250 Mr. J. W. L. Glaisher on [Feb. 3, 



Hirn (G. A.) Exposition analytique et experiment ale cle la Theorie 

 Mecanique de la Chaleur. 3 e Edition. Tome II. 8vo. Paris 1876. 

 Sur l'Etude des moteurs therniiques et sur quelques points de la 

 theorie de la Chaleur en general. 4to. 1876. The Author. 



Jones (T. Wharton), E.E.S. Evolution o£ the Human Eace from Apes 

 and lower Animals a doctrine unsanctioned by Science. 8yo. London 

 1876. The Author. 



Oil-Painting of the Hon. Eobert Boyle, by Kneller, in gilt frame. Oil- 

 Painting of Sir Charles Wheatstone, by Charles Martin, in gilt 

 frame. 



Thirteen Engraved Portraits of Erancis Baily, Dr. ¥m. Buckland. Sir 

 Henry De la Beche, Earaday, Sir John Eranklin, Thomas Graham, 

 Sir Henry Holland, Moll, Sir Roderick Murchison, Sir James Eoss, 

 Canon Sedgwick (framed and glazed). 



Six Photographic Portraits of Amici, Liebig, Priestley, &c. (framed and 

 glazed). 



The Bequest of the late Sir Charles "Wheatstone, E.E.S. 



February 3, 1876. 



WILLIAM SPOTTISWOODE, M.A., Treasurer and Vice- 

 President, in the Chair. 



The Presents received were laid on the table, and thanks ordered for 

 them. 



The following Papers were read : — 



I. " On Eormulse of Verification in the Partition of Numbers/'' 

 By J. W. L. Glaisher,, M.A., E.E.S. Eeceived December 18, 

 1875. 



In writing down all the partitions of a number it is convenient to 

 have tests which will verify that none have been omitted ; and it is the 

 main object of this paper to give formula? which are available for this 

 purpose. 



At the Edinburgh Meeting of the British Association (Eeport 1871, 

 Transactions of the Sections, p. 23), Sylvester communicated the elegant 

 and useful test-formula 



I. 2(1 — x+xy — xyz+ &c.) = 0, 



where in any partition x denotes the number of l's present, y the number 



