and 



U2 Mr. E. H. Barton. Electrical Interference [June 15, 



It must now be recollected that, since the electrometer needle is 

 uncharged, it takes no account of the sign of the potential difference 

 between E and E', fig. 1, but gives a deflection proportional to fy~dt, 

 taken between the proper time limits. 



18. Hence, if E denotes the electrometer constant, and I , I#, and 

 I r , its deflections for the passage of the wave-train, without the con- 

 denser, after transmission through the condenser (as shown in fig. 1), 

 and by reflection from the condenser, respectively, we have 



EI = [ yjdt 



Jo 



= I yo dt\ \yo j [~yijdt+ 1 \y 1 1/1 i ^ ay ^ ,-,r,\ 

 Jo St. M > (17). 



+ .... + J 



+ .... ad inf. 



And in these equations everything is expressible in terms of quan- 

 tities considered known. 



19. The evaluation of the second part of (17) (being a doubly- 

 infinite series of definite integrals) is a somewhat long process, but 

 rigidly performed to infinity, and the result divided by that for EI 

 to eliminate E, and the like operation for I r , we have 



;+u, i 



1,/Io^-S-U, M18). 



_ 

 where - 



20. The following results of equation (18) may be noticed. 



(1) I;/I + l r /I = 1 or It + Ir = Io for all values of 6. and 2 , as should 

 be the case. 



(2) On putting 1 2 = or 6 = 0, that is, removing the condenser, 

 we have 



I;/I = i or If = I , all transmitted, 



and I r = 0, none reflected. 



On the other hand, with & = 1, we get all reflected and none trans- 

 mitted, unless t 2 = 0. 



(3) On differentiating U to 2 , and putting 3U/3^ 2 = to obtain 

 the values of I which give the stationary values of 1^ and I r , we 

 obtain siny3 2 = 0, whence I = ;j(^ 2 ), where n is any integer. 



