element is absent. One thing is quite certain. The colouration is
not due to an accumulation of helium atoms, _i.e._ of spent alpha
rays. The evidence for this is conclusive. If helium was
responsible we should have haloes produced in all sorts of
colourless minerals. Now we sometimes see zircons in felspars and
in quartz, etc., but in no 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 neighbouring areas of
fclspar 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 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,
primâ 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.
236
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
237
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, no oftener than once in a
century; and possibly at still longer intervals.
The equilibrium amount of radium contained in some nuclei may
amount to only a few atoms. Even in the case of the larger nuclei
and more perfectly developed haloes the quantity of radium
involved is many millions of times less than the least amount we
can recognise by any other means. But the delicacy of the
observation is not adequately set forth in this statement. We can
not only tell the nature of the radioactive family with which we
are dealing; but we can recognise the presence of some of its
constituent members. I may say that it is not probable the
zircons are richer in radium than I have assumed. My assumption
involves about 3 per cent. of uranium. I know of no analyses
ascribing so great an amount of uranium to zircon. The variety
cyrtolite has been found to contain half this amount, about. But
even if we doubled our estimate of radium content, the remarkable
nature of our conclusions is hardly lessened.
It may appear strange that the ever-interesting question of the
Earth's age should find elucidation from the