Proceedings. 211 



quantity of the fabric placed at his disposal was not sufficient 

 to enable him to identify the colouring matter employed in 

 the production of the dye, not an easy matter under any 

 circumstances in the case of yellow dyes. All he could say 

 was that the mordant employed in dyeing this colour was a 

 mixture of alumina and oxide of iron, and that the dye 

 contained fatty as well as colouring matter. 



Mr. Harry Grimshaw, F.C.S., exhibited some varieties 

 of forms of crystallisation of ammonium chloride, under 

 varying conditions of concentration of the solution from 

 which the crystals were obtained, and under varying con- 

 ditions of temperature and rate of cooling of the liquid. The 

 most interesting, from a technical point of view, was a mass 

 of crystals which had assumed the form and substance of the 

 sublimed ammonium chloride, or sal ammoniac of commerce, 

 as, if it were possible to always obtain this form, the necessity 

 for sublimation might be done away with. 



The following note " On the k-partitions of R and 

 of the R-gon " was read by the Rev. Thomas P. KiRKMAN, 

 M.A., F.R.S. :— 



" In my endeavour to complete, as I believe I have com- 

 pleted, what has been hitherto imperfectly done in partitions 

 into a finished theory, I have been most agreeably surprised 

 by the discovery, with satisfactory proof, of the following 

 Theorem : — If /^ and x be any two numbers, equal or not, and 

 if ,,tR^ stand for the sum of all possible permutations of ^Q 

 the /^-partitions of x, whose parts are positive or zero and 

 may be repeated — then 



fc1R, = the k'" coefficient in (i-l-i)"+^-' 



e.g., x= 5, /^= 3, the 3-partitions of 5, 



005, 113, 221, 014, 023=3Q3, 



whose permutation symbols are 



yaab A- 2abc, 

 give, as products of partitions and their permutations, 



