d helium would exhibit such a colouration, 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.

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It is common to find haloes developed perfectly in this granite,
and having a nucleus of zircon less than 5 x 10-4 cms. in
diameter. The volume of zircon is 65 x 10-12 c.cs. and the mass
3 x 10-10 grm.; and if there was in this zircon 10-8 grm. radium
per gram (a quantity about five times the greatest amount
measured by Strutt), the mass of radium involved is 3 x 10-18
grm. 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 3.4 x 1010, 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, then 150 millions of rays built up the
halo. If geological time since the Devonian is 400 millions of
years, then 1,200 millions of alpha rays are concerned in its
genesis. The number of ions involved, of course, greatly exceeds
these numbers. A single alpha ray fired from radium C will
produce 2.37 x 105 ions in air.

But haloes may be found quite clearly defined and fairly dark out
to the range of the emanation ray and derived from much less
quantities of radioactive materials. Thus a zircon nucleus with a
diameter of but 3.4 x 10-4 cms. formed a halo strongly darkened
within, and showing radium A and radium C as clear smoky rings.
Such a nucleus, on the assumption made above as to its radium
content, expels one ray in a year. But, again, haloes are
observed with less blackened pupils and with faint ring due to
radium C, formed round nuclei

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of rather less than 2 x 10-4 cms. diameter. Such nuclei would
expel one ray in five years. And even lesser nuclei will generate
in these old rocks haloes with their earlier characteristic
features clearly developed. In the case of the most minute
nuclei, if my assumption as to the uranium content is correct, an
alpha ray is expelled, probably,