294 



SUPPLEMENT TO CHAP. XTV. 



For = 0, A = A of, and A y = A y*, hence 



A>', and o-c' = 



[CHAP, rv 



-(A -A') , oi 



O-0' = -iPz ....... (V.) 



For = a, A a? = 0, A y = 0, and f or x = a, A x' = 0, A y' = 0, 

 hence, 



= + iM a - -frHAa' - |Va 4 + ^Pa* (3a - 8) + i Aa* + B, 



= + *M. a" - iVH h a? - (V - F)a - i Pza' + Aa + O, 



The addition and subtraction of the two first and two last of these equa- 

 tions gives, when we put for A +A', A A', B B', O O', their 

 values above : 



B + B' = -iVa 4 + - 2 \Pa*(3a-4a) .' . . . (VI.) 

 2M a l -HAa t + iP(3a 4 -8a3 + 6a a 3 9 -2 4 ) = . . (VII.) 

 O + O' = - Mo a 1 + i H ha 9 - fc Pa (a 4 - 3a + 3a) . . (VIII.) 



Equations HL and VIL contain only H and M unknown. Their solu- 

 tion gives 



H = 5,P^' . . . (36) 



M=- 



From IX. we find directly 



(38) 



These are the equations given in Art. 160. From them we have the fol 

 lowing table : 



