346 MR. P. O. PEDERSEN ON THE SURFACE-TENSION OF LIQUIDS 



the cylinder form, and I have similarly used a method for the measurement of the 

 wave-lengths that even permits of a really good determination for small divergences. 

 This matter is more fully considered later. 



2. This hypothesis is also of great importance for the development of the theory, 

 but, on the other hand, not satisfactory in practice. The liquid has always some 

 viscosity even though, as in many cases, it is only small. It is, however, possible for 

 the most part to determine the influence of viscosity on the time of vibration, and 

 in this manner to correct the errors caused by it. 



The calculation of this correction rests upon the following supposition, which will 

 be very nearly true as long as the viscosity is small : 



The harmonic vibration of the jet corresponding to the normal co-ordinate b H is 

 changed by the viscosity to a damped harmonic vibration. 



Let the logarithmic decrement of the vibration be S ; we have then 



where N, is the frequency of vibration with damping, N is the frequency without it. 



For the determination of the surface-tension we have instead of (2) the following 

 equation 



8M .<-)., 



The experimental determination of 8 is described later. 



3. The velocity of the thin jets investigated in this work will certainly be nearly 

 the same over the whole cross-section, and correspond to that calculated from the 

 cross-section and the discharge of the jet. 



4. The surface-tension is in many cases dependent upon whether the surface 

 extends or contracts (compare, for example, the damping action of oil films on 

 waves) ; but with the fresh surfaces as used here the surface-tension is certainly very 

 nearly constant. 



Calculation of the Coefficients p. n (x). 



2. The use of the formula [(2), 1] for the determination of the surface-tension 

 demands the calculation of the coefficients p n (z) determined by the formula [(3), 

 1], or 



Here 



I n (x) = i-"J n (ix), 



where J, is the BESSEL'S function of the n th order. 



