Discharge in a De La Rive's Tube. 501 



be considered when we are dealing with the relative influences 

 of different streams. 



3. Consider now any two (parallel) streams. The re- 

 sultant action due to electric and magnetic forces due to two 

 charges e, e', moving with equal velocities q, was calculated 

 by J. J. Thomson (Phil. Mag. April 1881), and shown to be 



ee' / q 2 \ 

 a repulsion of magnitude j-^( 1— ^ 2)5 where k is the S.i.C. 



of the medium, r the distance between the charges, and v, 

 the velocitv of light (the moving charges being assumed to 

 be spherical). 



Suppose, now, there are n positive and N negative charges 

 in the first stream and n', W in the second (per unit length 

 of each stream), and q is the velocity of a positive ion, and 

 — q' that of a corpuscle. 



Then, the mutual repulsion between the elements ds, ds' 

 will be (if e, e' be the charges of the particles in the two 

 streams) 



ee 



h 



^ S ^[„n'(l-| 2 ) + NN'(l-£) 

 -«N'(l+g)w N (l + g)] 

 = ^ d sds>[V-W)(n-N) - W + Wg + N'g^ 



In the case of a discharge, since all the streams are 

 similar, n = n / , N = N X . 



Therefore the repulsion ^^' [(„-N)»- ( " g tj q ' f ] , (1) 



the ions and corpuscles in any one stream being a self- 

 equilibrating system. 



There will be certainly repulsion, therefore, when n is 

 large or small compared with N ; for in this case, the ex- 

 pression within square brackets becomes 



» 2 ( 1 -£)(N = 0), (2) 



^C 1 " 6 )•(»=<>) (3) 



while the resultant action will be certainly an attraction if 

 n=N. 



Phil. Mag. S. 6. Vol. 24. No. 142. Oct. 1912. 2 L 



