Art. 166. 



PORTALS POSTS PARTIALLY FIXED. 331 



R+P 



'I [ a (|a+c)-ar/(a+c)] 



If a=a' and a? 1 ==a? 1 / , 5'== 



4- 1 



/ ' i 



=(B+P) 



(151) 



(152) 



Equations (149) and (150) determine H and H' when a?! 

 and #/ are known. These depend upon M 2 and 3f 2 '> which in 

 turn depend on V. We must therefore solve by approximation. 

 This can be more readily done if we transfer (150) as follows. 

 From the derivation of (150) above, 



J ~ * v (153) 



H 1 ~ <z/'[a(-Ja+c) x (a-}-c)] 



For convenience let m'==a'(-Ja'+c'),^'==(a'-j-c'), m=a(Ja-f c) 



and 



, then - r = 



- 



TUT 



Now from (145) ,^^ 



Then arH(mnxJ=a'IH'(m'n'Xi') 



TUT I 



x^= -- . . . (same as 94). (154) 



substituting from (154) 



arHmaI'nM 2 =a'IH' m'a'In'M 2 ' 

 since H=R+PH' 



TT/ 



al' [m(R+P) nM 2 ] +a'In'M z ' 



a'lm'A-al'm 



7T= 



al'[a(ia+c) 



(155) 



When a=a', c=c r , (m=m', 



a-\- c 



H'=y 2 [R+p+ 



and /=/' 

 %' 3f a )].. ..(156) 



Get V and F r from equation (124) or (125). 

 R=H and R 9 '=H' . 



a 



i TT,- 



and R^= \B. - 



(157) 

 (158) 



Q=R 1 +H and (? / =- J K 1 / +H / (See Eq. (129) ) . . . . (159) 

 To solve any particular problem, first find the approximate 

 mean value of x^ and x\ by 



=X " (for a=a } 



