38 Mr. It. Moon on the Solution of Linear Partial 



°=^ A > < 6 > 



O=^+0A 1 + 7l , ..... (7) 



&c. &c. 



where 



■ft— + S-^- +T— + P — +Q— 



/Q— fifcff 2 03?% Off 2 Off fly 



«ar «a;a?/ ftz/ 4 Off ay 



(8) 



2R*+S^ 

 aa? ay 



^^IxS^Al + T^ 1 + P^- 1 -f O— l + UA 

 aa? 2 aayay oy a dx dy l 



aa? ay 



&c. &c. 



(6) gives us 



Ae/^=c, 



where c is constant, it being understood that, if y3 contains y, 

 the latter variable must be eliminated before the integration by- 

 means of the equation 



ftj= const., 



and the constant so introduced must be eliminated after inte- 

 gration by means of the same equation. 

 Hence we shall have 



A =ce-/^, 



A, =0,6-/^ — 6-/^ §dx . yje/M*, 

 A g = c 2 e-yf4*— 6-/P*JVfe . 7 2 e/^, 

 &c. &c. 



It is clear, however, that the substitution of these values would 

 give rise to a term in z 



= €-/**. {c^)+^- 1 ( M )+c 2 (/»- 2 M + &c.}, 



