THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



AUGUST 1914. 



XXII. The Equilibrium of Revolving Liq 



Force. By Lord Rayleigh, O.M.] 



THE problem of a mass of homogeneous incompressible 

 fluid revolving with uniform angular velocity (to) and 

 held together by capillary tension (T) is suggested by well 

 known experiments of Plateau. If there is no rotation, the 

 mass assumes a spherical form. Under the influence of 

 rotation the sphere flattens at the poles, and the oblateness 

 increases with the angular velocity. At higher rotations 

 Plateau's experiments suggest that an annular form may be 

 one of equilibrium. The earlier forms, where the liquid still 

 meets the axis of rotation, have been considered in some 

 detail by Beerf, but little attention seems to have been given 

 to the equilibrium in the form of a ring. A general treat- 

 ment of this case involves difficulties, but if we assume that 

 the ring is thin, viz. that the diameter of the section is small 

 compared with the diameter of the circular axis, we may 

 prove that the form of the section is approximately circular 

 and investigate the small departures from that figure. It is 

 assumed that in the cases considered the surface is one of 

 revolution about the axis of rotation. 



* Communicated by the Author. 



f Pogg. Ann. vol. xcvi. p. 210 (1855) ; compare Poincare^s Capil- 

 larity 1895. 



PMl. Mag. S. 6. Vol. 2S. No. 164. Aug. 1914. M 



