89 



On Circulating Functions, and on the Integration of a Class of Equa- 

 tions of Finite Differences into which they enter as Coefficients. By 

 John F. W. Herschel, Esq. F.R.S. Read February 19, 1818. 

 [Phil Trans. 1818,^. 144.] 



The subject of recurring series, says the author, has been almost 

 exhausted ; but there is a class of series nearly allied to them, which 

 contain a species of functions, which he calls circulating functions, 

 which have never been systematically considered. Mr. Herschel 

 proceeds to explain a direct method of solving all equations contain- 

 ing this kind of functions ; and in the course of his investigation re- 

 marks a curious formula, which expresses the integer part of the 

 quotient arising from the division of any one number by any other, 

 a circumstance which he observes may prove of considerable use 

 in the theory of numbers. 



On the Fallacy of the Experiments in which Water is said to have been 

 formed by the Decomposition of Chlorine. By Sir Humphry Davy, 

 LL.D. F.R.S. Read February 12, 1818. [Phil. Trans. 1818, 

 p. 169.] 



Some experiments having been communicated to the Royal So- 

 ciety of Edinburgh, leading to the inference that water is formed 

 during the action of muriatic acid upon certain metals, and conse- 

 quently that chlorine is decomposed, Sir Humphry was induced to 

 repeat them ; and ascertained that the water being derived from 

 sources not suspected by the authors, their conclusions are un- 

 founded. Muriatic acid gas was passed through red hot tubes of 

 flint glass, and small portions of water were formed in consequence 

 of its action upon the oxide of lead and the alkali of the glass. 



When muriatic acid gas was passed over red hot iron in tubes 

 containing common air, more water was formed in consequence of 

 the union of the hydrogen of the acid with the oxygen of the air ; 

 but when every precaution was taken to avoid such sources of 

 oxygen, the decomposition of muriatic acid gas was unattended by 

 the smallest deposition of aqueous vapour. When muriate of am- 

 monia is passed through tubes containing metals, it offers results 

 analogous to those of the muriatic acid, and when moisture appears 

 it may be referred to similar causes. 



The author concludes with noticing a paper in the Me"moires 

 d'Arcueil, by M. Berthollet, containing some slight mistakes as to 

 the progress of his views upon the theory of chlorine. M. Berthol- 

 let states that MM. Ampere and Dulong had embraced the idea of 

 the simple nature of chlorine previous to Sir H. Davy, an assertion 

 which is disproved by reference to the date of the author's first 

 paper, and also by a quotation of a letter from M. Ampere, written 

 on the 1st of November 1810. 



