through Gases between Parallel Plates. 671 



Thus 



F(q, b. c, 1) -1 r(c)r(c-a-6) -r(c-6)I>-a) 

 a ~ aY(c — b)Y(c—a) 



_1 r(c-a)~r(c) V(c) Y(c-a-b)-Y(c-b 



~Y(c — a) —a Y(c — a)Y(c — b) —a 



Taking the limit when a becomes zero we have 

 F(a,6,c,l)-l __r(<0 _ Y'(c-b) 

 hta =° a ~ Y(c) Y(c-b)' 



But 



y F(a, 6, <?,!)-! _ 6 1 6(6 + 1 ) 1 6(6 + l)(6 + 2) 

 ljtffl=0 a ~c + 2c(c+l) i "3c(c + l)(c + 2)" i " + 



and if we put ^ 



i 



C - 2(1-6) 



this becomes 



+ 1, 



2-e 1 (2-6)(4--36) 1 (2-e)(4-36)(6-5€) f 



3-2e + 2(3-2e)(5-46) 3(3-Z6)(5-46)(7-66) ' i " 



Thus for a = the series given bv (8) takes the value 



"■(mbitO r (i). 



(12) 



r' 



(For tables of — functions see Gauss, Werke, Bd. iii. p. 161.) 



As regards the limiting value of the third integral 



If — 



- i cosh 1_e ft) da, we have 



- I cosh 1-6 codco = cosh 1_fi a>sinhft> + I cosh i ~ e coda* . (13) 



If -J- 

 For infinite values of a the value of - j cosh 1 -* coda given 



1-e — 6 J 



by equation (9) is cosh 1-6 © if the value of e be less 



than \. Thus, if the series is to represent the same integral 

 as (13). we must insert oo as the lower limit of the integral 

 on the right-hand side of the latter equation. Further, if ^ 



e < J, then e ~~ is negative. Thus the series of equation (9) 



1 — 6 



