386 MAJOR P. A. MAcMAHON ON COMBINATORIAL ANALYSIS 



Art. 19. In conclusion, it may be remarked that there is i<o difficulty in evolving 

 a mixed theory which involves the operation both of the infinitesimal calculus and of 

 the finite calculus. Operations and functions may be designed which lead to lattices 

 which are not rectangular. The theory may be connected with complete or 

 incomplete lattices in three or more dimensions ; and finally one of the most 

 promising paths of research appears to be connected with a multipartite zero. These 

 matters may be the subjects of future investigation. For the present enough has 

 been said to indicate the apparent scope of the new method. 



