Wehnelt Cathode-Ray Tube Magnetometer. 389 



The law of the series is apparent. The convergence is 

 slow, but the coefficients are easily evaluated if it is noted 

 that the series of the first two terms in (6) when multiplied 



rrr 



by ^ is the E series of the elliptic functions when the 

 modulus is one. Its value is then unity, so that 



(IV /l 3\ 2 1 /l 3 5\ 2 1 

 2) "HO) 3 + V2TT76J 5 + • " • = 1 ' 00000 " °' 63662 = °' 36338 > 



and so forth. 



Then, neglecting terms of the power five and higher 

 because the fourth significant place in M is not affected, 

 there results 



M=2 TO n ( ?L=I. 0-63662 . log < a + *'~ r ^ a + r ) 

 t 2a 6c (a - Xl + r )(a-r) 



-\. 0-63662. log e ^ 



(»!-»•)• 



'} 



+ fi=r. 0-36838.^ -i .0-36338 .^^r) 



a z a 2 2 



+ *=?■ 0-11338. («!-?' + '' 

 a o 



-i. o-ii338. i^-r) 4 ~ r 



cr 4 



It should be remarked that in evaluating 



we have assumed the same distribution of the field along the 

 actual path of the beam as along the diameter of the coil. 

 It was the plan at first to use opposed fields so that the 

 beam would follow the diameter very closely, but it was 

 noted on Plate No. 26 and two previous ones where de- 

 flexions were taken in both directions, that, so far as 

 measurements indicated, there was no difference in the 

 distances from either of the spots to the middle one corre- 

 sponding to no current in the coil. The assumption as to 

 the distribution is thus justified. 



