662 Mr. C. G. Barkla on the Velocity oj 



first pulse reaches R, may be written 



3Xx 



b n ae 2 +ab n ~ } e 2 + . . . 



ae~ 



(»+§)Ax * 



(i) 



in which b is the damping factor for the primary corre- 

 sponding to e~ kx in the secondary. 

 This expression may be written 



ae 



njn + l_ e -(n + l)\x} 



(/> say. 



(2) 



b—e~ kx 



The oscillations at R reach a maximum of intensity when 

 n is such that 



Jjn + \ __ e -(n+l)\x > l ) n+2_ e -(n+2)\x 



and ->b n — e~ nkx , 



i. e 



. when 



bn+i(l-b)>e-<- n+l ^{l 



i. e. when 



and b\l — b)<e- 



1 -6 



: (l-e' kx ), 



,-Ax v n+l 



lies between / — — j and ( '-j- ) 



The amplitude of oscillation determining the demagnetiza- 

 tion of the detector-needle is given by substituting the value 

 of n in the expression (2) . 



The rate of variation of amplitude (due to damping) with 

 the change in position of the bridge is 



dx bt kx -l 9 



(n + Y)\ 



[ ) n+\ t (n+\)kx__^ 



4>-«4>- 



* It may be argued that b is not constant for each oscillation in the 

 primary because of the action on the primary by the secondary, which 

 action must increase with the intensity of oscillation in the secondary. 



In that case (1) should be written 



_Xx _ 3A* 



bfi. 2 b 3 ... b n ae 2 +b l b. i .. .bn-V-te 2 + . . . b : ae-( n -i)^+ae-(n+i)te. 



Bat it was shown experimentally that the position of a maximum was 

 not altered by the variation in the distance between the two circuits, and 

 that when the distance was so great that the intensity of the waves 

 induced in the secondary was small even when the circuits were tuned, 

 and consequently the effect of the secondary on the primary very small, 

 the maximum was given with the bridge in the position obtained when 

 the circuits were near. 



When the circuits were thus separated the effect of the secondary on 

 the damping of the primary must have been negligible, and hence b was 

 constant. 



We may therefore consider the measurements taken as those given 

 when the circuits were so separated that the influence of the secondary 

 on b was practically nil, and b was therefore constant throughout. 



