526 TRANSACTIONS OF SECTION A. 



To 



replaced by an atom. Further, if we write A — B = — , where B denotes the chemical 



formula of a substance, the quantities for which B stands and the quantity A have 

 the same values for a group of substances possessing similar properties, but which 

 vary from group to group. Thus, for example, in the case of the esters we would 



To To 



have A-(20 + a(C + 2H)) = — — = , which may be written A,— oB, = =-,wherea 



2 vm A 2 v»i, 



denotes an integer. The values of A, and B, are found to be the same for each 



ester. 



The various chemical compounds can be divided into groups in the above ways, 



and it is found that this grouping coincides with that obtained from purely chemical 



considerations. The amines thus fall into three groups corresponding to the 



primary, secondary, and tertiary amines. The nitrites fall into a group, and so also 



do the ethers, the primary alcohols, and the secondary alcohols (omitting two 



alcohols which we know are, to a great extent, polymerised). The study of the 



To 



properties of the quantity = may therefore be of great assistance in the classifica- 



2 v in , 



tlon of chemical compounds into groups, and to obtain various other connections 



between the compounds. 



4. Report on Solubility. By Dr. J. V. Eyre. — See Reports, p. 425. 



5. The Deduction of Hydration Values of Acids from the Bate at which 



they induce Hydrolysis. By F. P. Worley. 



Mathematical Department. 



The following Papers and Reports were read : — 



1. On Functions derived from Complete and Incomplete Lattices in Two 

 Dimensions and the Derivation there from of Functions which enume- 

 rate the Two Dimensional Partition of Numbers. By Major P. A. 

 MacMahon, F.R.S. 



2. On a certain Permutation Group. By Dr. H. F. Baker, F.R.S. 



If n different letters be written down in a certain order and then rearranged, by 

 writing tbe last first, the first second, the last but one third, the second fourth, and 

 so on, and this rule of rearrangement be then again applied, and so on repeatedly, 

 required to find the number of rearrangements before the original order is regained. 



For instance, the set of six letters gives in turn by this rule : — 



