Royal Society. 133 



highest mountains bear to the radius of the earth, and also the re- 

 lation which the body of the earth itself bears to the sun. Measured 

 by such a scale, the highest peaks of the Himalah appear utterly 

 insignificant, and the greatest disturbances which have affected the 

 surface of our planet seem too small and trifling to produce any 

 appreciable effect upon the great mass of the interior of the earth. 



Figures of this nature, as the author observes, give more correct 

 and definite ideas of the relative value of things than can be con- 

 veyed by voluminous pages of description, unaccompanied by 

 drawings that represent their true proportions. 



XXV. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



1830. A PAPER was read, entitled, Researches in Physical 

 Dec. 16. -flL Astronomy ; by John William Lubbock, Esq. V.P. 

 and Treasurer of the Royal Society. 



The author has shown in a former paper, published in the last 

 part of the Philosophical Transactions for 1830, that the stability 

 of a system of bodies subject to the law of gravitation, is always 

 preserved, provided they move in a space absolutely devoid of re- 

 sistance. This conclusion results from the analytical expressions 

 for the variations of the elliptic constants in the theory of the 

 Planetary Motions. 



In the present paper he extends his researches to the problem of 

 the precession of the Equinoxes, which admits of a similar solution 

 to the former. Of the six constants which determine the position 

 of the revolving body, and the axis of instantaneous rotation, at any 

 instant, three have only periodic inequalities ; while the other three 

 have each a term which varies as the time; but from the manner in 

 which these constants enter into the resulting expressions, the equi- 

 librium of the system may be inferred to be stable, as in the former 

 case. By the stability of the system, the author wishes to be un- 

 derstood to mean that the pole of the axis of rotation has always 

 nearly the same geographical latitude, and that the angular velocity 

 of rotation, and the obliquity of the ecliptic vary within small limits ; 

 and that its variation is periodical. 



The author also gives new methods of obtaining the inequalities 

 of longitude, and the radius vector, in the planetary theory, retain- 

 ing the square of the eccentricities. When only the first powers 

 of the eccentricities are retained, these expressions admit of sim- 

 plification. He subjoins, as a numerical example, the calcula- 

 tion of the coefficients of two of the inequalities of longitude in the 

 theory of Jupiter disturbed by Saturn ; and points out the requisite 

 substitutions for rendering the formulae applicable to the case of a 

 superior planet disturbed by an inferior planet. 



Dec. 23. A paper was read, On the Hour Lines of the Ancients; 

 by W. A. Cadell, Esq. F.R.S. 



The hour lines on the sundials of the ancient Greeks and Romans 



correspond 



