Electric Discharge in a Transverse Magnetic Field. 51 



Fig. 1. " Band " discharge which rotates when the electro- 

 magnet is excited. (Pressure 55 millimetres.) 



Fig. 2. " Glow " discharge at pressure 2 millimetres. 

 (The induction-coil (A) used in these cases gives a 

 spark-length in atmospheric air of 29 millimetres.) 



Figs. 3 & 4 are photographs o£ the discharge at the same 

 pressures as in 1, 2 respectively, with the induction- 

 coil (B) giving a spark-length in atmospheric air of 

 13*4 millimetres. The discharge-tube (No. 1) is the 

 same in both cases. In the latter group, no band 

 discharge appears, and consequently the rotatory 

 effect is absent throuo-hout the entire range. With 

 a smaller tube (No. 2), however, and the induction- 

 coil (B) the discharge shows the various types referred 

 to on page 50. 



5. It is a priori evident that there must be a definite 

 relation between pressure in the tube, the voltage of the 

 induction-coil, and the length of rotatory discharge. What 

 the nature of this relation should be would appear from the 

 following considerations. 



If n is the number of corpuscles per unit length (along x) 

 per unit area of cross-section of a discharge, then the 

 equation of continuity (J. J. Thomson, ' Conduction of 

 Electricity through Gases') is 



3>i ~d(nu) nu r /XA ~"1 



where u is the velocity of a corpuscle ; 



\ = mean free path ; 



/ is a function, which determines the number of 

 collisions resulting in ionization, of the mean 

 kinetic energy X^A, of an ion given to it by the 

 electrical field of intensity X ; 



/3 is the fraction of collisions resulting in re- 

 combination ; 



p = pressure ; 



e — charge on an ion (+ and — ). 



Now, for steady rotation both -=- and ^- — must vanish, 

 and we must have ® x 



.'. — = £', say. 

 E 2 



