612 Proceedings of the Royal Soeiety 
The following simple scheme shows the decomposition of 10 and 
of all inferior numbers. The number of parts increases rapidly with 
the order of the term : for there are 2 ; for 3 ; for x^, 5 ; for 
7; for x^, 11; for x’^, 15; for x^, 22; for x^, 30; and for 42 
parts. 
1+1+1+1+1+1+4 
1 + 1 + 1-1-1 + 1 + 2 + 3 
1+1+1+1+1+5 
1+1+1+1+3+3 
1 + 1 + 1 + 1+6 
1+1+1+2+2+3 
1 + 1-1-1 + 2 + 5 
1+1+1+3+4 
1+1+1+7 
1 + 1 + 2 + 2 + 2+2 
1+1+2+2+4 
1+1+2+3+3 
1 + 14-2 + 6 
1+1+3+5 
1+1+4+4 
1 + 1+8 
l + 2 + 2 + 2-> 3 
1 + 2 2 + 5 
1+2+3+4 
1 + 2 + 7 
1 +3+3+3 
1 + 3 + 6 
1 + 4 + 5 
1+9 
2 + 2 + 2 + 2+2 
2+2+2+4 
2+2+3+3 
2 + 2 + 6 
2 + 3 + 5 
2 + 4 + 4 
2 + 8 
3 + 3 + 4 
