175 



ntegrals affords us a new class of results, which I next consider. 

 A continental mathematician, M. Smaasen, has given, in a recent 

 volume of Crelle's Journal, certain methods of combining series 

 together which give us the means of reducing various multiple inte- 

 grals to single ones. The series hitherto considered are what have 

 been denominated "factorial series;" but, lastly, I proceed to show 

 that analogous processes extend to series of a very complicated 

 nature and of an entirely different form, and for that purpose sum 

 by means of definite integrals certain series, whose values are obtained 

 in finite terms in the " Exercices des Mathe"matiques " by means 

 of the Residual Calculus. The total result will be the evaluation 

 of an enormous number of definite integrals on an entirely new type, 

 and the application of definite integrals to the summation of many 

 intricate series. 



November 30, 1854. 



Anniversary Meeting. A Report of the Proceedings will appear 

 in a future Number. 



December 7, 1854. 

 Colonel SABINE, V.P., in the Chair. 



The Chairman announced that the President had appointed the 

 following noblemen and gentlemen Vice-Presidents for the ensuing 

 year : 



The Earl of Rosse, K.P., M.A. 



Colonel Sabine, R.A. 



Sir Benjamin Brodie, Bart. 



Thomas Bell, Esq. 



Charles Darwin, Esq., M.A. 



Charles Wheat&tone, Esq. 



Robert Hunt, Esq., was admitted into the Society. 



