1879.] 



the Capillary I'henomena of Jets. 



79 



Pressure. Wave-length.. V (Pressure). Corrected. 



192 20 19-8 19-3 



167* 18-!* 18-5* 18-0 



136 161 16-6 16-1 



107 14 14-8 14-2 



87 13 13-3 12 7 



65 lOf 11-5 10-8 



47 8J 9-8 8-9 



The third column contains numbers proportional to the square roots 

 of the pressures. In the fourth column a correction is introduced, 

 the significance of which will be explained later. 



The value of X, other things being the same, depends upon the 

 nature of the fluid. Thus methylated alcohol gave a wave-length 

 about twice as great as tap water. This is a consequence of the 

 smaller capillarity. 



If a water jet be touched by a fragment of wood moistened with 

 oil, the waves in front of the place of contact are considerably drawn 

 out ; but no sensible effect appears to be propagated up the stream. 



If a jet of mercury discharging into dilute sulphuric acid be 

 polarized by an electric current, the change in the capillary constant 

 discovered by Lipmann shows itself by alterations in the length of 

 the wave. 



When the wave-length is considerable in comparison with the 

 diameter of the jet, the vibrations about the circular form take place 

 practically in two dimensions, and are easily calculated mathematically. 

 The more general case, in which there is no limitation upon the mag- 

 nitude of the diameter, involves the use of Bessel's functions. The 

 investigation will be found in Appendix I. For the present we will 

 confine ourselves to a statement of the results for vibrations in two 

 dimensions. 



Let us suppose that the polar equation of the section is 



r=a + a n cos 7i0 . ..... (1), 



so that the curve is an undulating one, repeating itself n times over 

 the circumference. The mean radius is a ; and, since the deviation 

 from the circular form is small, a n is a small quantity in comparison 

 with a . The vibration is expressed by the variation of ct)i as a har- 

 monic function of the time. Thus if a n occos (jpt — e), it may be proved 

 that 



p=*Wp-*A-*</(n*-^n) (2). 



In this equation T is the superficial tension, p the density, A the area 

 of the section (equal to 7ra 2 ), and the frequency of vibration isp-^-^w. 



For a jet of given fluid and of gi ven. area, the frequency of vibration 

 varies as y/(n 3 — n) or V (n— l)?i(w + l). The case of n—1 corre- 



