3» 



The Rev. Thos. P. Kirkman 



on 



We then take at random G 2D = 235614, on which we form 

 G 2e i> G 2e2 , G 2e3 , to be marked out ; and then we proceed to 

 register 14 different standards G mD ,each in a line with three 

 marked out by it, all by lf 0,,, 3 , as follows : 



2 = a/3yy££. 



16315. 2 : 



^635, 23 

 56514, 24 

 HI35. 2t 



>5 I 43» 2t 



>53 I 4, zf 



55 2 6i, 34 



51625, 4^ 



35 6l2 » 3' 



5 5 2I 3, 4; 



22315, 3< 



55321, 3 ( 



'253i> 4! 



54231, 5^ 



The 14 standards are retained as all giving different 

 functions of twelve terms. 



As to the numbers of their values, we see, by 34, 56, 21, in 

 its line, that G 9d , if any, has a symmetry under 2, that may 

 for some = C in I m make a, art. 3, true. We soon find that 

 each of the 3 0's is such a C, and that (3g D is thereby four 

 times repeated in Oik' ", and thus has only 15 values. 



Q 9d is the following 15-valued function (§>0) : 



a/3 a/3 yyec yy^c 

 (12 + 21X3456 + 5634) 

 (34 + 43)(5 6l2 + i256) 

 (56 + 65X1234 + 3412) 



which is all to be read under 2, i*2 i3 3' J, 4''5 8 6 s + &c. We 

 have thus proved that there are constructible under 



2 = a/3yy?£. 



16 different functions, namely 



