II. Memoir on the theory of the compositions of numbers

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 nomenclature I have followed H. J. S. Smith and J. W. L. Glaisher. What are called “unipartite” numbers are such as may be taken to enumerate undistinguished objects.