284 MR. N. BOHR ON THE DETERMINATION OP THE 



from (3) and (2) it follows that 



Vp = ............ (4) 



Putting 



i 3 i 3x> i dp , / c \ 



u = -r-^-+u l , v = ^-^+v l} a> = - r ^+<a l .... (5) 

 cbp fix cbp dy cop tiz 



we get 



(V-t&^w^O, (v-ib^v^O, (V-ib^w^O, ... (6) 



It I p-J 



and 



3z 



Now introducing polar co-ordinates r and (.-r = / cos &,y = r sin 3), and the radial 

 and tangential velocity a and /3, we get, by help of the following relations, 



3 ^ 1 ^ 



a = a cos .5 /3 sin , (^ = a, cos ^ R sin 3, ^ = cos ^ - -- sin 5 - ^-, 



ex or r dy . . 



1^ 



1 ^ -i j\ 



v = a sin S + B cos 5, '! = aj sin -9 + /3j cos , ^- = sin -5^- + cos 3 - ^-, 



o?y o?' T o-t 



from (5) 



....... (9) 



p\2 i o 1 r) 2 J5 2 



and from (6) and (7), considering V = ^ + - ^- + - 2 ^ + ^, 



and 



3o 1 a i l3 J 8 1 3a. 1= 



Now supposing that p, a, ft, <a, and consequently a u /S^ &)i, have the form 

 /(r)e"'* + ''*-', we get from (4) 



of which the solution, subject to the condition to be imposed when r = 0, is 



......... (12) 





in which J n is the symbol of the BESSEL'S function of rt th order. 

 From (6) we get 



which gives 



. . . . (14) 



