536 Royal Society : — 



apply them to the assumed diameter at mean distance of the 

 Earth from the Sun (namely, 32' 1"80 to the end of 1852, and 

 32' 3"64 from the beginning of 1853), to produce a corrected 

 diameter of the Sun at mean distance, we form the following 

 Table :— 



Instruments 

 employed. 



Period. 



No. of obs 



Corrected 

 horizontal 

 diameter. 



No. of 

 obs. 



Corrected 

 vertical 

 diameter. 



Transit and 1 

 Mural Circle J 



Transit Circle \ 



1836 to 1850 



{1851 and 1852} 



{1853 to I860} 



Mean 1851 to 1860 



1502 



{190} 



{795} 



985 



32 3-68 



{32 3-20} 



{32 2-65} 



32 276 



1625 



{218} 

 {851} 

 1069 



32 3-58 



{32 2-85} 

 {32 2-61} 

 32 2 66 



Thus the observations with both classes of instruments, in ag- 

 gregate number 2487 for horizontal diameter, and 2694 for ver- 

 tical diameter, agree in showing that the horizontal diameter 

 exceeds the vertical diameter by only 0"'l, a quantity smaller 

 than we can answer for in these or in any other methods of ob- 

 servation. 



A consideration of the number and excellence of the observa- 

 tions fully supports the view which I have stated in introducing 

 this subject, — that the only result which 'could be deduced from 

 the trial of new apparatus would be to test the apparatus, but 

 not to add to the certainty of the conclusion as to the equality 

 of diameters. 



The diameter adopted now in the Nautical Almanac was in- 

 ferred from observations made with the Transit and Mural Circle, 

 and therefore agrees very closely with that here deduced from the 

 use of those instruments. That obtained with the Transit Circle 

 is less by 0"-93. 



Royal Observatory, Greenwich, 

 December 28, 1861. 



LXX. Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Continued from p. 485.] 



January 10, 18G1. — Major- General Sabine, It.A., Treasurer and Vice- 

 President, in the Chair. 

 THE following communications were read : — 

 " On the Equation for the Product of the Differences of all but 

 one oi the Hoots of a given Equation." By Arthur Cayley, Esq., 



F.R.S. 



