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XXXVI. Notices respecting New Books. 



Problems of Cosmogony and Stellar Dynamics. By J. H. Jeaxs, 

 M.A., F.B..S. Being an essay to which the Adams Prize of the 

 University of Cambridge for the year 1917 was adjudged. 

 Cambridge : at the University Press, 1919. 293 pp., 5 plates. 



r PHE essay is a daring attempt, in continuation of previous 

 attacks initiated by Maclaurin, Kant and Laplace, and 

 followed up by Boche, Jacobi, Kelvin, Poincare, and G. 11. 

 Darwin, to continue the investigation of possible configurations 

 of a rotating gravitating fluid mass, and of its stability, and 

 to carry it on to a gaseous conglomeration, as of the spiral and 

 other nebulae. 



The book falls then into two parts : in the first six chapters a 

 homogeneous incompressible gravitating liquid is postulated, and 

 the shape investigated which it can assume, starting from a 

 spherical form, and then endowed with rotation gradually in- 

 creasing which causes it to assume a variety of shape, passing- 

 through the Maclaurin spheroid into the Jacobian ellipsoid, and 

 this again into the Poincare pear-shaped figure, finally breaking 

 cataclysmicallv into two parts, a main body and its satellite, or the 

 state of a double star, the final object of Darwin's research. 



In these last two investigations the mathematical difficulties 

 are almost insurmountable, and extraordinary approximations are 

 required to arrive at any definite result, and even then the 

 methods are not of universal acceptance, and much controversy 

 has been excited. 



The difficulty of the existence of a free surface, and its stability, 

 is the chief impediment to progress : and the various stages are 

 very instructive in revealing the branch points where the class of 

 surface changes place. 



Throughout the subject the angular velocity w appears involved 



with the density p, in the form of the fraction — , so that o is here 



the astronomical density, of the dimensions of the square of an 

 angular velocity, or (time)- 2 . Astronomical density p is converted 

 into C.Gr.S. density 3(g/cm 3 ) by the factor G, the constant of gravi- 

 tation, G== 666 x 10- 10 , according to the experiments of C. V. Boys, 



and then the fraction becomes ^-ftv The astronomical unit of 

 mass is then — = 10 7 x 1-5, g, or 15 metric tons. 



This fraction can be made more intelligible physically by intro- 

 ducing Maxwell's idea, of the grazing satellite of the' stationary 

 spherical globe ; then if K is the grazing velocity, and r the radius 



