204 THE REV. T. P. KIRKMAN ON NON-MODULAR GROUPS. 



guished members of the Society, I cannot help feeling that 

 the description herein given of his character and labours 

 falls short of the real position which they occupy in the 

 public mind ; and although I have had much pleasure in 

 reading and collating the discoveries of Mr. Hodgkinson, 

 I regret that the preparation of this memoir has not been 

 placed in abler hands. One thing, however, consoles me, 

 and supplies me with an ample reward, which no criticisms 

 on my effort can possibly cancel ; and that is, I have been 

 engaged, to the best of my ability, in the endeavour to 

 perpetuate the memory of a great and good man, whose 

 singular praise it is to have spent his life and his great 

 powers for the good of mankind, with a single aim to truth 

 and science, without desiring or gaining pecuniary reward. 



XIV. — On Non-modular Groups. By the Rev. Thomas P. 

 KiRKMAN, M.A., F.R.S., and Honorary Member of the 

 Literary and Philosophical Societies of Manchester and 

 Liverpool. 



Bead April 29tli, 1862. 



If we form with fifteen elements the five triplets 



aa^a^^j hhfi^, c c^c^, dd^d-^^ ee^Bj^y . . (E) 



the ten triplets 



abc, a d^e^j a^h^e, a^c^d^, dzb-^d, a^c^e^y 



b^c^d^, b^c^e^, b d^e^, cde, . . . (F) 



in which no two have the same three letters, nor any of 

 them a duad before employed, and next the six quintuplets 



