88 



Lord Kayleigh on 



[May 15, 



the drop during one complete vibration, and is therefore (as Plateau 

 shows) proportional cceteris paribus to the square root of the head. 



The time of vibration is of course itself a function of the nature of 

 the fluid and of the size of the drop. By the method of dimensions 

 alone it may be seen that the time of infinitely small vibrations varies 

 directly as the square root of the mass of the sphere and inversely as 

 the square root of the capillary tension ; and in Appendix II it is 

 proved that its expression is 



*=^if) ^ 



V being the volume of the vibrating mass. 



In an experiment arranged to determine the time of vibration, a 

 stream of 19"7 cub. centims. per second was broken up under the 

 action of a fork making 128 vibrations per second. ^Neglecting the 

 mass of the small spherules (of which more will be said presently), we 

 get for the mass of each sphere 19" 7 -r-128, or '154 grm. ; and thence 

 by (10), taking as before T = 81, 



t=-0473 second. 



The distance between the first and second swellings was by measure- 

 ment 16*5 centims. The level of the contraction midway between the 

 two swellings was 36*8 centims. below the surface of the liquid in the 

 reservoir, corresponding to a velocity of 175 centims. per second. These 

 data give for the time of vibration, 



T=16-5-h36-8 = -0612 second. 



The discrepancy between the two values of t, which is greater than 

 I had expected, is doubtless due in part to excessive amplitude, 

 rendering the vibration slower than that calculated for infinitely small 

 amplitudes. 



A rough estimate of the degree of flattening to be expected at the 

 first swelling may be arrived at by calculating the eccentricity of the 

 oblatum, which has the same volume and surface as those appertaining 

 to the portion of fluid in question when forming part of the undis- 

 turbed cylinder. In the case of the most natural mode of resolution, 

 the volume of a drop is dtra 3 , and its surface is 187ra 2 . The eccen- 

 tricity of the oblatum which has this volume and this surface is '944, 

 corresponding to a ratio of principal axes equal to about 1 : 3. 



In consequence of the rapidity of the motion some optical device is 

 necessary to render apparent the phenomena attending the disintegra- 

 tion of a jet. Magnus employed a rotating mirror, and also a rotating 

 disk from which a fine slit was cut out. The readiest method of 

 obtaining instantaneous illumination is the electric spark, but with 

 this Magnus was not successful. " The rounded masses of which the 

 swellings consist reflect the light emanating from a point in such a 



