K)8 



(hieing 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 be more thoroughly examined, we may expect 

 to be able to trace the phenomena under consideration to their true 

 source. 



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

 F.R.S. Read April 29, 1830. [Phil. Trans. 1830, p. 327.] 



The analytic expressions for the variations of the elliptic con- 

 stants given by Laplace in his Mtcanique 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 shows in the present paper 

 that these conditions are not necessary to the stability of a system of 

 bodies subject to the law of attraction which governs our system ; 

 and he gives expressions for the variations of the elliptic constants 

 which are rigorously true, whatever power of the disturbing force be 

 retained. 



On the Error in Standards of Linear Measure, arising from the thick- 

 ness of the Bar on which they are traced. By Captain Henry Kater, 

 V.P. and Treas. R.S. Read June 17, 1830. [Phil. Trans. 1830, 

 p. 359.] 



While engaged in the adjustment and verification of the copies of 

 the Imperial standard yard destined for the Exchequer, Guildhall, 

 Dublin, and Edinburgh, the author discovered a source of error arising 

 from the thickness of the bar, upon the surface of which measures of 

 linear dimension are traced. A notice to that effect was published 

 in the Philosophical Transactions for 1826; and the object of the pre- 

 sent paper is to give an account of the experiments the author has 

 since made on this subject, and to describe a scale which he has had 

 constructed, so as almost entirely to obviate the source of error thus 

 introduced. 



From the experiments detailed in the first part of the paper, the 

 following conclusions are deduced : First, that in a standard of 

 linear measure, traced upon the surface of a bar, an error arises from 

 the thickness of the bar when it is placed upon a table the surface 

 of which is not plane ; Secondly, that this error in bars of the same 

 material, and of unequal thickness, is within certain limits as the 

 thickness of the bar, and depends upon the extension of that sur- 



