Wehnelt Cathode-Ray Tube Magnetometer, 387 



Letting 2 ec be the deflexion then produced we have, 

 similarly, 



mvj 



(H + IH c )(d? 1 -.f)^. 



(2) 



H is constant so that, integrating (1) and the first term of 

 the right-hand member of (2), we have 



e n ^ 2 

 mv 2 



(3) 



and 



Because of the low velocity of the electrons and the high 



e 

 vacuum used, the factor '- is constant and is eliminated by 



mv J 



dividing (4) by (3). Solving for H the formula appears 

 H = — g * — * I H (x 1 — x)dx. 



Xi Zee 2e Jq 



In the circular coil, used because of ease of construction 

 and to secure compactness, the field H c is not constant along 

 the path of the beam, bat must be expressed as a function of 

 the distance from the cathode. 



Calling x' the distance from the centre of the coil to the 

 point in question^ we have, per unit current*, 



w 



here 



EL= 



Aan 



M> E > 



1 . 3\ 2 1 x'* 



"-MS-fcffiS-H- 



but x' = x-r, so that we have for the field, in terms of the 

 distance from the cathode, the centre of coordinates, 



Ziran r /l\ 2 ( x-r) 2 /l . 3\ 2 1 (s-r)* "I 



■ u «- a i_( - ._ r )»L X \2) a? V2.4/3 a* J 



Let Cxi ' ' ' (5) 



M = l R c (x 1 — x)dx 



and substitute the value of H c from (5), we have, using four 



* A. Kussell, Phil. Mag. vol. xiii. pp. 420-446 (1907). 

 2D2 



