



It is plain, then, that the coefficients of the several terms in 

 Fare not independent of one another, and cannot therefore 

 be arbitrarily assumed. In fact there are among these coeffi- 

 cients nine equations of condition, whose existence is a ne- 

 cessary consequence of the hypothesis of independent action. 

 Now neither the function used by Professor Mac CuUagh, 

 nor that used by Mr. Green, satisfy these conditions. The 

 author infers, therefore, that in media such as these writers 

 suppose the ether to be, the state of each particle, i. e. its 

 absolute power of producing motion in another particle, is 

 changed by the displacement of the surrounding particles. 



The author has then proceeded to investigate the equa- 

 tions of motion on this more extended supposition. He finds 



