PROCEEDINGS 



U 



OF 



THE ROYAL SOCIETY 



May 5, 1859. 

 Sir BENJAMIN C. BRODIE, Bart., President, in the Chair. 



In accordance with the Statutes, the President read the following 

 list of Candidates recommended by the Council for election into the 

 Society : 



Samuel Husbands Beckles, Esq. 

 Frederick Grace Calvert, Esq. 

 Henry J. Carter, Esq. 

 Douglas Galton, Esq. 

 William B. Herapath, M.D. 

 George Murray Humphry, Esq. 

 Thomas Sterry Hunt, Esq. 

 John Denis Macdonald, Esq. 



William Odling, Esq. 

 Robert Patterson, Esq. 

 John Penn, Esq. 

 Sir Robert Schomburgk. 

 Thomas Watson, M.D. 

 Bennet Woodcroft, Esq. 

 Lieut.-Col. W. Yolland. 



The following communications were read : 



I. " Propositions upon Arithmetical Progressions/' By F. ELE- 

 FANTI, Esq. Communicated by ARTHUR CAYLEY, Esq. 

 Received April 6, 1859. 



(Abstract.) 



The author sketches the investigation of the way of throwing 

 various series of integer terms into arithmetical progressions, such as 

 the sums of squares, cubes, &c. of figurate numbers, of the powers 

 of a number, &c. He also gives the resolution of a given number, 



VOL. x. B 



