fiS Notices respecting New Booh. 



as his expressions show,) in a vertical circular orbit of which the 

 radius decreases very rapidly as the depth below the surface increases. 

 We may point out to Mr. Green that this conclusion had already 

 been virtually drawn by Laplace in his Memoir on the Tides, pub- 

 lished by the Academy of Sciences in 1775. We may, however, 

 observe that this result has acquired a new interest since the ex- 

 perimental researches of the Webers on this subject, with which it 

 is incomplete accordance. Mr. Green has in another case (that of 

 a canal with a triangular section) compared his theoretical results 

 with the experiments of Mr. Russell, and finds the agreement much 

 more close than that which is given by Mr. Russell's own empirical 

 formula. 



The constitution and motions of the supposed fluid of light and 

 heat form a wider subject of investigation. Ever since it appeared 

 by the great discoveries of Young and Fresnel, that the hypothesis 

 of transverse undulations explains with such marvellous exactness 

 the most complex phaenomena of light, mathematicians have been 

 endeavouring to demonstrate the mechanism of such undulations, 

 and to determine their laws under various circumstances. 



M. Cauchy in France, Sir William Hamilton and Prof. MaccuUagh 

 in Ireland, Prof. Airy, Mr. Green, Mr. Kelland, Mr. Tovey in Eng- 

 land, have employed on investigations of this kind all the higher 

 resources of mathematics. In the volume now before us, we have, 

 bearing on this subject, Mr, Green's memoir " On the Laws of the Re- 

 flection and Refraction of Light at the common surface of two non- 

 crystallized Media;" and Mr. Earnshaw's " On the Nature of the 

 Molecular Forces which regulate the Constitution of the luminife- 

 rous^ther." Mr. Green explains the peculiar starting-point of his 

 researches in this manner. M. Cauchy had considered the lumini- 

 ferous aether, and the bodies which act upon it, as systems of mole- 

 cules in which every two particles act upon each other in the direc- 

 tion of the straight line which joins them. But this supposition, 

 Mr. Green says, seems to involve too narrow a restriction ; for 

 many phaenomena, those of crystallization for instance, seem to in- 

 dicate certain polarities in the particles, which have never yet been 

 shown to be resolvable into direct attraction and repulsion. Hence 

 he selects for his basis a wider assumption, which may be expressed 

 analytically, and which involves the precarious jjhysical hypothesis 

 of M. Cauchy as a particular case. He obtains from this principle 

 vaiious results, and in the first place this ; that in the luminiferous 

 cether the velocity of transmission of waves propagated by normal vi- 

 brations is very great compared with that of ordinary light. Mr. 

 Green investigates the intensity of the waves reflected at the com- 

 mon surface of two media ; and in the case of light polarized in 

 the plane of incidence, obtains precisely the values given by Fresnel. 

 In the case of light ])olarized perpendicular to the plane of inci- 

 dence, it a])pears from the present investigations, that the expressions 

 given by Fresnel are not rigorously true, but are only very near ap- 

 proximations. It appears that the intensity of the reflected wave 

 will never become absolutely null, but only obtain aminimum value j 



