PLEOCHROIC HALOES—JOLY. 319 
here we possess a means of at once confirming or rejecting the view 
that the halo is a radioactive phenomenon and occasioned by alpha 
radiation; for we can calculate what the range of these rays will 
be in biotite, availing ourselves of Bragg’s additive law, already 
referred to. When we make this calculation we find that radium C 
just penetrates 0.033 millimeter and thorium C 0.040 millimeter. 
The proof is complete that we are dealing with the effects of alpha 
rays. Observe now that not only is the coincidence of measurement 
and calculation a proof of the view that alpha radiation has occas- 
ioned the halo, but it is a very complete verification of the important 
fact stated by Bragg, that the stopping power depends solely on the 
atomic weight of the atoms traversed by the ray. 
We have seen that our examination of the rocks reveals only the 
two sorts of halo, the radium halo and the thorium halo. This is 
not without teaching. For why not find an actinium halo? Now, 
Rutherford long ago 
suggested that this ele- 
ment and its deriva- 
tives were probably an 
offspring of the ura- 
nium family; a side 
branch, as it were, in 
the formation of which 
relatively few trans- 
forming atoms took 
part. On Rutherford’s Fig. 3. 
theory, then, actinium should always accompany uranium and ra- 
dium, but in very subordinate amount. The absence of actinium 
haloes clearly supports this view. For if actinium was an indepen- 
dent element we would be sure to find actinium haloes. The differ- 
ence in radius should be noticeable. If, on the other hand, actinium 
was always associated with uranium and radium, then its effects 
would be submerged in those of the much more potent effects of the 
uranium series of elements. 
Tt will have occurred to you already that if the radioactive origin 
of the halo is assured the shape of a halo is not really circular, but 
spherical. This isso. There is no such thing as a disk-shaped halo. 
The halo is a spherical volume containing the radioactive nucleus 
at its center. The true radius of the halo may, therefore, only be 
measured on sections passing through the nucleus. 
In order to understand the mode of formation of a halo we may 
profitably study on a diagram the events which go on within the 
halo sphere. Such a diagram is seen in figure 3. It shows to rela- 
tively correct scale the limiting range of all the alpha-ray producing 
