562 Life of Radioactive Substances. 



3 n 2 e 2 

 energy of a volume charge ne of radius r is ^ , so that 



-f- = - . -= . Neglecting forces other than electrical, the 

 dr 5 r 5 ° G ' 



compressibility is thus : 



15 

 2 



7 3 V4/3 in * A 



so that the velocity q — ne\/ ^ y , T . The time r taken by 

 J * V 15Mr 2r / 3()y 3 M J 



the strain to traverse the nucleus is t = — = . 



q ne 



Inserting this value 



log X=N (log 5-76 . 10 20 + log "~^) + 2/3 N log R 

 or 



log \=N (30-819 + log^~-) -f 2/3NlogR, 



If Geiger and Nuttall's formula logA, = A + BlogR were 



strictly true, one would be forced to the conclusion that N, 



the number of particles which determine the instability, is 



Mr 3 

 constant, and that —^ is constant, n of course being the 



atomic number. These consequences are not improbable, 

 though a more searching test of the formulae, using the 

 data now available, might be advisable. In the meantime 

 it is of considerable interest to see to what values of N 

 and r the formulae lead. In all the three families B = 53*3, 

 i. e. N = 80. This in conjunction with the fact that the 

 atomic numbers of all the radioactive elements lie between 

 80 and 90 would seem to show that the moving particles 

 whose position determines the stability of the atoms are 

 the positive particles, as was to be expected ; further, that 

 nearly all the free charges must conspire to bring about 

 the explosion of the nucleus. The first constant A varies 

 for the three radioactive series, the formula being : 



logio ^= —36*9 + 53*3 log 10 R for the uranium radium family 

 log 10 X=— 38*4 + 53*3 log 10 R for the thorium series, and 

 logio ^= —39*6 -f 53*3 log 10 R for the actinium series. 



It will suffice to evaluate the radius of the nucleus for one 

 element, say radium. Taking 226 as the atomic weight and 

 88 as the atomic number, one finds r==3*85 . 10" 13 . This 

 is in fair agreement with the radius of the nucleus o£ 



