631 Prof. J. Joly and Mr. A. L. Fletcher : 



In selecting halos for investigation several sources of error 

 must be borne in mind, the neglect of which lias doubtless 

 been largely responsible for the general failure of peno- 

 logists to recognize their wonderful obedience to law. In 

 the first place it is apparent that onlv a central section of 

 the sphere can give the true radius or, if there is differentia- 

 tion, a correct ratio of the radii. Thus in complex halo* a 

 section off the centre tends to exaggerate the dimensions of 

 the iris compared with that of the pupil ; and iu simple or 

 structureless halos the radius of an excentric section of the 

 halo must be misleading. "With respect to this source of 

 error the only safeguard is the certain presence of the origi- 

 nating radioactive particle. When this is plainly defined we 

 cannot be far from a central section. 



A second source of error arises when the originating 

 radioactive mineral has dimensions which are not negligibly 

 small compared with the radius of the halo. When the 

 radius of the nucleus is, relatively, not negligible, its mean 

 diameter should, in genera!, be deducted from the diameter 

 of the halo. This is so because in many cases it is demon- 

 strable that rays leaving the surface — or from points near the 

 surface — of the nucleus have determined the boundary. 

 Thus a large square zircon-section may show a sub-circular 

 halo enclosing its sides ; the measurements from the boun- 

 daries of the zircon being correct for radium C. In general 

 halos occasioned by large nuclei are badly defined and hazy 

 upon the edge owing to rays coming from different distances 

 in the nucleus spoiling the boundary definition. In very 

 small nuclei there is but little error due to the passage of 

 central rays through the nucleus. Thus for zircon the 



\/atomic weight . ' . . „ , .. . 



quantity — , -, — ^— is 1*1; in the case or thorite it 



1 J density 



is 1*2; in uraninite about 1; and in the cases of hornblende 

 and biotite about 1*8 and 1*6 respectively. There is, there- 

 fore, some retardation in nuclei formed of the radioactive 

 minerals ; but it is easy to see that the error introduced by 

 neglecting it is of quite a different order from that which- 

 arises when the ranges in air of rays proceeding from beneath 

 the surface of a solid film are being observed. The correction, 

 such as it is, seems to be in most cases subtractive. Thus in 

 the case of a nucleus having a radius of, say, 0*0021 mm. 

 we cannot well assume that the outer boundaries are defined 

 either by rays proceeding from the very surface, nor yet 

 from the very centre of the radioactive particle. If we 





