Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/415

"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.^[1] If the axis of z be taken parallel to the magnetic force H, the equations of motion of a particle of mass m, charge e, and velocity (u, v, w) are

$mdu/dt=evH,\qquad mdv/dt=-euH,\qquad mdw/dt=0$.

The last equation shows that the component of velocity of the particle parallel to the magnetic force is constant; the other equations give

$u=A\sin(eHt/m),\qquad v=A\cos(eHt/m)$,

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. Tait^[2] in 1880 remarked that if the particles are moving with great velocities, the periods of the luminous vibrations received from then 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.

1. Gött. Nach., 2 February, 1891; reprinted, Ann. d. Phys. xiii (1881), p. 191.
2. Proc. Roy. Soc. Edinb. x (1880), p. 430.