Light and, Electrons. 179 



■changes only discontinuously by integer mutations, hence 



±ir L m 



which is the same for all atoms, since m is the mass of an 

 electron. 



Combining (1) and (2) we get, — 

 for the critical velocity 



3ac 2 2-irm T 



7 * ( h V X M>> 



for the critical distance 

 2 



3ac 5 

 and for the critical frequency 



/3ac 2 \ 2 /27rm\ 3 N 2 rK , 



n =\T) •■\nr) -s- • • ' (5) 



'They are all of the right dimensions, and vb is independent 

 of the atomic number N. 



Interpreting them in c.g.s. measure, and using Prof. 

 Millikan's experimental values for h and e, 



, .1 = 6-547 xlO~ 27 , 

 viz 



fA = 6'547 

 U=4-774 



•774xl0" 10 if /c = l 

 or 1*591 xlO- 20 if /a=1, 

 ,the consistent mass and size of an electron being 

 m = '9x 10 ~ 27 gram, and 



^ixe 2 

 a——-— = 1*875 X 10" 13 centim., 

 dm 



we find that s is nearly unity, or more accurately 



.1*16 c.g.s., while 



^ = 2-53 xlO 8 c.g.s. 



Hence it turns out that the critical distance at which a 

 fully-formed electron can escape is, by (4), 



•53 ,. , 



b = ■ „ ^ >,- ■ centimetres ; 



so break occurs inside the conventional boundary of the atom, 



N2 



