Faraday 8 "Magnetic Lines" as Quanta. 529 



which the semi-axes are a and b. Then the rate of descrip- 

 tion of area by the radius vector is irabv. But this is also 



equal to ±r 2 4> = ^—. Hence p — lirahnv. Substituting for 



x • m 



j? the value nhj2nT and for a and b the values given by 

 Soinmerfeld, • 



A 2 ' A 2 



a=-r^ 2 — Jn + n') 2 , b=- 2 2 n(n + n f ), (S. 14) 

 ^it-me 47r-m<r 



we obtain 



47T 2 ??16 4 



~~h*(n + ri)* ^ 



, -. . ,-, < 2ir 2 me 4L n 



It may be noted, in passing, that as — Tg — =v , the 



fundamental Rydberg frequency, 



2v. n 



(n + 7i')' 



(6) 



8. If a particle move in a conic section under the action 

 of a force to a focus, it is well known that the velocity at 

 any point can be resolved into two constant velocities, the 

 first, v u perpendicular to the radius vector, the second, v 2> 

 perpendicular to the major axis. This result is in harmony 

 with the expression above for the kinetic energy, for the 



e 2 , e 2 



component velocities are i'i=— and v a =e— inclined at an 

 angle <f>, which give for the square of the resultant velocity 



V 2 =~ |(l + 26 COS c/) + € 2 ). 



Consider the angular momentum about the focus for each 

 component. 



For the component i^, the angular momentum is mn^. 



Also 



C 2 « i, C 2lT P 2 d<t> P 77 d6 



I mrv 1 dq> = mV\\ — ^~ - — =» 1 - — — 



J ^ M me 2 (l + ecos(£) F % \ 1 + 6COS0 



9 7T 



=.p — ~ . , . (from S. 9 c) 



V f — e 2 



= {n + n')h (7) 



For the component y 2 j the angular momentum is mxv 2 . 



