He 



nee 



Rays of Positive Electricity. 703 



^d 2 i/ dd> 

 mw J -: > =e- j: , 

 dx~ dx 



hence 



mv 2 -jt =<?(^ p — ^ ), 



dx x 



wbere -~ is the value of —> at a point P ; d> P is the value of 



ax ax L 



(f> at P and <£ the value of <f> at the place where the rays 

 leave the narrow tube inserted in the cathode ; the value of 



- 7 - at this place is assumed to be zero. Hence if y is the 

 dx r J 



displacement of the particle on the screen, 



mv 2 y~ i <{(f)p — <l>o)d*, 

 Jo 



i 



(J3 s dx + elfo, 



-i 



where I is the distance of the screen from the end of the 

 tube. Along the median plane 



dx Ct_ 

 dt ~t + l' 



</> P = Blog(i + 0; 



hence 



e j cj) F dx = eBC\ — = log -(l + t)dt 



= ,BC[(l + 01og(H-0-(l4/)-ilog 2 (l + 0]^ 



where A refers to the screen and to the end of the tube. 

 Hence 



2 y=BC[(i + 0l°g(i + 0-(i + 0-ilog 2 (i + 0] A +Blog(i + « y. 



If the distance of the end of the tube from the edge of 

 the plates is a considerable multiple of the distance between 

 the plates an approximate value of ^ is —1. 



