PROCEEDINGS 



OF 



THE ROYAL SOCIETY. 



1834-1835. No. 18. 



November 20, 1834. 



JOHN WILLIAM LUBBOCK, Esq., M.A., V.P. and Treasurer, 

 in the Chair. 



A paper was read, entitled, " On the Determination of the Terms 

 in the disturbing Function of the fourth Order, as regards the 

 Eccentricities and Inclinations which give rise to secular inequali- 

 ties." By. J. W. Lubbock, Esq., V.P. and Treas. R.S. 



The author observes, that the magnitude of the terms of the fourth 

 order in the disturbing function, relating to the inclinations, in the 

 theory of the secular inequalities of the planets, does not admit of 

 being estimated d, priori ; and consequently the amount of error 

 which may arise from neglecting them cannot be appreciated. The 

 object of the present investigation is to ascertain the analytical ex- 

 pressions of these terms ; and the method adopted for this purpose 

 is derived from principles already explained by the author in a for- 

 mer paper. He has bestowed great pains in putting these expres- 

 sions into the simplest form of which they are susceptible ; and has 

 finally succeeded, after much labour of reduction, in obtaining ex- 

 pressions of remarkable simplicity. He exemplifies their application 

 by the calculation, on this method, of one of the terms given by Pro- 

 fessor Airy as requisite for the determination of the inequality of 

 Venus ; and arrives, by this shorter process, at the same result. The 

 same method, he remarks, is, with certain modifications, applicable 

 to the developement of the disturbing function in terms of the true 

 longitude. 



A paper was also read, entitled " Note on the Astronomical Re- 

 fractions." By James Ivory, Esq., K.H., M.A., F.R.S. 



The object of this communication is to show how far the author 

 has been successful in establishing the true theory of astronomical 

 refractions, in his paper published in the Philosophical Transactions 

 for 1823, by comparing the results of that theory with the best and 

 most recent observations ; namely, those recorded in the " Funda- 

 menta Astronomic" of Bessel, and the " Tabulae Regiomontanse" 

 of the same author. This comparison is made by taking the first 

 and second differences of the series of the logarithms of the refrac- 

 tions in each table ; from which it results that these differences, de- 

 rived from the numbers in Bessel' s tables, are very irregular; but 

 that their mean very nearly coincides with that of the numbers given 

 in the tables of the author. 



