207 



II. That the electric attraction gives the centripetal force for 

 the circular motion is expressed by the equation 



Bohr's condition for the stationary circular paths gives 



rh 

 mr^ (£ =: — — 



^ 2jr 



where t is a whole number. 



For the r^^ circle the energy is therefore 



(«-2) 

 _2(«-2) _^ jL „_4. 



h' J 2(n — 2) ' 



where ?2 > 2. 



For Rn too we suppose the radiated frequencies to be calculable 

 from 



V^ T =■ 



h 



For n = 4: we have a singular case. Equation (.4) becomes then 



r* (f' = - 



f m 



so that 



7nr^ ff =z e [/m . 



The moment of momentum can thus have only one perfectly defined 

 value: e\/m, so that the coeflficient of attraction must be connected 

 with h if the quantum condition (necessarily with only one value 

 of r) remains. For ?i ^ 4 we find 



where x is a positive fraction in general. Thus we obtain 

 series in the spectrum which for constant t and increasing <j contain 

 lines in the ultraviolet which become more and more distant from 

 one another. 



III. The solution of the equation of vibration for a membrane 

 can be derived from that for a three-dimensional body by supposing 

 in the latter case the disturbances of equilibrium to be in the 

 beginning independent of one of the rectangular coordinates e.g. of 



2 

 to an infinite distance without velocity, — u. divided by — on the other hand the 



m 



energy required to carry it without velocity to the distance 1 from the centre, 



