342 Analysis of Books. 



polarization, the ray has the same properties in all its sides, and 

 the angles of reflexion at which it is restored to simple polarized 

 light in different azimuths are all equal, like the radia of a circle 

 described round the ray. In the case of metallic reflexions, the 

 new phenomena discovered by Dr. Brewster may be designated by 

 the term elliptic polarization, because the angles of reflexion at 

 which this kind of light is restored to polarized light may be repre- 

 sented by the variable radius of an ellipse. In circular polarization 

 the restored ray has its plane of polarization always inclined 45 

 to the plane of the second system of reflexion. In elliptic polari- 

 zation the inclination of the plane of the restored pencil is always 

 less than 45. In the former case this plane continues by successive 

 reflexions to oscillate on each side of the plane of reflexion, with a 

 never varying amplitude + 45 to 45. While in the latter case the 

 same plane oscillates with an amplitude continually diminishing 

 till it is brought to Zero in the plane of reflexion. In steel the 

 polarization is highly elliptical, and the amplitude of the oscillations 

 of the plane of restoration is quickly brought to Zero ; but in 

 silver, whose polarization approaches nearly to circular, the oscil- 

 lations diminish very slowly in amplitude. The peculiar character 

 of elliptic polarization shews itself also in another manner, in the 

 variable position of the ellipses which regulate its angles of resto- 

 ration upon steel. In the third section of his paper, the author 

 treats of the complementary colours produced by successive reflexion 

 from the polished surfaces of metals. 



He concludes by observing, that although we do not understand 

 the nature of the forces by which metals reflect the two oppositely 

 polarized pencils, yet we are certain they do not act exactly in the 

 same manner as the second surfaces of transparent bodies : when 

 producing total reflexion setting out from a perpendicular incidence, 

 the least refrangible rays begin to suffer the double reflexion sooner 

 than the mean ray, and they sooner reach their maximum of elliptic 

 polarization, thus exhibiting the inversion of the spectrum. The 

 theory of circular polarization, as given by Fresnel, will, no doubt, 

 embrace the phenomena of elliptic polarization, and when the nature 

 of metallic action shall have been more thoroughly examined, we 

 may expect to be able to trace the phenomena under consideration 

 to their true source. 



6. Researches in Physical Astronomy. By John William Lubbock, 

 Esq., F. R. S. [Read April 29, 1830.] 



THE analytical expressions for the variations of the elliptic constants 

 given by Laplace, in his Mechanique Celeste, are true only when the 

 square and higher powers of the disturbing forces are neglected in 

 the computation : and by proceeding on the supposition that all the 

 planets move in circular orbits and in the same direction, he has 

 demonstrated that the eccentricities and inclinations vary within 

 small limits, and that the stability of the planetary system is always 

 eventually preserved. But Mr. Lubbock shews, in the present paper, 



