August 2, 19 17] 



NATURE 



457 



composition and its densit}-. We can, accordingly, 

 calculate what the range of these extreme rays should 

 be in mica. When we do so we get exactly the dimen- 

 sions of the two sorts of halo. We shall presently 

 see that even this evidence is but a part of the case 

 for the radio-active origin of the halo. 



Uranium halos — that is to say, those in which 

 uranium is the parent radio-active mineral contained 

 in the central zircon — are common. Such are not 

 generally capable of accurate measurement. But in 

 clear, flawless mica, viewed on the plane of cleavage, 

 halos of extraordinary delicacy and sharpness of out- 

 line are sometimes met with. Again, the halo is often 

 ccHiipletely blackened up. Such halos may be described 

 as "'over-exposed." As in the case of different expo- 

 sures in photography, we find every gradation in the 

 amount of detail according to the amount of action 

 which has taken place. 



We must remember that the causes which have 

 given rise to the halo are highly complex. We may 

 represent the several rays concerned as generating a 

 number of concentric spheres of ionisation, the radii 

 of which are in correct relative proportion to the pene- 

 tration of the several tavs. 



7. 2. 3 4-. S. 6 7. crt. 



Fig. 2. — The eight ionisation curves forming the uranium halo. 



But this fails to represent the full complexity of the 

 conditions. Each ray behaves in a very remarkable 

 way. To enter into this matter here is impossible. 

 We must be content to recall that the effects of the 

 a ray in ionising the medium in which it travels varies 

 along its path. It appears certain that its influence on 

 the mica, or in whatever mineral it generates the 

 halo, depends upon its power of ionising the atoms 

 with which it comes into effective contact. Now the 

 number of ions created along its path remains at first 

 fairly constant, but rapidly increases towards the close 

 of its career, just before its effects become naught. 

 Bragg 's well-known curve shows the manner in which 

 the ionising effects in air of a single a particle vary 

 along its course. This curve applies to all rays, how- 

 ever short the range ; we must simply curtail the length 

 of the earlier part of the curve when the range is 

 short. 



Now, if we assume that the distribution of effects of 

 the ray along its course in the mica are much the same 

 as they are in a gas, we see that along any radius of 

 the halo-sphere we must admit the effects of eight 

 rays, each ray penetrating a distance depending on its 

 initial velocity ani acting upon the mica in the manner 

 XO. 2492, VOL. 99] 



10 

 9 



8 



7 

 6 



5 



4 

 3 

 2 



I 



3 4 5 6 



7 8 



cm. 



Fig. 3. — Integral curve of ionisation for uranium 

 halo. 



represented by the Bragg curve of ionisation. Fig. 2 



shows you this state 01 affairs. We assume that by 

 adding the ordinates at any point we can find the 



integral or total ionisation due to all eight rays so 



far as they produce an effect at that point. The curve 



of total .ionisation 



follows (Fig. 3). iz 



But even this 



cur\'e does not re- 

 present the entire 



conditions. It may 



be said to repre- 



s e n t the effects 



along a radius of 



the sphere which 



has been traversed 



by all the eight 



rays. But the 



radii of the sphere 



are, of course, 



diverging from the 



centre. The net 



effects which gene- 

 rate the halo must 



therefore grow 



weaker outwards. 



When we make 

 the requisite allow- 



a n c e for this, 



nearly all the de- 

 tail of the last 

 curve disappears, 



and we are given as the theoretical structure of the halo 

 a steadilv diminishing density outwards until we reach 

 such a distance from the centre that RaCi or ThC, — 

 as the case may be — begins to exert its separate effects. 

 These effects then 

 appear as a pen- « 

 umbra-like border 

 surrounding the 

 inner darkening. I 

 now show you, for 

 the case of the 

 uranium halo, this 

 final curve of de- 

 velopment (Fig. 4). 

 Halos exhibiting a 

 character in ifair 

 conformity with 

 the curve are not 

 uncommon. 



But, as I have 

 said above, less ex- 

 posed halos show 

 considerable detail. 

 We find, in fact, 

 that separate and 

 individual rings 

 are developed in 

 the growing halo. 

 Plainly this should 

 not be if the de- 

 velopment was in 

 accordance with 

 the last curve. 

 Under favourable 

 conditions such re- 

 calcitrant halos are 

 met with. It is 

 quite e\'ident that 



they are out of agreement with the theoretical 

 curve. The growth has not been one of uniform 

 darkening outwards with the final addition of 

 the penumbra due to RaC,. And, most contradictory 

 of all, we see that the effects of RaCi show themselves 



c/n. 



Fig. 4. — The integral curve modified by 

 spreading of the raj's. 



