490 DR G. PLARR ON THE DETERMINATION OF 



becomes now 



( Y '-^)a=0. 



The equation — - s — Z = may be easily transformed by the help of the pre- 

 ceding one. 



We have, namely, by § XL, 



Y + Z=-u*W 1 . 

 This gives 



Z = (« 2 W 1 ' + Y')A 



Z = 2(a 2 « 1 2 a 1 6 1 c 1 + a 2 a 1 3 5 2 c 2 )A 



= 'Eaht^b^ + \c 2 )\ 



= — (Sa^&gCg) A . 

 We put 



Z' = '2a 2 a 1 s b 3 c 3 ; 



then the equation in question becomes 



[ z -_^'] A= o. 



Generally we treat the case in which a\ b\ c 2 are different from one another. 

 The equations are therefore 



Y '=! w *' do 



Z ' = >3 • • ... (II.) 



In order to render these equations rational in respect to Sets, So/, &c, we 

 require only one squaring of both members in each equation. This is not 



W 



the case with the equation 2 — ■ = . 



We may put the two equations under the form 



u 3 _yd 2 a } s 

 v ~ a 2 



u s „rt 2 a, 3 



= 2 



w a n 



and remark as a curiosity the relation drawn, as, for example, from the first 



/(Say)3_ v r(q ai )s-| 



V (2«V)~ t(aa s )J' 



so that the second member expresses a certain mean value of the terms 

 appearing in the first member. 



