1890.] Stability of a Rotating Spheroid of Perfect Liquid. 367 



laboratory* does not usually render a water surface unfit to exhibit 

 the camphor movements. 



The thickness of the oil films here investigated is of course much 

 below the range of the forces of cohesion ; and thus the tension of 

 the oily surface may be expected to differ from that due to a com- 

 plete film, and obtained by addition of the tensions of a water-oil 

 surface and of an oil-air surface. The precise determination of the 

 tension of oily surfaces is not an easy matter. A capillary tube is 

 hardly available, as there would be no security that the degree of 

 contamination within the tube was the same as outside. Better 

 results may be obtained from the rise of liquid between two parallel 

 plates. Two such plates of glass, separated at the corners by thin 

 sheet metal, and pressed together near the centre, dipped into the bath. 

 In one experiment of this kind the height of the water when clean was 

 measured by 62. When a small quantity of oil, about sufficient to 

 stop the camphor motions, was communicated to the surface of the 

 water, it spread also over the surface included between the plates, 

 and the height was depressed to 48. Further additions of oil, even 

 in considerable quantity, only depressed the level to 38. 



The effect of a small quantity of oleate of soda is much greater. 

 By this agent the height was depressed to 24, which shows that the 

 tension of a surface of soapy water is much less than the combined 

 tensions of a water-oil and of an oil-air surface. According to 

 Quincke, these latter tensions are respectively 2*1 and 3*8, giving by 

 addition 5*9 ; that of a water-air surface being 8"3. When soapy 

 water is substituted for clean, the last number certainly falls to less 

 than half its value, and therefore much below 5*9. 



\ 



V. 44 On the Stability of a Rotating Spheroid of Perfect 

 Liquid." By G. H. Bryan. Communicated by Professor 

 G. H. Darwin, F.R.S. Received March 12, 1890. 



1. In my communication on " The Waves on a Rotating Liquid 

 Spheroid of Finite Ellipticity,"t I stated that it did not appear 

 possible to give a complete investigation of the criteria of stability of 

 Maclaurin's spheroid when the liquid forming it is free from all traces 

 of viscosity, and equilibrium is liable to be broken by a disturbance of* 

 a perfectly general character. As the problem in question appeared to be 

 one of considerable interest, I have, since writing the above paper, put 

 the question to the test of numerical calculation in the case of the 

 simpler types of disturbance, and the results thus obtained have been 

 such as to allow of extension to a perfectly general disturbance. 



* In the country. 



f ' Phil. Trans.,' A, 1889, p. 187. 



