202 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1907. 
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 @ 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 of attraction will not be that of the inverse square. It is 
a certain simplification to suppose that scattering 1s mainly respon- 
sible for the fading away of a stream of £ particles. The experi- 
ments of Allen, McClelland, and others show that the secondary ra- 
diation has a velocity not much less than that of the primary; and, 
therefore, that this simplification is justifiable; though, clearly, it 
can not be pushed too far. This allows us to concentrate our atten- 
tion on the deflections of the particles only; but even then the diffi- 
culties 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 we turn from the theoretical to the experimental investiga- 
tion we find a much more encouraging prospect. The experiments of 
Lenard are practically a complete graphical 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 
condensed 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. 
4Jn his ‘‘ Conduction of Electricity through Gases,” 2d edition, p. 876, Pro- 
fessor Thomson investigates the motion of a stream of 6 particles through an 
absorbing layer. It appears to me—I say it with very great diffidence—that 
the solution does not take a true account of the facts. The solution may be 
stated briefly thus: Taking wu, v, w as the components of the velocity V of the 
moving corpuscle, an expression is found for the probable change in wu at the 
next encounter. Calling this change 6u, we have 6uw=——wk, say where K 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 
atomie 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 
6x along the axis of 7, from which follows an exponential law for w in terms of «. 
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 uw, for in advancing a distance 67 along the axis of # the 
corpuscle moves a distance Vé2/u, not 6a. If this change is made, the expo- 
nential 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 cor- 
puscle 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. 
