245 



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 was read '^ On Non-Modular Groups," by the Rev. 

 T. P. KiRKMAN, 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 which contain the 

 same small letter, thus, the order of two small figures being 

 indifierent : — 



157 157 517 517 571 571 751 751 

 327 237 327 237 431 341 431 341 

 467 647 647 467 261 621 621 261 



175 175 715 715 372 372 732 732 273 273 

 365 635 365 425 452 612 542 612 653 563 

 425 245 245 635 162 542 162 452 143 413 



(A) 



723 723 674 674 764 764 746 746 476 476 

 653 563 254 314 254 314 126 216 126 216 

 413 143 134 524 314 254 536 356 356 536 



where every triad and every 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 2M0 couplets possible with the 21 triads, 157, 

 571, &c. 



Pboceedings— Lit. & Phtl. Society— Xo. 16.— Session 1861—62. 



