318 REV. T. P. KIRKMAN ON THE THEORY OF 



Let US form 



VxPiPl 123468975 



o i>li^i^2 ^ 975i23468 ^ g^^ 

 PiPiVi 123468975 ^"> ^^ 



03=^1^^=^5468^^ 

 IP^lhPl 123468975 



^^.^1^^468123975^ 68152739 

 PxP^Pl 123468975 



0^^^^^975468x23^ ^^g^ 



PIP'IPI 123468975 ^'^^^ 



We have 



QiG = 46893725i 

 684715392 

 846529173 



026 = 975182634 

 759243816 

 597361428 



036 = 123987654 

 231745896 

 312569478 



046 = 468152739 

 684293517 



846371925 



'^5G = 975436281 

 759618342 

 597824163 . 

 If we arrange the grouped group 



G+(Oi + 03+Q3 + Q4 + Q5)Gi- 

 as a group of powers J of a principal substitution and its 

 two derived groups, it is 



123456789 597361428 684715392 

 684293517 1.23987654 597824163 

 312874965 759243816 468937251 



