1890.] of Electrification on Ripples. 71 



This quantity depends on X, as might have been expected, for 

 the mechanical effects of an electric charge on the surface cannot be 

 represented as a diminution of surface tension. To produce a 

 simple reduction of tension electrically we must have the double 

 condenser larger than has been assigned by von Helmholtz as the 

 cause of voltaic polarization. 



When, as in the case of voltaic polarization, the ripples occur at 

 the interface between two liquids of densities p x and p 2 the above 

 formulas will clearly be applicable on substitution of p x + p 2 for p 

 andgfa-pj/fa + pjfarg. 



The actual values here deduced come from the form of <jf> that 

 belongs to fluid of some depth compared with X ; but it is obvious 

 that the surface tension effect combines with the electric effect in 

 the same way in every case, and that the statement just made 

 holds generally. 



As the length of the ripples diminishes, the effect of the electri- 

 fication is ultimately negligible compared with that of the surface 

 tension, though it persists much longer than the influence of 

 gravity. 



In the special case considered above the period becomes 

 imaginary if X lie between the values 



so that, if a can be made so great that these limits are real, the 



wave lengths that lie between them cannot exist. For a given 



period there will be a wave length above these limits for which 



gravity is chiefly operative, and one below them for which surface 



tension is chiefly operative. 



To obtain a rough numerical estimate : On a circular plate of 



radius a changed to potential V the electric density at distance r 



i 

 from the centre is a = F/7r 2 (a 2 — r 2 )' 2 , while on a sphere of the same 



radius the electric density is er = Vj^ira, which is rather less than 

 that at the centre of the plate. At the centre of the plate the 

 effective diminution of surface tension will be 4 V 2 X/7r 4 a\ If we 

 take a 10 cm. and X 1 cm. this gives about F 2 /2500 in C.G.S. units. 

 The value 33 for V makes the striking distance in air between 

 balls 2 cm. in diameter about '3 cm., while according to Mascart the 

 value 400 makes the striking distance between balls 22 cm. in 

 diameter about 10 cm.; the former value gives an effective diminu- 

 tion of surface tension of \\, the latter gives 64. For water the 

 actual surface tension is about 80, for mercury 540. The electric 

 effect is therefore considerable : thus Prof. C. Michie Smith (Proc. 

 R. S. Edin., March, 1890) has observed an effective diminution of 

 20 per cent, in the case of mercury owing to electrification. 



