334 The Rev. Thos. P. Kirkman on 



A, as well as each of its duplicates, A' and A", is a one- 

 valued function of six terms. 



B is a one-valued function of 1 5 terms. 



C is a one-valued function of 60 terms : freed from the 



common multiplier abcdef, C is the sum of 60 



triplets, a'^b^c^, &c. 

 D, as well as its duplicate D', is a six-valued function of 



60 terms under S = ajSyySS' 



E is a six-valued function of 30 terms under S = aajSjSyy. 



Of the 243 terms of this six-valued product of five 

 factors, 153 are wasted on a tight and baffling twist of 

 useless symmetricals and duplicates. 



The function D is my Y (M.M. p. 351), and the function 

 E is my U, (p. 352). 



These functions, U and Y, are read in my pages, along 

 with the full tale of the eleven other possible six-valued 

 functions of six letters ; they are not hidden away in clumsy 

 packing, out of sight and guessing, but are all really given 

 with their values, rapidly readable in the columns of the six 

 equivalent maximum groups, one of which, J (p, 350), is 

 fully written out ; the others being given in the same page 

 as its equivalents. All the functions given in my § 11. (p. 

 344), are " des fonctions bien definies," of the Prize-question. 

 How far my complete accounts of the possible functions of 

 four and of five letters were new, I know not. 



All this over 30 years ago. A forgotten story now. I 

 have had the sense, of course, to keep my peace. For, in 

 these islands, a thinker has often to be content with 

 " audience fit though few," himself, and his guardian angel. 

 We have had some private fun together ; but is it very 

 wicked in me to be heard laughing one little laugh before 

 I die? 



The Academy were not content, and saw no reason to 

 award their prize. I thought, 30 years ago, that I had done 



