282 MR N. BOHR ON THE DETERMINATION OF THE 



to be sure, first, that the theoretical treatment is sufficiently developed, and secondly, 

 that the phenomenon satisfies, to a sufficient degree, the assumptions on which the 

 theoretical treatment rests. 



The main purpose of the present investigation is to try to show how this can 

 be done. 



In spite of the great advantages of the above-mentioned method for the deter- 

 mination of surface-tension, it has, however, not been very much used. Except by 

 Lord RAYLEIGH,* the method has till recently been used only by F. PiccARDt and 

 G. MEYER| for relative measurements. During the completion of this investigation a 

 treatise on this subject has been published by P. O. PEDERSEN. 



The Theory of the Vibration* of a Jet. 



The theory of the vibrations of a jet of liquid about its cylindrical form of equilibrium 

 has been developed by Lord RAYLEIGH for the case in which the amplitudes of the 

 vibrations are infinitely small and the liquid has no viscosity. 



The equations found by Lord RAYLEIGH can, when the amplitudes have small 

 values and the viscosity coefficient is small, be considered as a good approximation ; 

 but if the equations are to be used for exact determination of the surface-tension, it is 

 of importance to know how great the approximation is under the given circumstances. 

 In the first part of this investigation we will therefore attempt to supplement the 

 theory with corrections both for the influence of the finite amplitudes and for the 

 viscosity. 



Calculation of the Effect of the Viscosity. 



Under the influence of the viscosity the jet will execute damped vibrations. If 

 the problem is to find the law according to which the amplitudes decrease, this can, 

 when the viscosity-coefficient is small, be done with approximation by a simple 

 consideration of the energy dissipated. Some authors || are of opinion that the 

 correction on the wave-length (time of vibration) due to the viscosity for a problem of 

 this kind can be found directly from the logarithmic decrement of the wave- 

 amplitudes 8 by means of the formula Tj = T (l + S 2 /47r 2 ) 1/2 , where T! is the time of 

 vibration with damping, T is the time of vibration without it. This application of the 

 formula given does not, however, seem to me to be correct. For the formula is 

 established for a problem by which the only difference between the equation of motion 



* RAYLEIGH, ' Roy. Soc. Proc.,' vol. XLVIL, p. 281, 1890. 

 t PiCCARD, 'Archives d. Sc. Phys. et Nat.' (3), XXIV., p. 561, 1890 .(Geneve). 

 J MEYER, ' WIED. Ann.,' LXVL, p. 523, 1898. 

 PEDERSEN, 'Phil. Trans. Roy, Soc.,' A, 207, p. 341, 1907. 



|| P. 0. PEDERSEN (loc. cit., p. 346) ; and PH. LENARD (' WIED. Ann.,' XXX., p. 239, 1887) in his paper 

 about the analogous problem, the vibrations of a drop. 



