ANALYTICAL FOBMUL.E. 133 



P. S. In stating in my last letter, that the result I htid Statement in a 

 observed, of dry oximuriaticncid gas not acting on carho./ic confirnied by 

 oxide gas, was confirmed by the very same result having Mr. Davy, 

 been obtained by Gay-Lussac and Thenard, I ought to 

 have added, that it had also been obtained by Mr. Davy. 

 In his account of " a combination of oximuriatic gas and 

 oxigen gas," he states, among other properties of oximu- 

 riatic gas prepared in its pure state, that ** it does not act 

 on nitrous gas, or muriatic acid, or carbonic oxide, or sul- 

 phureous gasses, when they have been carefully dried*.'* 

 That Mr. Davy does not state this on the authority of others 

 is evident, not only from the manner in which the sentence 

 is expressed, but also from this, that he is giving an ac- 

 count of the properties of this gas in its state of purity, ia 

 ivhich state there was no certainty of its having been ob- 

 tained in former experiments, as chemists were not aware, 

 that it might have an intermixture of oxigen, by which its 

 properties and chemical agencies are materially modified. 

 He gives this as a property of the pure gas, and of course 

 he would not have done so without having ascertained it. 



VIII. 



Analytical Formul<e for the Tangent^ Cotangent, ^c. In a 

 Letter from a Correspondent. 



To W. NICHOLSON, Esq. 

 SIR, 



JlJlAVING frequently noticed in your valuable Journal Analyik-al for- 

 remarks and discussions on mathematical subjects, I have mul<eforthe 

 been induced to send you one or two theorems, the investi- !^"^^"!' ^ 

 gation of which has atforded me Some degree of amuse- 

 ment; under the impression, that they may not be quite 

 uninteresting to that class of your numerous readers, who 

 have not made very profound advances in analytical science. 

 They are, as far as my reading goes, new, and lead to the 

 summation of some series, hitherto, I believe, unattempted. 



♦ Phil. Trans, for 1811, p. 156 j or Journal, vol. XXIX, p. 269. 



1. Cotan. 



