Proceedings. 213 



"Has any mathematician observed that, forty years ago 

 in these J/^;;/o/>j- (Vol. XII., 1853-4, p. 129), appeared a 

 demonstrated formula of three terms, by which the tabula- 

 tion to any extent of ,,Pj. (the /^-partitions of ,f, from which 

 zero parts but not repetitions are excluded) is made an easier 

 task than any yet invented for little boys in Algebra or 

 Arithmetic ? No number is therein required to be written 

 which is not the exact sum of two given numbers already 

 entered in their places. The expression of ^Fx in x, in the 

 paper above quoted, was a superfluous exhibition of brute 

 force. Its author had the pleasure of knowing that, 

 whenever and so far as the numbers ,c^^, kKx, are wanted, 

 they will be rapidly tabled by his formula. There is a 

 similar formula of three terms lor the tabulation, if required, 

 of the numbers ^O^ ; but these can be instantly obtained 

 from the table of ^P^, as can also the numbers of the par- 

 titions in which no part is repeated." 



A paper entitled " Notes on a small collection of plants 

 made by Mr. J. Cardwell Lees in South-west Colorado," by 

 James Cosmo Melvill, M.A., F.L.S., was also read. 



