RECENT ADVANCES IN SCIENCE 371 



L. Bianchi (ibid. 379-401) solves the problem of deter- 

 mining all the cases for which a certain property relating to 

 what the author calls the " facettes " of surfaces applicable to 

 quadrics, holds true in all deformations of the surfaces S in 

 question. In this part of the theory of transformations of 

 deforms by flexure is an extension of the concepts introduced 

 by Sophus Lie in his researches on the transformations of 

 surfaces of constant curvature. 



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

 Greenwich. 



Stellar Evolution. — In these notes reference was made recently 

 (Science Progress, 12, 14, 191 7) to a paper by Mr. J. H. 

 Jeans on " The Part Played by Rotation in Cosmic Evolution," 

 the conclusions arrived at being that the existence of binary 

 systems, of spiral nebulae and possibly also of ring nebulae, 

 could be explained by evolution from a rotating mass of gas, 

 but that it was impossible to explain in this way the existence 

 of our solar system. This paper should be studied in conjunc- 

 tion with a cognate paper by Mr. Jeans, " The Motion of 

 Tidally Distorted Masses, with special reference to Theories 

 of Cosmogony " (Mem. R.A.S. 72, pt. i. 191 7), in which the 

 tenability of the tidal theory of planetary evolution is discussed. 

 This theory supposes the near approach of two masses of 

 matter. Each by itself, in the absence of rotation, will assume 

 the spherical form, but the near approach of the two masses 

 will raise tides in them which will have their maximum 

 amplitudes at the ends of the diameters on the common axis. 

 Thus, at any rate at first, the bodies will assume a spheroidal 

 form, just as a rotating mass does. The problem is to deter- 

 mine whether a stage is at length reached at which insta- 

 bility will occur and one of the bodies throw off a satellite. 

 The discussion is again based on Poincare's theory of lir^ar 

 series and points of bifurcation. Considering first the ca^e in 

 which the primary is homogeneous and incompressible, it is 

 found that, if the tidal action causes the eccentricity to exceed 

 a certain definite value, instability sets in and the primary 

 rapidly changes its shape ; if the tidal forces diminish sufficiently 

 quickly, the primary may regain stability and gradually sink 

 back into a spherical form. Otherwise, furrows will develop 



