No. 2] TRIAD SYSTEMS— WIIITE, COLE, CUMMINGS. 89 



The column e of 32 has no (hiplicato in 35; hence the two systems are noncongruent. 



Wo have derived, then, iia Part 5 a new method of comparison for triad systems by means 

 of the two-column indices and the table of interlacings for the system. 



Tlois method of comparison, since it naturally yields at least a partial, in some cases a com- 

 plete, separation into sets of transitive elements for the system, will also facihtate the deter- 

 mination of the group belonging to the system. 



CONCLUSION. 



Lookmg toward the census of triad systems in more than 15 elements, we have in the 

 foregoing memoir four modes of classification which woidd bo applicable to the construction 

 and comparison of systems. Of these wo venture to express the behef that the method of 

 indices will bo found most convenient for comparisons, whUe for construction there is no doubt 

 that a group, where one can be prescribed, is the most direct auxiliary. Any exhaustive 

 census, certainly for 31 or more elements, is out of the question in finite time; but systems 

 admittmg, for example, certain cychc groups are not numerous nor difficult of construction, 

 the method of indices showang very quickly their noncongruency. In the present state of the 

 theory the most desirable forward step would be a demonstration that some one of these methods 

 is (or is not) a sufficient means of provuig congruency for triad sj'stems of any nxmaber of elements 

 above 15. 



WASHINGTON : QOVEENMEXT PRINTING OITICE : 1919 



