114 



MAJOR P. A. MAcMAHON ON THE COMPOSITIONS OF NUMBERS. 



n = 4. 



n = 5. 



n = 6. 



To explain, observe that the number at the intersection of the row N 3 and the 

 column (2 8 1 2 ) shows that ^ . , = 93. 



These tables will be of constant service in verifying results to be obtained. 

 Art. 74. From the relation 



* = ^m i J OT -1 o 



\ L 1 \ * / 



we can obtain a system, for, summing each side from m 



N m +N m _ 1+ ...+N, = G.- 



= 1 to m = m, 



