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MR. J. G. LEATHEM ON THE THEORY OF THE 
- Whrjo^ {A,e^ + A/e-® - - A^-^), 
HmEe“‘™'‘ = H' [m^A-fi^ — + m^A^e'^ — 
- (7}i^Age® — ?>igA/e"® — m^A^e^ + WoAg'e"'^), 
- = H'(Aie® + A/e"® — A^e^ — A\e-’^) 
- H'^tT^g (Aie« + A/e-® + AoC^ + A.y-^), 
H77ZtFc^'"‘"''' = H' (— m^A-^e^ + ??7jA/e“® + m^A^e^ — m^A^e~^) 
+ H'”i 7^3 (?UjAg6® — m-^A{e~^ + m.^A^e'^ — m^Aoe~^). 
If, for brevity, we put H't-^g = t, and notice from equations (25) that in the 
present problem 
7?7g/M = 1 d- 1^, 7)7 o/M = 1 — 
■we readily reduce the boundary conditions to the following :— 
yy/ (Aq “h A) = Ag + Ag' + An + AJ — t (Ag + Ag' — A, — AJ) 
IT M — A) — Ag — Ag' + Ag — A, — \t (Ag — Ag' — Ag + An') 
^ tB = Ag - Ag' - An + Ag' - {t (Ag - Ag' + Ag - An'), 
Fe—= Age® + Ag'e"® + AnC*^ + Ag'e”^ - t (AgC® -j- Ag'e"® - AgC^ - Ao'e-^) 
H ^ 
- ^ tFe-"”'' = Age® -f- Ag'e'® - Age-^ - Ag'e"^ - t (Age® + Ag'e"® + AgC^ + Ag'e"^) 
- ~ tFe-‘™'‘ = Age® - Ag'e"® - Age^^ + Ag'e"^ - (Age® - Ag'e"® + AnA^ - Ag'e"^). 
Fliminating B, E, and F from the last six, and representing 7)2/M bj’ x, we get 
