il38 



(«' - «) K + (.r - «') v + {a — x) v' -^E-^ = («' — «) F^ 



(^' - i^)Vi-(y- 15') t' + (/?- ^) t'' - ^^ = (i^' - /^) ^.- 



(«' - cc) II + {,v — «') 7i + (« — .r) 7/ + ^ V- = («' — «) ^^y 



8iï 



(6) 



Wlieii we replace ^, V, H, x and // by E„ V„ H^, .r, and ï/j 



ÖF ÖF \ 



rr— 'v-etc. rest unchanged we obtain the corresponding quantities 



O// o.?; / 



1^1.,/, Vi.x, Hi,jj and /7i ^. 



The following relations exist between these eight (piantities, as 

 we nia}^ easily deduce. 



Ei Vy - EVx,, = El V, - EVi,, j 



We liiul another relation by elinniiat'iig E^ and E from both 

 these equations. 



Substituting- in (4) and (5) their values for A, B etc., we find 

 with the aid of (6) : 



E {rt - s') dx — [(«' - a) V,, . s f iii' — (?) F,. t] dP 



- [(«' - «) H, . . + (ii' - i?) ƒƒ,. . q dT 



E, {rt - .s^) dx = [(«' - a) Fi.,/ . .s + (,i' - ji) Fi.., . t] dP 



- [(«' - a)Hu, s + (^' - /?) ƒƒ!.,,. ^] .^7' 

 Eliminating dx from (8) and (9) we find, when we make use of 



the relations (7) : 



E^ E, 



Hi 1/ Hy II\ X ^T" • Ilx 



dP '' E ^ '■=" E 



— = = .... (10) 



^^ V. ^^ V V^ -^ V 



^■•" ~ W • '' '■' E • ' 



Herein Hy, H^ etc. have the meaning indicated in (6) ; from (10) 

 it follows however, that this is also true when the term, in which 

 E or E^ occurs, is omitted in each of the eight relations (6). 



Further we may deduce from (8) and (9) -. 



(8) 

 (9) 



{rt-s^)E[Hi.,-^ H^ 



dP ^ _ , 



^ ^ («'- «)( VyHi — Vi~Hy)s-[-[^^'—^){ V,.Hi.— Vi.A)t ' ^^^^ 



' ^^ (.._.^)^(F..-f F.) 



da N 



(12) 



