324 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
tions of thickness obtaining in rock sections. It is well known 
. that there is in biotite a maximum absorption of a plane polarized 
light ray when the plane of vibration coimcides with the plane of 
cleavage. A section across the cleavage then shows a maximum 
amount of absorption. A halo seen on this section simply produces 
this effect in a more intense degree. This is well shown in figure 1 
(plate 1) on a portion of the halo sphere. The descriptive name 
“»leochroic halo”’ has originated from this fact. We must conclude 
that the effect of the ionization due to the alpha ray has not been 
to alter fundamentally the conditions which give rise to the optical 
properties of the medium. The increased absorption is probably 
associated with some change in the chemical state of the iron present. 
Haloes are, I believe, not found in minerals from which this element 
is absent. One thing is quite certam. The coloration is not due 
to an accumulation of helium atoms, 1. e., of spent alpha rays. The 
evidence for this is conclusive. If helium was responsible we should 
have haloes produced in all sorts of colorless minerals. Now we 
sometimes see zircons in feldspars and in quartz, etc., but inno such 
case is a halo produced. And halo spheres formed within and 
sufficiently close to the edge of a crystal of mica are abruptly truncated 
by neighboring areas of feldspar or quartz, although we know that 
the rays must pass freely across the boundary. Again it is easy 
to show that even in the oldest haloes the quantity of helium involved 
is so small that one might say the halo sphere was a tolerably good 
vacuum as regards helium. There is, finally, no reason to suppose 
that the imprisoned helium would exhibit such a coloration, or, 
indeed, any at all. 
I have already referred to the great age of the halo. Haloes are 
not found in the younger igneous rocks. It is probable that a halo 
less than a million years old has never been seen. This, prima facie, 
indicates an extremely slow rate of formation. And our calculations 
quite support the conclusions that the growth of a halo, if this has 
been uniform, proceeds at a rate of almost unimaginable slowness. 
Let us calculate the number of alpha rays which may have gone 
to form a halo in the Devonian granite of Leinster. 
It is common to find haloes developed perfectly in this granite 
and having a nucleus of zircon less than 5107-* centimeter in 
diameter. The volume of zircon is 65 X10-” cubic centimeter and 
the mass 3107! gram, and if there was in this zircon 10~* gram 
radium per gram (a quantity about five times the greatest amount 
measured by Strutt), the mass of radium involved is 3 x 10~ gram. 
From this and from the fact ascertained by Rutherford that the 
number of alpha rays expelled by a gram of radium in one second is 
3.410", we find that three rays are shot from the nucleus in a year. 
If now, geological time since the Devonian is 50 millions of years, 
