52 The Rev. Tiios. P. Kirkman on 



We have proved that there are given under 



2 = aa/3/3/3/3. 

 ©A = (234561) having 6 terms and 60 values, 

 © 2 A = (342615) having 6 terms and 10 values, 

 ©5 = (356142) having 3 terms and 15 values. 



2 = a/3/3/3/3/3. 



There is one function of 6 terms and one value. 

 14. We appear to have constructed on the first 60 equiva- 

 lent transitive maximum groups of 6 letters, whose title is 



6-2 = l+2 6 +2 33 + 4 222 +3 22 „, Q=60, 

 all possible many-valued functions, viz. : 



under aftycerj, 

 60 functions each of 12 terms and of 60 values : 



under a/3y3ee, 

 30 functions of 12 terms and of 60 values : 



under o/3yc)c)c>, 

 g functions of 12 terms and of 60 values ; 



1 function of 12 terms and of 10 values : 



under a/3yycc, 



2 functions of 6 terms and of 60 values ; 

 1 function of 12 terms and of 15 values ; 

 13 functions of 12 terms and of 60 values : 



under «/3yyyy, 

 1 function of 6 terms and of 15 values ; 

 1 function of 12 terms and of 60 values ; 

 1 function of 12 terms and of 10 values : 



under a/3/3yyy, 

 1 function of 6 terms and of 10 values ; 

 1 function of 6 terms and of 60 values ; 

 4 functions of 1 2 terms and of 60 values : 



under no/3/3yy, 

 1 function of 6 terms and of 15 values; 

 6 functions of 6 terms and of 60 values ; 

 4 functions of 1 2 terms and of 60 values : 



