Mass of Air confined by Walls at Constant Temperature. 321 



This is the equation from which m is to be found, after which 

 h is given by (9). 



In the further discussion we will limit ourselves to the case 

 °f 9 = ®> when (41) reduces to 



m 



3a{3{mcotm-l), .... (42) 

 in which a has been put equal to unity. Here by (40) 



D=-C/«/3. 

 Thus we may set as in (23), 



*-B^ + B,r-** + ) ■ m > 



s = B l e-^ t s 1 +B 3 «- V^ 2 + ) 



in which 



Q $\\\m x r sinra^ sin m,r 1 sin mi a ,... 



Vi= , Si=— a — —,(44) 



m x r m Y a m x r /3 m x a v ' 



and by (9) h l = vm 2 l /y. Also 



, , n 1 + a/3 sin m\a ,._,. 



S a + 1 = -^ l - (45) 



The process for determining B b B 2 , . . . . follows the same 

 lines as before. By direct integration from (44) we find 



2W!W 2 ( l 



2 + /3/a . s^s 2 )r % dr 



_ sin (m, — m 2 ) sin (m 1 -f m 2 ) 2 sin m 1 sinw? 2 

 mi—m 2 W]+m 2 3a/3 



a being put equal to unity. By means of equation (42) 

 satisfied by m 1 and m 2 we may show that the quantity on the 

 right in the above equation vanishes. For the sum of the 

 -first two fractions is 



2??7 2 sin m x cos in 2 — 2m 3 sin m 2 cos m x 

 ?><, — w* 



of which the denominator by (42) is equal to 



Sa^{m l cot m 1 — m 2 cot m 2 ). 



ingly \\e& 



Jo 



Accordingly {0& + P/* . s&ydr^Q. . . . (46) 



