246 
Annual Meeting, April 29th, 1862. 
J. P. Joule, LL.D., F.R.S., President, in the Chair. 
Mr. Andrew Knowles was elected an Ordinary Member of 
the Society. 
A Paper Avas read “ On Non-Modular Groups,” by the Rev. 
T. P. Kikkman, A.M., F.R.S., and Hon. Mem. of the Literary 
and Philosophical Societies of Manchester and Liverpool. 
From the seven triads which exhaust the duads of seven 
elements, 157 261 372 413 524 635 746, we can write 
twenty-one triads containing each a capital and two small 
figures, thus : — 
157 571 715 261 612 126 372 723 237, &c. 
We can collect the triplets of these triads Avhich contain the 
same small letter, thus, the order of two small figures being 
indifferent : — 
157 157 517 517 571 571 751 751 
327 237 327 237 431 341 431 341 
467 647 647 467 261 621 621 261 
175 1 75 7 15 7 15 3 72 3 72 732 732 2 73 2 73 , ^ 
365 635 365 425 452 612 542 612 053 563 ' 
425 245 245 635 162 542 162 452 143 413 
723 723 6 74 6 74 764 764 746 746 4 76 476 
653 563 254 314 254 314 126 216 126 216 
413 143 134 524 314 254 536 356 356 536 
where every triad and everv^Vertical row containing three 
figures is one of the seven fundamental triads. We have thus 
formed twenty-eight triplets of triads, and have exhausted 
3-7-4 of the Sl’10 couplets possible Avith the 21 triads, 157, 
571, &c. 
Proceedings— Lit. & Phil, Society— No. 16 .— Session 1861 — 62 , 
