86 



proportional to the square root of the atomic weight, and the 

 eflFects appear to be exactly additive. 



On the other hand, if we consider a stream of (i particles 

 projected into matter, and attempt to find the history of their 

 motion, we are faced with a problem of great complexity. If 

 we look for an answer expressed statistically we must find the 

 number of particles in each unit volume of the absorbing mat- 

 ter as a function of the time, the velocity, and the direction 

 of motion. If, on the other hand, we try to follow the motion 

 of any one particle, we must find the chance that the particle 

 considered has any particular position, velocity, and direction 

 of motion at any given time; which is really equivalent to 

 finding the function just mentioned. Moreover, the data are 

 very uncertain. We know so little of the interior of the 

 atom that we are unable to say with what forces the electrons 

 will be influenced when it penetrates within; whether, for 

 example, we may neglect the action of the positive electricity 

 of the atom, and consider only the electrons as repelling the p 

 particle with a force varying as the inverse square of the dis- 

 tance, or whether we are to consider positives and negatives 

 arranged in doublets, whose moment will be the important 

 power, and whose law of 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 /3 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 deflections 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. (1) 



(1) In his Conduction of Electricity Through Gases, 2nd 

 edition, p. 376, Professor Thomson investigates th^ motion of a 

 stream of ^ particles through an absorbing layer. It appears 

 to me — I say it with very great diflfidence — that the solution does 

 not take a true account of the facts. The solution may be stated 

 briefly thus: — Taking u, r, \v 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 bn. we 

 have 8)1 — -1I.K, sixy, where K is a function of the mass of the cor- 

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

 the vdocity V of the corpuscle, which is taken as constant, the 

 atomic charge, and the shortest distance between two corpuscles 

 in the atom. K is then multiplied by the probable number 

 of encounters in moving a distance Sa^ along the axis of x, 

 from which follows an exponential law for v in terms of x. It 

 seems to me, in the first place, that, assuming such a multipli- 



