Theory of the Double Resonator. 233 



In (8) if S'/S be very small, p 2 approximates to p ± 2 or 

 to p 2 2 , and this is the case of greatest importance in 

 experiment. 



If fix and p 2 2 differ sufficiently, we may pursue an 

 approximation from (8) founded on the smallness of S'/S. 

 But it is of more interest to suppose that p 2 and p 2 2 are 

 absolutely equal, which nothing precludes. Then 



... (9) 

 . . . (10) 



p 2 differing but little from p 2 or p 2 2 . 

 Referring back to (5), we have 





f- 



?(ip 



i s +§^i 2 )+i> 



L 4 = 0, 



whence 













f 

 rf 



= 1 + 



S±n/(?+ 



S' 2 \ 

 4SV ; 



or, if S'/S be small enough, 





x 2 -x 



-se-5- i vs> 



6-v© <» 



when we introduce the value of p 2 from (11). Thus 



x, 



We may now compare effects in the two component 

 resonators, and here a certain choice presents itself. The 

 condensations in the interiors are (X : — X 2 )/S and X 2 /S', and 

 the ratio of condensations is 



X 2 /S' _ •(S/SQ _ // S\ n ,. 



(Xi-X^/S ~ 1- V (S'/S) ~ V V S7 ' ' l ; 



approximately. It appears that the condensation in the 

 second resonator may be made to exceed to any extent that 

 in the first by making the second resonator small enough, 

 which sufficiently explains the advantage found in expe- 

 riment to attend the combination. 



In some forms of the experiment we may have to do 

 rather with the flow through the passages than with the 

 condensations in the interiors. In (12) we have the ratio of 

 the total flows already expressed. But we may be more 

 concerned with a comparison of flows reckoned per unit of 



