PROF. J. .TOLY ON THE GENESIS OF PLEOCHROIC HALOES. 
59 
width and depth of colour we infer that the halo, before reversal, was evidently 
much blackened. The entire central region has been more or less reversed. The 
narrow ring or shell which is almost the only internal feature left may be either a 
survival or a feature due to fresh ionisation. 
I have, on rare occasions, previously found haloes having a similar appearance to 
this reversed halo ; but their true significance was not appreciated by me. Whether 
they represent reversal as the result of the different stimuli successively acting, or 
as the result of over-exposure or “ solarisation,” it is impossible to say. But in 
either case they support the view that the halo partakes of the character of the 
latent photographic image. 
Effect of the Nucleus. 
The nucleus is not a mathematical point. Its dimensions must play some part in 
contributing to the radial dimensions of the halo, and, consequently, in disguising 
the true range of the rays. 
Exact evaluation of the nuclear effect is difficult or impracticable. Its effect 
probably varies with the stage of growth attained by the halo. Fortunately, in 
haloes such as enter into our present considerations, the nuclear effect is in any case 
small, and if the correction applied is not quite adequate, the remaining error must, 
of course, be still smaller. 
We must consider the nucleus as composed of some substance possessing a stopping 
power differing from that of the mica. This applies to nuclei composed of zircon 
or uraninite, and to many other possible minerals. Zircon is the most probable of 
all. Within a zircon nucleus there will be a certain retardation of the ray in excess 
of what occurs for a similar travel in mica. Thus, availing ourselves of Bragg’s 
Law, we may calculate that, in the mica (haughtonite) of Co. Carlow, a range of 
1 cm. in air of density 0‘0012 is represented by 0‘0000473 cm. In this calculation 
the quotient cijd enters, where a is the average square root of the atomic weight 
of the retarding substance, and d is its density. Now for haughtonite the quotient 
has the value 1*6 ; for uraninite it is 1, and for zircon it is IT. The range is 
therefore less in zircon than in haughtonite as IT : 1‘6. We may take it as 2 : 3. 
If we assume the rays to proceed from all points of the nucleus it is easy to show 
that the halo should exhibit, at least in its period of development, a border possessing 
a width about three times the radial dimensions of the nucleus, and shaded off both 
in its inner and outer margins. This border would exhibit a maximum depth of 
colour somewhere outside its mean radius, and if we measured the halo to this circle 
of maximum effect we should subtract one-third the radius of the nucleus in order 
to get the true range. In this reasoning the nucleus is supposed to be small com¬ 
pared with the size of the halo and sensibly spherical. Or we might expect at a 
later stage that the band would be darkened uniformly. If we then find the mean 
radius of this band the correction on this in order to determine the true range will be 
half the nuclear radius. 
VOL. CCXVII.-A. 
K 
