536 
MAJOR MAGMA HON ON SYMAIETRIO FUNCTIONS. 
PiO.-z '' • • •) possesses no separations of specification cl^i, . . .) but 
not otherwise.” 
The law may be verified in the case of the table of separations of (10- 01^), for the 
symmetric functions (22), (21 01), (12 10), (11^), (H 10 01) for none of these five 
functions can be separated so that the specification is (20 02). On the other hand 
the group law does not hold for (20 01®) because the separation (20) (01®) has a 
specification (20 02). 
§ 16. Conclusion. 
81. All the preceding results can be easily extended to the in-partite theory 
connected with m systems. The weights are ?n-partite as also the parts of the 
partitions. As a general rule rro suffices appear in the symbols. The laws of symmetry 
and their consequences, the symmetrical tables, the correspondences between the 
algebras of quantity and differential operation, the partition linear and obliterating 
operators, the law of groups of coefficients (and in fact the whole investigation here 
presented) proceed pari- 2 mssu with the bipartite theory above set forth. The uni- 
partite or ordinary theory of the single system is also absolutely included in every 
respect. 
In its applications, llie results will be chiefly of use in the theory of elimination in 
the most general case. In this regard Schlafli’s memoir (loc. cit.) may be consulted. 
