2G4 Prof. W. Peddie on the 



Consequently, when an electron enters the atom from 

 without with speed V, and attains radial rest in the region n, 

 its energy is equally divided into potential energy and energy 

 of circulatory motion, the magnitude of each being qlw. 

 But the total^energy is Jiv n . Therefore g = l/2, and the in- 

 dependently found condition ^ = 1/4 might result from closer 

 approach of centres, during collision or under attraction in 

 the liquid state, than to one full diameter. The same final 

 result is attainable, however, if the intrinsic strength of the 

 repulsion is three times greater than that of the attraction. 



Prom the expression 



1 _ 'lirhnC r 1 J_ \ 

 r a 2 ~ qk \p{ 2 p 2 P 



together with the estimated value, 3'7(10) -13 cm., of the 

 diameter of an electron, we can calculate the maximum 

 allowable value of p n in Balmer's series on the assumption 

 that r n -i — r n is not less than that diameter. If p n — 21, 

 r n would be about 2.10 -8 cm.; if j p«=40, r n would be about 

 H.10" 8 cm., by the limitations ?* n _i — r„ = 3"7 (lO) -13 and q=l. 

 In accordance with the preceding estimate of the minimum 

 and maximum radii, the value of p n must lie within these 

 extremes. The greatest observed value is 35. The same values 

 follow if g=l/2 and r n _ Y — r n equal to ^/2 times the diameter 

 of an electron. 



But we must make r n -i—r n a considerable multiple of the 

 diameter of an electron. It is really r n " — r n ' which must 

 not be less than that diameter. If we make the multiple 

 100, q must be made equal to 10~ 4 to give the same value 

 of p n . With 35 as the maximum value of n, we now find 

 ?* 38 — 2'6'2 (10)~ 10 cm.; and the first line (n=2) in the series 

 originates at ?- 3 = 3*5 (10) ~ 10 cm. 



§ 4. The Magnetic Field and the Magneton, 



In the preceding discussion no account has been taken of 

 the magnetic field due to the rotation of the electriti cation! 

 The tangential component of the field due to the distribution 

 P(§2)is 



H*= - it sin 6 1 piCo x 7\ l~\ di\ — -tt sin 6 \ piw^d^ 



*s a. */r 



where ft is the external radius, if we regard the negative 

 core as having no rotation. The condition of equilibrium of 



