52 



nomy." By J. W. Lubbock, Esq. V.P. and Treasurer of the Royal 

 Society. 



The first part of this paper relates to the theory of the moon. 

 The method of solution pursued by Clairaut consisted in the inte- 

 gration of differential equations, in which the true longitude of the 

 moon is the independent variable : the time is then obtained in 

 terms of the true longitude ; and by the reversion of series, the lon- 

 gitude afterwards obtained in terms of the time. This method 

 is the one adopted by Mayer, Laplace, and Damoiseau. The au- 

 thor has been led, by reflecting on the difficulties of this problem, 

 to believe that the integration of the differential equations in which 

 the time is the independent variable would be at least as easy as 

 the former process ; and it would possess the advantage of employing 

 the same system of equations for the moon as for the planets. The 

 lunar theory proposed by the author, and developed in this paper, 

 is an extension of the equations given in his former Researches in 

 Physical Astronomy, already published in the Philosophical Trans- 

 actions ; by including those terms, which, in consequence of the 

 great eccentricity of the moon's orbit, are sensible ; and by sup- 

 pressing those which are insensible from the great distance of the 

 sun, the disturbing body. He has not yet attempted to obtain nu- 

 merical results, but proposes at some future time to engage in their 

 computation. 



In the second part of the paper, he investigates the precession of 

 the equinoxes, on the supposition that the earth revolves in a re- 

 sisting medium ; an investigation which may also be considered as 

 a sequel to the author's last paper on Physical Astronomy. The 

 effects of the resistance of such a medium is to increase the latitude 

 of the axis of rotation (reckoned from the equator of the figure) 

 till it reaches 90°. Such is now the condition of the axis of the 

 earth : but as the chances are infinitely great against this having 

 been its original position, may not its attainment of this position be 

 ascribed to the resistance of a medium of small density acting for 

 a great length of time, — a supposition which may account for many 

 geological indications of changes having taken place in the climates 

 of the earth ? The operation of such a cause would be also sen- 

 sible in the case of comets: and the accuracy with which the ec- 

 centricity of the Halleian comet of 1759 is known, would appear to 

 afford a favourable opportunity of verifying this hypothesis. 



A paper was read, entitled, " An Account of the Construction and 

 Verification of the Imperial Standard Yard for the Royal Society." 

 By Captain Henry Kater, F.R.S. 



The scale of the standard, of which an account is given in this 

 paper, is constructed in a manner described in the Philosophical 

 Transactions for 1830. The support is of brass 40 inches long, 

 17.5 inches wide, and 0.6 of an inch in thickness. A brass plate 

 seven-hundredths of an inch thick was made to slide freely upon the 

 support in a dove-tail groove formed by two side plates, and was 

 then fixed to the support by a screw passing through its middle. 



