from Faraday to J . J . 71wmson. 395 



" a new state of matter " he understood simply a state in which 

 the free path is so long that collisions may be disregarded. 



Crookes found that two adjacent pencils of cathode rays 

 appeared to repel each other. At the time this was regarded as 

 a direct confirmation of the hypothesis that the rays are streams 

 of electrically charged particles ; but it was shown later that 

 the deflexion of the rays must be assigned to causes other than 

 mutual repulsion. 



How admirably the molecular- torrent theory accounts for 

 the deviation of the cathode rays by a magnetic field was shown 

 by the calculations of Eduard Riecke in 1881.* If the axis of 

 z be taken parallel to the magnetic force H t the equations of 

 motion of a particle of mass ra, charge e, and velocity (u, v, w) 



are 



mdu/dt = evH, mdvjdt = - euH, mdw/dt = 0. 



The last equation shows that the component of velocity of the 

 particle parallel to the magnetic force is constant; the other 

 equations give 



u = A sin (eHt/m), v = A cos (eHi/m), 



showing that the projection of the path on a plane at right 

 angles to the magnetic force is a circle. Thus, in a magnetic 

 field the particles of the molecular torrent describe spiral paths 

 whose axes are the lines of magnetic force. 



But the hypothesis of Varley and Crookes was before long 

 involved in difficulties. Taitf in 1880 remarked that if the 

 particles are moving with great velocities, the periods of the 

 luminous vibrations received from them should be affected to a 

 measurable extent in accordance with Doppler's principle. 

 Tait tried to obtain this effect, but without success. It may, 

 however, be argued that if, as Crookes supposed, the particles 

 become luminous only when they have collided with other 

 particles, and have thereby lost part of their velocity, the 

 phenomenon in question is not to be expected. 



* Gott. Nach., 2 February, 1881; reprinted, Ann. d. Phys. xiii (1881), p. 191. 

 t Proc. Roy. Soc. Edinb. x (1880). p. 430. 



