1 1 8 Royal Society. 



order every eight years ; some multiple, therefore, of the periodic 

 time of Venus is nearly equal to eight years. It is easily seen that 

 this multiple must be thirteen ; and consequently eight times the mean 

 motion of Venus is nearly equal to thirteen times the mean motion of 

 the earth. The difference is about one 240th of the mean annual 

 motion of the earth ; and it implies the existence of an inequality of 

 which the period is about 240 years. No term has yet been calcu- 

 lated whose period is so long with respect to the periodic time of the 

 planets disturbed. The value of the principal term, calculated from 

 the theory, was given by the author in a postscript to the paper 

 above referred to. In the present memoir he gives an account of the 

 method of calculation, and includes also other terms which are neces- 

 sarily connected with the principal inequality. The first part treats 

 of the perturbation of the earth's longitude and radius vector ; the 

 second of the perturbation of the earth in latitude ; and the third of 

 the perturbations of Venus depending upon the same arguments. 



The computations of the quantities themselves being effected by 

 means of algebraical equations of great complexity, and of numerical 

 calculations of considerable length, which afford in themselves no 

 ready means of verifying their accuracy, the author has been under 

 the necessity of examining closely every line of figures before he pro- 

 ceeded to another. Upon the whole he is certain that there is no 

 error of importance in the numbers he obtained ; and that the only 

 probable source of error is the inevitable rejection of figures beyond 

 a certain place of decimals. 



In concluding this investigation, the most laborious, probably, that 

 has yet been made in the planetary theory, he remarks that the term 

 in question is a striking instance of the importance to which terms, 

 apparently the most insignificant, may sometimes rise. As an illus- 

 tration of the magnitude of the errors which might under other cir- 

 cumstances have arisen from the neglect of this term, he further ob- 

 serves, that if the perihelion of Venus and the earth had opposite lon- 

 gitudes, and if the line of nodes coincided with the major axis, the 

 eccentricities and inclination having the same values as at present, 

 the coefficient of the inequality in the epoch would be 8""9, and all 

 the other terms would be important. A very small increase of the 

 eccentricities and inclination would double or treble these inequa- 

 lities. 



Anniversary Meeting, Nov. .^0. — His Royal Highness the Duke of 

 Sussex, K.G., President, in the Chair. 



The President delivered the following Address : — 



Gentlemen, 

 The period, provided by our Statutes, has again come round, when 

 your Officers and Council must be reconstituted by your authority ; 

 and I feel myself called upon, in conformity with the custom which 

 has been sanctioned by my predecessors, to address you upon such 

 subjects connected with the Royal Society and its administration, as 

 the events of the last year may have rendered proper to be noticed 



by 



