390 Dr. Barton and Mr. Lownds on Reflexion and 



61. It is seen on reference to Table XI. that there is a 

 considerable discrepancy between the experimentally-deter- 

 mined values o£ the ratios of electrometer-throws and those 

 calculated from the approximate theory. This theory, used 

 as a first working approximation, takes i-0 in the original 

 incident wave-train e-^pt cos (pt + i.), and omits the expo- 

 nential term introduced on reflexion at the condenser. This 

 was done because the value of c is unknown. Let us now 

 determine the maximum correction needed to the above 

 theory, the results of which are placed in the last column of 

 Table XI. Assume for i such values as to make for each 

 condenser 1 + /3 — 0. This makes the coefficient of the ex- 

 ponential term a maximum. Further, let us suppose (what 

 is not possible) that the coefficient of the exponential term 

 retains its maximum value all through; i. e., put i + /3 + 2/c=0 

 or 77, i + /3 + -1k=0 or 4-7T &c. for the successive reflexions and 

 transmissions. In order to convert the time-integral of the 

 square of the amplitude, on the approximate theory, to its 

 true value when the exponential term is retained, let A 2 and 

 B 2 be now replaced by pA 2 and tB 2 respectively. 



Then we shall have 



I 



[Ac-Zpt cos (pt + i + a) — B cos + /3)e- 2 P* jX '] 2 dt 



'} 



I 



[Ae-fy* cos (pt + i + ct)Ydt, 

 and > (55) 



t = [B*-*P*cos (pt + i + /3)-B cos + /3>- V/x'] 2 dt 



r- 



-=- [Be- k Pt cos (pt + i + p)]*dt 



where i + /3 is to be written equal to zero. 



Further, since t has now a finite value, and different for 

 each condenser, equations (26) and (42) need modifying by 

 the introduction of t. We thus obtain the following cor- 

 rected equations: — 



For the transmitted system: 



and for the reflected system: 



mean y = F + pQ; 



