RECENT ADVANCES IN SCIENCE 189 



R. Moritz in a paper on Hill's Cusped Orbit (M.N., R.A.S., 

 78, 48-53, 191 7) and E. Lindsay Ince on the General Solutions 

 of Hill's Equation (ibid. 14 1-7) continue the detailed discussion 

 of one of the classical problems of celestial mechanics. 



L. Becker (ibid. 77, 655-62, 191 7) investigates the law of 

 density of a spheroid that will account for the spiral arms 

 of nebulae. 



Vessiot (Comptes Rendus, 165, 99-102, 191 7) shows how to 

 pass from one set of canonical co-ordinates to another in celestial 

 mechanics, without successive transformation of variables. 



Mechanics of Fluids. — Lord Rayleigh (Phil. Mag. (6) 

 34, 94-8, 191 7) simplifies and extends Besant's work on the 

 pressure developed in a liquid during the collapse of a spherical 

 cavity, to explain the sound emitted by water on the boil owing 

 to the collapse of air bubbles as they rise through cooler water. 



S. Banerji (Phil. Mag. (6) 35, 97-1 11, 191 8) writes on 

 " Aerial Waves Generated by Impact," investigating the wave 

 motion set up in air by the impact of solid bodies, especially 

 the effect of the sizes and densities of the bodies on propagation 

 of the sound in various directions. 



T. H. Havelock (Proc. Roy. Soc. 93, A, 520-32, 191 7) in 

 a paper entitled " Some Cases of Wave Motion due to a Sub- 

 merged Obstacle " extends Lamb's two-dimensional work to 

 the case where the obstacle is a sphere. 



K. Terazawa (Sc. Rep. of Tohoku Imp. Univ. 6, 169-81, 

 191 7) examines the " Oscillations of the Deep Sea Surface 

 caused by a Local Disturbance," (1) with the initial displacement 

 given, (2) with the initial impulse given. The solution depends 

 on the function y(x) = e' x 'f x e p dt, which is fully investigated 

 by the author and tabulated for a wide range of values of x. 



H. Jeffreys (Phil. Mag. (6) 34, 112-28, 449~58, 19*7) in 

 two papers " On Periodic Convection Currents in the Atmo- 

 sphere " considers the effect of eddy viscosity in the equations 

 of motion. He finds that the terms dependent on the vertical 

 velocity may be neglected in some cases, but that in others, as 

 e.g. for a small circular island, they must be retained. 



ASTRONOMY. By H. Spencer Jones, M.A., B.Sc, Royal Observatory, 



Greenwich. 



Determination of Telescopic Flexure. — An accurate knowledge 

 of the flexure of a telescope used for fundamental meridian 

 13 



