103 







( rfi+n. / ffgip^ .dip, \"\-^/dip,Y'\ 



f , 



Now, if we differentiate F as a function of the three independent 

 variables a, /S^ 2r,, we have by (B) and (I), ,^j „ ^^ ., 



J r rfF dV 



we have also V z= (ji^z^ — i^W-"^ , when «^, ^,, vanish ; and therefore, 



z, being considered as constant in the integrations, and the integrals 

 being so determined as to vanish with a^, j8^. Substituting in this 

 expression (N), the developments of a, (2, and performing the inte- 

 grations, we find the following development for - j 



- = z,- wm + ^ |(z, -}. ^) «/ + (z," + B) ^;} 



4. 2 * " </«," dJF V t^*, ^/3/ V d^^ \d^' / . /Q) 



M'hich is another form for the integral of the partial differential 

 equation (J), obtained from the elimination (D). And if we wish 

 to introduce any other rectangular coordinates x, y, z, into the ex- 



