235

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, 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.

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