58 
PROF. J. JOLY ON THE GENESIS OF PLEOCHROIC HALOES. 
same distance the chance is p 2 /r 4 . Hence the reversing effect falls off outwards, 
ceteris paribus, with the fourth power of the radius. But the weakening effect of 
the geometric conditions falls off as the square of the radius. If we could suppose 
the effects limited to these two only, we appear to possess a mechanism whereby the 
geometric law is disposed of, for the rate of diminution of the reversing effect 
outwards is such as must occasion an accumulation of effects per unit volume in the 
outer shells of the halo even greater than what takes place within. 
If we supposed that the effect, say, of the slowest moving ray, at any particular 
distance from the centre, was exposed to reversal by all the faster moving rays which 
might pass within effective distance thereto, we can evidently account for an 
additional diminution of destructive effects outwards, for the several rays fall out one 
by one as the radius increases. It is in this way I would account for the early 
appearance of the effects of RaC or of’ ThC 3 ; for of all the rays which go to build the 
halo, these alone are unaffected by such reversal effects; and, where overlap with 
other rays ceases, succeeding stimuli possess the same, or nearly the same, velocity. 
The geometric law indeed affects and must affect the growth of density in this part 
of the halo as in all other parts, but here alone it is the chief or only source of 
diminished density. 
From this it will be seen that the complication of the effects responsible for the 
halo is probably very great. The possibilities are not exhausted with what has 
already been stated. But although exact treatment of the subject appears impracti¬ 
cable, I think it is probable that the solution of the difficulties is to be found 
somewhat on the lines indicated. 
I have not been able to arrive at any alternative explanation on the basis of 
modifying the form of the Bragg or Geiger curve. However much, within reason, 
we accentuate the final effects of the ray, the geometric law of spreading destroys 
the accentuation of those features of the integral ionisation curve which plainly 
account for the structure of the halo. Moreover, it is evident that no modification 
of the elementary ionisation curve can account for the early prominence of the outer 
ring ; for whatever modification we apply to the ionisation curve for a single ray 
must affect all the constituent rays alike, and hence all features of the integral curve 
rise and fall together. 
It might appear that by studying the effects obtaining in the mica where two 
haloes overlap, we might get evidence as to the existence of reversal effects. 
Unfortunately these effects seem very variable. Sometimes there is overlap with 
little or no increased depth of colour. This is favourable to the reversal theory. 
But, again, and when we have reason to believe that there is true overlap in the 
same plane, there is increase of darkening. 
Since the above was written, I have found what seems to be a “ reversed ” halo. 
I give a drawing (Plate 1, fig. 5) shaded as nearly as I can judge similarly to the 
original. The dark outer band is due to BaC and has not been reversed. From its 
