286 MR. N. BOHR ON THE DETERMINATION OF THE 



Let us suppose that the equation of the surface is 



r-a = = De" s+d ". 

 The general surface-condition gives 



D , /a/33 a \, n 



(r-a-Q = -.+ e- +w -(r-a-Q = 0, 



whence we get, neglecting quantities of the same order of magnitude as above, 



- !- l = ~lk" ......... < 22) 



In the same manner we get further, if the principal radii of curvature are Rj 

 and R 2 , 



J_ J_ 1 L 1^_^ 1 i(n'-l + yq') (23 . 



ft, K 2 a 2 2 as 2 W ~ <t a 2 cb 



Let Pr, PS, Pz be respectively the radial, tangential, and axial component of the 

 traction, per unit area, exerted by the viscous fluid across a surface-element 

 perpendicular to radius-vector. Taking the radius-vector concerned as X-axis, and 

 using the notation generally employed, we have 



D du T3-, /dv , ou\ -rj idw , 'du 



pr-.= P ^= - P+ ^-, P^ = ^,.V = /^^+^J> n -A--/*^ + 



Using the relations (8), and after the differentiation setting & = 0, we get 



a dw\ ,.% 



+ _. . (24 ) 



Calling the surface-tension T and assuming that there is no " superficial viscosity," 

 the dynamical surface-conditions will be, using the same rate of approximation as 

 before, 



+ ^Wpr = const., PS = 0, Pz = ; ..... (25) 



.;_:> 



(26) 



from (25) we get, using (23) and (24), 



a 3_A = /a. |px =a -- } 



r 8^ 8r r/,- = \3z or/,- = a 



Introducing in these conditions the values of p, a, y8, w found by (12) and (21), we 

 get, after the elimination of B/A and C/A, an equation for the determination of 6. 



