54 
PROF. J. JOLY ON THE GENESIS OF PLEOCHROIC HALOES. 
radius compared with the ranges of the rays concerned. In this case the several 
rays move along the radii of a sphere having the nucleus at its centre. They 
therefore diverge like rays of light from a luminous point, and the intensities, or 
more accurately the closeness of approximation, of the effects, upon successive 
spherical surfaces, must diminish outwards with the inverse square of the distance. 
But this inverse square law is departed from in the particular that the effect of 
any one ray is not in itself a uniform one along its path. The observations of 
Bragg and others have shown that, just before the electrified particle loses its 
kinetic energy, there is a rapid increase in its power of ionisation. A limit to this 
increase is attained some little time before the power of ionisation ceases. The 
curve depicting these facts is well known. Its definition, as determined by 
Geiger,* is used in the applications of it which I make in what follows. 
We seem, then, entitled to expect that a halo would show' features in general 
accordance with the following scheme of development. We first assume that the 
medium possesses the stopping power and other properties of air. Along a horizontal 
axis we then repeat the Geiger curve for each constituent a-ray concerned in 
generating the halo, placing the outer termina¬ 
tion of the curve accurately according to the 
range of each ray. At sufficiently close points 
along the horizontal axis we then add the 
ordinates of the overlapping curves. The 
summation of these ordinates gives us such a 
curve of ionisation as would correspond to the 
action of a parallel sheaf of rays. Bragg 
obtained observationally such a curve in the 
case of radium and its derived elements. 
But this curve does not take into account 
the spreading of the rays which, from our 
knowledge of the spherical form of the halo, 
is a mere geometrical necessity, and cannot be 
evaded. When, now, we divide the successive 
integral ionisation ordinates by the square of 
their abscissae, we obtain a curve which should, 
according to the assumptions already made, 
p define the gradation of density outwards from 
the centre of the halo. Bock sections of 
ordinary thickness, and cleavage Hakes of mica, include only a part of the halo sphere— 
perhaps one-third or one-fourth of it—and this will modify the appearance a little. 
I give here the results of these successive operations. Fig. 1 is the result of an 
accurate summation of the ordinates of the Geiger curve, placed according to the 
* ‘ Roy. Soc. Proc.,’ A, vol. 82, p. 486 (1909). 
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