On a Method of Estimating Minute Quantities of Iodine. 185 



it follows from what has preceded that it is quite as easy to de- 

 monstrate the corresponding theorem for the factorial [m] p . But 

 the theorem being true for the factorial [m] p , & * s a * once seen 

 that the product of the series for (1 + x) m and (1 + x) n is iden- 

 tical with the series for (l+x) m+n , and thus it becomes ww- 

 necessary to employ for the purpose of proving this identity the 

 so-called principle of the permanence of equivalent forms; a 

 principle which, however, in the case in question may legiti- 

 mately be employed. 



XXVI. Note on a Generalization of the Binomial Theorem. 

 By A. Cayley, Esq.* 



npHE formula (Crelle, vol. i. p. 367) for the development of 

 * the binomial (x + a) n } but which is there presented in a 

 form which does not put in evidence the law of the" coefficients, 

 is substantially equivalent to the theorem given by me as one of 

 the Senate House Problems in the year 1851, and which is as 

 follows : — 



"If {a + /3 + 7 . . .} p denote the expansion of (a + /3 + y...) p , 

 retaining those terms ~Na. a /3 b y c B d ... only in which b + c + d„*p — l, 

 c + d+ ...p—2, &c, then 



1 1 .& 



1.2.3 

 The theorem is, I think, one of some interest. 



XXVII. On a quick Approximative Method of Estimating Minute 

 Quantities of Iodine. By Thornton J. Herapath-|\ 



THE estimation of minute quantities of iodine is not always 

 accomplished without difficulty. I have, however, recently 

 discovered a simple means of effecting this object, which I think 

 is worthy of being generally known. The method in question 

 is based on the mode of analysing silver coin proposed by Gay 

 Lussac, and on that employed by Mr. Horsford for the determina- 

 tion of lead in potable waters ; modifications of which processes 

 have been since successfully applied to the quantitative estimation 

 of many other substances. It is the method of graduated solu- 

 tions. The reagent I use is a salt of palladium, which, as is 



* Communicated by the Author, 

 t Communicated by the Author. 



