396 



that a pencil of light reflected from the second surface of a transpa- 

 rent plate, and reaching the eye after two refractions and an inter- 

 mediate reflexion, contains, at all angles of incidence, from zero to 

 the maximum polarizing angle, a portion of light polarized in the 

 plane of reflexion. Above the polarizing angle, the part of the pencil 

 polarized hy reflexion diminishes until the cosine of the sum of the 

 angles of incidence and reflexion equals the cube of the cosine of 

 the difference between these two angles, when it disappears, and the 

 whole pencil has the character of common light. Above this last 

 angle, the pencil contains a quantity of light polarized perpendicularly 

 to the plane of reflexion, which increases to a maximum, and then 

 diminishes to zero, when the angle has attained 90. The effect of 

 the two refractions in M. Arago's experiment, was to make the two 

 quantities of light appear equal, whenjn fact the one was exactly 

 double of the other. 



The paper concludes with formulae and tables for computing the 

 exact quantities of polarized light at all angles of incidence. 



Observations made with the Invariable Pendulum (No. 4. Jones), at 

 the Royal Observatory, Cape of Good Hope, for the purpose of 

 determining the Compression of the Earth. By the Rev. Fearou 

 Fallows, F.R.S. Astronomer of the Cape Observatory. Communi- 

 cated by the Lords Commissioners of the Admiralty. Read February 

 18, 1830. \Phil. Trans. 1830,;?. 153.] 



Of the two methods employed for determining the figure of the 

 earth, namely, the direct measurements of arcs of the meridian, or of 

 ascertaining the variations in the length of the seconds pendulum in 

 different places, the author remarks that the former is attended with 

 the collateral benefit of fixing the geographical position of certain 

 stations in the country surveyed ; but the latter possesses the ad- 

 vantage of enabling the observer to concentrate, under his own im- 

 mediate eye, the results of his inquiries. The Observatory at the 

 Cape of Good Hope having been furnished by the Lords Commis- 

 sioners of the Admiralty with the invariable pendulum of Jones, which 

 had for several years been strictly examined by Capt. Sabine, the 

 author was anxious to begin a series of experiments with it ; and as 

 it was not likely that the observatory would be completed for a con- 

 siderable time, he caused a strong brick pier to be built in an ad- 

 joining outhouse for the support of a transit instrument, the same 

 which he had used in forming his catalogue of southern stars. He 

 gives a detailed account of his mode of fitting up the clock, and other 

 parts of the apparatus necessary for the pendulum experiments. He 

 was ably assisted by Capt. Ronald and Lieut. Johnson, who took an 

 active part in all the observations. He remarks, that the near agree- 

 ment of the three independent series of observations, made by him- 

 self and these two gentlemen, and which accompany the paper, is no 

 small argument in favour of their accuracy. The difference in the 

 number of vibrations of the seconds pendulum at the Cape, from that 



