229 



It would be more convenient if we could express in terms of , 

 but this can only be done approximatively, as in the following : 



'^---^zji^ 



If greater accuracy is required, the rule is to find from ])y 

 (2), then substitute it in (1), and compute this compared with 

 the true value shows the alteration to be made in tg_ to obtain its 

 true value. 



In conclusion the author observes, it might be expected, without 

 reference to theory, that the curve deduced from the uncorrected 

 temperatures should not show, in its continuation above 100, any 

 abrupt divergence from its regular course ; nevertheless from 100° to 

 111*74 the direction of the chord shows such a break in the law of 

 continuity, and which there appears no way of accounting for, unless 

 by a fault in the observations above 100°. Their divergence from 

 the law of density is shown in the Chart. 



The Society then adjourned over the vacation to Thursday, No- 

 vember 18, 1852. 



November 18, 1852. 



COLONEL SABINE, Treasurer, in the Chair. 



In consequence of the public funeral of His Grace the late Duke 

 of Wellington having been fixed for this day, the business of the 

 Meeting, out of respect to the memory of the deceased, was confined 

 to reading the Statute giving notice of the ensuing Anniversary 

 Meeting. 



November 25, 1852. 

 The EARL OF ROSSE, President, in the Chair. 



The Rev. B. Price, and Mr. Wyndham Harding were admitted 

 into the Society. 



The following Gentlemen were elected Foreign Members of the 

 Society : — 



A. T. Brongniart. I M. V. Regnault. 



Benjamin Peirce. I Dr. Lamont. 



The following papers were read : — ■ 



1. *'New solution of Kepler's Problem." By Professor P. A. 

 Hansen. Communicated by G. B. Airy, Esq., Astronomer Royal, 

 F.R.S. &c. Received November 18, 1852. 



It is well known how much labour has been bestowed by geometers 

 on the solution of Kepler's Problem, and what complicated results 

 have been obtained for the coefficients in the expression for the 

 Equation of the Center. I have lately found a new solution of this 

 problem, which differs so strikingly from former solutions in this re- 

 spect, that it leads to an unexpectedly simple law of coefficients. It 

 is as follows : — 



Proceedings of the Royal Society. Vol. VI. No. 91. i6 



