290 



Major MacMahon. Memoir on the 



Specific Ionic Velocities. 

 I. Aqueous Solutions. 



[Nov. 24 y 



II. Alcoholic Solutions. 



II. " Memoir on the Theory of the Compositions of Numbers." 

 By P. A. MACMAHON, Major E.A., F.R.S. Received 

 November 17, 1892. 



(Abstract.) 



In the theory of the partitions of numbers the order of occurrence 

 of the parts is immaterial. Compositions of numbers are merely 

 partitions in which the order of the parts is essential. In the nomen- 

 clature I have followed H. J. S. Smith and J. W. L. Grlaisher. What 

 are called "unipartite" numbers are such as may be taken to- 

 enumerate undistinguished objects. " Multipartite " numbers enu- 

 merate objects which are distinguished from one another to any 

 given extent; and the objects are appropriately enumerated by an 

 ordered assemblage of integers, each integer being a unipartite 

 number which specifies the number of objects of a particular kind ; 

 and such assemblage constitutes a multipartite number. The 1st 



* Preliminary determinations. 



