Natures of curious Electric Radiations. 437 



as repelling the (3 particle with a force varying as the inverse 

 square of the distance, or whether we are to consider positives 

 and negatives arranged in doublets, whose moment will be 

 the important power, and whose law o£ attraction will not be 

 that of the inverse square. It is a certain simplification to 

 suppose that scattering is mainly responsible for the fading 

 away of a stream of ft particles. The experiments of Allen, 

 McClelland, and others show that the secondary radiation 

 has a velocity not much less than that of the primary ; 

 and, therefore, that this simplification is justifiable ; though, 

 clearly, it cannot be pushed too far. This allows us to 

 concentrate our attention on the deflexions of the particles 

 only ; but even then the difficulties are still immense. It is 

 not like any problem in the kinetic theory of gases, for there 

 we deal with established conditions ; here with a gradual 

 development from initial conditions *. 



But if w r e tarn from the theoretical to the experimental 

 investigation we find a much more encouraging prospect. 

 The experiments of Lenard are practically a complete graph- 

 ical solution of the question. (See Taf. iv., Wied. Ann. 

 Bd. 51.) We know that an assemblage of atoms behaves 

 just the same in respect to these radiations, when it is con- 

 densed in a solid or spread out as a gas. Thus the sketches 

 which Lenard gives us showing the way in which the cathode 

 rays diverge from a small window and scatter in going 

 through various gases at different densities, must be quite 

 applicable to solids also. 



* In bis ' Conduction of Electricity through Gases/ 2nd edition, 

 p. 376, Professor Thomson investigates the motion of a stream of 

 J3 particles through an absorbing layer. It appears to me — I sa} r it with 

 ver} r great diffidence — that the solution does not take a true account of 

 the facts. The solution may be stated briefly thus : — Taking u, v, w as 

 the components of the velocity V of the moving corpuscle, an expression 

 is found for the probable change in u at the next encounter. Calling 

 this change 8u, we have 6^= — uK, say, where -ST is a function of the mass 

 of the corpuscle, the effective mass of the electron of the absorbing body, 

 the velocity V of the corpuscle, which is taken as constant, the atomic 

 charge, and the shortest distance between two corpuscles and the atom. 

 K is then multiplied by the probable number of encounters in moving a 

 distance &r along the axis of x, from which follows an exponential law 

 for u in terms of x. It seems to me, in the first place, that, assuming 

 such a multiplication to have any meaning, the proper factor should 

 have been greater than that adopted in the proportion of V to u, for in 

 advancing a distance 8x along the axis of x the corpuscle moves a 

 distance YSx/u, not 8x. If this change is made, the exponential form 

 disappears from the answer. But, apart from this, it does not seem that 

 the step is justifiable at all. It is tantamount to putting the corpuscle 

 back in its old track after each encounter, and is equivalent to neglecting 

 the existence of the function mentioned above, and the absolute necessity 

 of finding it . 



