PROCEEDINGS 



OF 



THE ROYAL SOCIETY. 



1836. . No. 27. 



November 17, 1836. 

 FRANCIS BAILY, Esq., V. P. and Treasurer, in the Chair. 



The following Gentlemen were, by ballot, elected Auditors of the 

 Treasurer's Accounts on the part of the Society, viz. : George Biddell 

 Airy, Esq., A. R. ; John Bostock, M.D.j the Rev. George Peacock, 

 M.A. ; William H. Pepvs, Esq.; and the Rev. Adam Sedgwick, 

 M.A. 



<l Researches in the Integral Calculus." Part II. Bv Henry Fox 

 Talbot, Esq., F.R.S. 



Having explained, in the first part of his paper, a general method 

 of finding the sums of integrals, the author proposes, in the second 

 place, to apply this method to discover the properties of different 

 transcendents, beginning with those of the simplest nature. With 

 this view, he first shows its application to the arcs of the circle and 

 the conic sections ; and demonstrates the possibility of rinding three 

 arcs, such that, neglecting their signs, the sum of two of them shall 

 be equal to the third, though not superposable in any part : an 

 equality which has been hitherto deemed impossible in the ellipse 

 and hyperbola, without the addition of some algebraic quantity. 



At a Special General Meeting of this Society, held after the or- 

 dinary Meeting of the 17th of November, to consider of an Address 

 to H.R.H. the President, on the happy recovery of his sight. It was 

 Resolved unanimously, That this meeting feels great pleasure in con- 

 gratulating H.R.H. the President of this Society, on the happy re- 

 storation of his sight, a blessing which they sincerely hope he may 

 long enjoy for his own happiness and for the benefit of science. 



November 24, 1836. 

 FRANCIS BAILY, Esq., V.P. and Treasurer, in the Chair. 

 Sir Edward Thomason, being balloted for, was not elected into the 

 Society. 



" Investigation of New Series for the Rectification of the Circle." 

 By James Thomson, LL.D., Professor of Mathematics in the Uni- 

 versitv of Glasgow. Communicated bv Francis Bailv, Esq., V.P. and 

 Treasurer R.S. 



2 K 



