324 Mr. G. U. Yule on the Passage of Oscillator 



The first and third terms in the square bracket may be 

 summed together, and also the second and fourth. Bringing 

 the two fractions thus obtained to a common denominator, 

 (1— 2o) 2 cos 2S + o) 4 ) divides out, as in the case of I 3 ', and 

 we obtain as our final value of I 2 " 



T " — 



A 2 .C 2 / 2 6>f 



2 V . b 2 1 - 2 w 2 f 2 cos 4f + v 4 £ 4 



f £ 2 cos (2S + <£-4^)-? 4 cos(/> \ 



w 1 -q) 2 rcos(28 + j)) + ^rcos(^ + ^)/ 

 X " 1 - 2f COS (25 - 4i/r) + f 4 * ^ D J 



Combining (44) (45) and (46) we have the total value of 

 I tJ the intensity of the transmitted ray, 



I^Ii + I^Ix+I/-!/' 



_ A 2 .c 2 / 2 ,f sec % (l-g 4 ) 



- 4t;6 2 W ^\(l-2Pcos2S + f)(l-6) 2 f) 



f (1 - f ) [cos - <w 2 f 2 cos (0 + 4^) ] 1 ^ 



t -2f sin (28-4^) [sin cj>-co^ 9 sin (<ft + 4^)] J L (47 



(l-2c» 2 f cos4i|r-ha) 4 | 4 )(l-2f 2 cos(2S-4^) + f^J 



But we want to compare this with the intensity of the ray 

 transmitted when there is no intervening layer of electrolyte. 

 Calling the intensity of this ray I , we have for its value 



f 00 A 2 



I =A 2 \ e-^sinPpzt .dt=j- (sec^— cos %). . (48) 



Dividing (47) by (48), 



I,_ c 2 / 2 .a)g / (l-P)sec X 



I ~/> 2 (sec%-cos % ) I (l-2f cos28+£ 4 )(l-ft) 2 f) 



f (l-£ 4 )[cos<£--*> 2 f 2 cos(<£ + 4^)] ) ^ 



\ -2g 2 sin(28-4^)[sin^)-a) 2 g 2 sin(c/) + 4i/r)] / I . (49) 



(l-2ft> 2 { 2 cos4^ + wT;( 1 -^ 2 cos (28-4^) +£*) j 



This formula is one of considerable generality, showing the 

 variation in the intensity of the ray transmitted through a 

 thin absorbent plate when the incident ray is logarithmically 

 damped. Two special cases are of interest: (I) when the 

 plate is not conducting; (2) when the incident ray is not 

 damped. Taking the first case, 



if a 2 = 0, ^ = ^'=0, h=p 2 t 2 , 



= 0, p = l, a>f=& 2 , . . r 



£ = &*-*% c 2y 2 =(l-& 2 ) 2 7 



}• 



