Mr. R. Hargreaves on 



A(/Lt) being the same determinant, viz., 

 latter part of (124) n is written 



J "FT."*.). 



A ll+/>llA*, 



«p«A 



VAOij 



(124),„ 



the variables in u p u A being l x . . . l n . 



The particular case in which p = A gives 



A(^)=A A (1 +/*)» = Aa^Hl + Z*)*, and therefore 

 fifo> 2c w 1 



and 



i 



dco 



n-2' v/A A 



2c, 



(136) 



(137), 



The expression for internal potential deduced as for three 

 dimensions from the value at the centre is 



n 



VA(/t) 



1 



u p{ua) 2 

 The expression for external potential is 

 ~ C dco r 



(»-2)(S/ ,.av) 8 



*]> . (129), 





O-iJffUq-^ 



Wa + /X7/« 



The direct proof of this formula is got by usino- Q37)ra o nr i 

 deducing by differentiation & ^ } ' 



lrhd<0 2Cn a rs 



.f, 



»(n-2)A a v/'A(rt 



It should also be stated that the method by which the 

 theorem akin to Maclaurin's was proved is applicable in n 

 dimensions, and in particular the theorem (98) for the addition 

 ot parameters. In the statement of that theorem the simpler 

 iorm belongs to the variable X. For the purpose of differenti- 

 ation of formulae with regard to A . . ., the use of jul is more 

 convenient ; what is wanted is the simpler result got by 

 taking \A a on both sides of the equations as independent 

 ot A. Ihe dimensions of A, are more convenient for the final 

 physical formulae. 



§ 38 In conclusion it is proposed to demonstrate that the 

 formula established in (130) for the interior of an ellipsoid, 

 is valid tor all uniform volume distributions, and applies to 

 external as well as internal positions. We take the simpler 



