102 TH& FUNCTION <j> AND 



If their values are varied, we shall have by differentiation, if 

 n >2 



v=o 



+ dai f*4. e ~e + *<l e + da, f|* <f + V + etc. (323) ' 

 J dci^ J da 2 



V=0 V=Q 



(Since e* vanishes with F", when n > 2, there are no terms due 

 to the variations of the limits.) Hence by (269) 



or, since ^ (325) 







<fy = ^0 - - dox - da, - etc. (326) 



ttCt^ tt^ 



Comparing iliis with (112), we get 



The first of these equations might be written* 



r) < 328 ) 



but must not be confounded with the equation 



d+\ fdf\ (de\ 



^A,~ W W*.. 



which is derived immediately from the identity 



=-\ L\ ( 330 ) 



* See equations (321) and (104). Suffixes are here added to the differential 

 coefficients, to make the meaning perfectly distinct, although the same quan- 

 tities may be written elsewhere without the suffixes, when it is believed that 

 there is no danger of misapprehension. The suffixes indicate the quantities 

 which are constant in the differentiation, the single letter a standing for all 

 the letters a 1} 2 , etc., or all except the one which is explicitly varied. 



