November 11, 1898.] 



SCIENCE. 



647 



cnoidal — can be propagated. They also 

 proved that a depressiou without a corre- 

 sponding elevation can move along, but such 

 depressions are generally unstable. Mc- 

 Cowan and Stokes have also treated these 

 waves. The existence of free oscillations 

 in canals has been investigated by Green- 

 hill, Lamb and MacDonald by Fourier's 

 methods. There is some doubt about 

 Lamb's results. MacDonald has shown 

 that it is necessary to take into account the 

 possibility of satisfying the surface condi- 

 tions and that simple formulse are not suffi- 

 cient; this point will be readily appreciated. 

 The criticism appears to be valid, but the 

 subject needs elucidation. 



An interesting problem is obtained by 

 considering the tiny waves formed in a 

 glass of water when the glass is made to 

 vibrate by means of a violin bow drawn 

 across its edge. Eayleigh has shown that 

 they are due to capillary action. It is 

 curious that the number of waves found 

 on the water in a given time is double the 

 number of vibrations made by the glass in 

 the same time. 



A good deal of interest has been taken 

 during the last two decades in the forms 

 assumed by masses of fluid rotating about 

 a fixed axis under their own attraction 

 only. Darwin and Poincare are mainlj' re- 

 sponsible for the developments which the 

 subject has received, although much has 

 been done by Madame Kowalewsky, Bas- 

 set, Dyson, Bryan and Love. To give an 

 account of all this work would take me far 

 outside the limits of this paper, and I shall, 

 therefore, simply mention some of the more 

 interesting results obtained by the first two 

 writers. 



In 1886 Darwin worked out fully the 

 various possible forms of the Jacobian el- 

 lipsoids, showing where the limits of sta- 

 bility came. In 1887 he took up the more 

 general problem of two nearly spherical 

 masses of fluid rotating like rigid bodies 



round a fixed axis under their own attrac- 

 tions only. This problem is of great im- 

 portance in theories of cosmogony. Es- 

 pecial attention is paid to the cases where 

 the two bodies get very near to one another. 

 When quite close they may coalesce and 

 form dumb-bell shaped figures. Or the 

 smaller mass may have a tendency to break 

 up into two parts, as shown by a furrow- 

 ing in its contour. 



Poincare took the subject up from a dif- 

 ferent point of view. He starts with the 

 rotating ellipsoidal form and investigates 

 what forms of relative equilibrium are 

 possible when small deviations from the 

 ellipsoid occur consistently with the con- 

 ditions. He figures a pear-shaped form of 

 possible equilibrium, and also discusses, 

 with much detail, the stability of the various 

 figures. 



I am indebted to Professor Darwin for a 

 reference to a paper by Schwarzchild, which 

 has just appeared in the Annals of the 

 Munich Observatory. In this memoir cer- 

 tain portions of Poincare's work, with 

 respect to the exchange of stabilities be- 

 tween two classes of possible figures of 

 equilibrium at the place where they meet, 

 are criticised. He also examines the sta- 

 bility of Roche's Ellipsoids by means of 

 Lame's functions, and shows that there is 

 no figure of bifurcation in this series. 



A considerable amount of attention has 

 been devoted to our last subject, the vis- 

 cosity of fluids, partly owing to the mathe- 

 matical interest of the subject and partly 

 to the difficulty of obtaining any close ap- 

 proximation to the results afforded by 

 natural phenomena. It must be stated at 

 the outset that in all the work hitherto 

 attempted the motion is supposed to be 

 sufficiently slow to enable us to neglect the 

 squares and higher powers of the velocities. 

 Practically this entails a serious limitation 

 on the usefulness of the results. Even the 

 most casual observation shows that when 



