180 Sir Oliver Lodge on 



even for hydrogen, and at still smaller distances for substances 

 of greater atomic weight. Shall we say at about half the 

 atom's radius for hydrogen, and at about one-fortieth of the 

 radius for the heaviest and presumably largest atoms. 

 (Cf. Broughall in Phil. Mag. for last June, p. 872.) 



The critical frequency of the radiation most suitable for 

 expelling an electron from a given element is, by (5), 



n =T -^ Xl0 16 X g-; 

 l*5b lir 



which is 6'53 x 10 15 for hydrogen, 



and increases with the square of the atomic number, 



attaining 5*5 x 10 19 for uranium. 



The critical velocitv with which an electron is expelled is,. 



by (3), 



which for hydrogen is 2*18 x 10 8 , and reaches two-thirds the 

 speed of light for N = 92. 



Only at that speed the inertia would have increased (by 

 reason of the ft factor) enough to make the break occur 

 rather earlier. 



Numerical results very like these have already been 

 obtained by Dr. Bohr's admirable treatment, but in a matter 

 of this interest and importance there seems no harm in 

 discussing the subject afresh in a simple manner and getting 

 the details more widely known. Moreover there are some 

 other points of view still to be considered. 



Note on Atomic Instability. 



In the Proc. Poy. Soc. for January 1918, vol. xciv. p. 281,. 

 Sir Arthur Schuster shows that a resonator will pick up 

 energy and have its swings increased by a random succession 

 of blows in every direction indiscriminately, such as may be 

 regarded as the equivalent of ordinary white light ; and that 

 in the absence of friction the amplitude under this irregular 

 stimulus would increase indefinitely, apart from any question 

 of resonance. 



Also that a particle without any natural frequency, beaten 

 about by random blows like a Brownian molecule or a football 

 in a scrimmage, will attain a definite translatory energy 

 comparable with that appropriate to the kinetic theory o£ 



