Age of JPleochroic Haloes. 653 



life of uranium. From this t is found. As an example of 

 the mode in which the figures in the ensuing table are 

 derived : — halo No. 4 has a nuclear mass of 418 x 10 ~ li gram, 

 and the uranium present is taken as 418 x 10~ 15 gram. The 

 radius of the halo is 0'016 mm._, and. as it is darker than spot 

 A we calculate that the number of alpha rays required, to 

 produce this halo is not less than 2' 9 5 x 10 8 rays, or 5'9 x 10 8 

 for the whole halo. Now 8 rays are produced for every atom 

 of uranium transformed. Thus the number of uranium 

 atoms transformed has been 0'74 x 10 8 . Taking the mass of 

 one atom of hydrogen as 1*6 x 10 ~ 24 *, the mass of an atom 

 of uranium is 381 x 10 ~ 24 . The mass transformed is, hence, 

 28 xlO -15 gram. The quantity present being assumed as 

 418 x 10 -15 , this becomes 0*9373 of the original mass. The 

 exponential tables now give the corresponding value of t/~L as 

 0'065, and as L is 7*2 x 10 9 , the value of t is found to be 

 0'47 x 10 9 years. The age is greater than this as the darken- 

 ing of the halo exceeds that of spot A, but in this case no 

 attempt was made to evaluate this excess. 



The following table contains the results of 30 measure- 

 ments of nuclei. There would have been no difficulty in 

 adding to this number almost indefinitely, but it is thought 

 that the number given is sufficient. Moreover, considerable 

 time and labour are required to complete the careful 

 measurement of each halo. In Nos. 24, 25, and 26 the 

 nuclei are well developed, apparently dimetric, crystals with 

 prismatic and terminal faces. The mass is probably some- 

 what exao-p-erated, as outside dimensions are a'iven. No 

 allowance is made for a slight elongation of the derived halo. 

 Both these facts will tend to lower the age. 



The nuclei of Nos. 29 and 30 have been photographed, and 

 are reproduced in Plate IX. No. 29 (fig. 1) is magnified 

 1450 diameters ; No. 30 (fig 2) is magnified 1400 diameters. 

 It is very difficult in such photographs to show at once the 

 nucleus and the halo, for the intense conditions of exposure 

 and development requisite to bring out the former are quite 

 unsuited to reproduce the latter. The nucleus of No. 29 is 

 characteristic of the granular type. Near it is a relatively 

 large nucleus of well crystallized zircon. It has given rise 

 to a less intense halo. The halo, No. 29 (which is developed 

 round the small nucleus), is of a rich brown colour and 

 certainly darker than spot A. Centrally it is so dark that 

 the exposure required to take it has resulted in complete 

 over-exposure of the surrounding halo. In calculating the 

 volume of this nucleus it is assumed to be ellipsoidal in 



* Rutherford and Geiger, Proc. R. S., A, Ixxxi. p. 162. 



