Prof. Thomson on some remarkable effects of Lightning, 53 



g, h, i,j, k, I, m. Consider separately the triads which contain 

 the letter n and the letter o; neither of these systems of triads 

 contains the letter, whatever it is, which forms a triad with n 

 and o. Hence, omitting the letters n, o, we have two different 

 sets, each of them of six duads, and composed of the same 

 twelve letters. And each of these systems of duads ought, by 

 the cyclical permutation in question, to produce the whole 

 system of the seventy-eight duads of the thirteen letters. 

 Hence arranging the duads of the thirteen letters in the form 



ab .be .cd. de . ef .fg . gh . hi . ij ,jk . kl . hn . ma 

 ac.bd.ee. df. eg .fh . gi . hj . ik .jl . km . la . mb 

 ad .be . cf. dg . eh .fi .gj.hk. il ,jm . ka . lb . me 

 ae . bf. eg . dh . ei .fj . gk . hi . hn .ja .kb.lc. md 

 af. bg . ch . di . ej .fk . gl . hn . ia ,jb . kc . Id . me 

 ag . bh . ci .dj.ek .fl . gm . ha . ib ,jc . kd . le . mf 

 and consequently the duads of each set ought to be situated 

 one duad in each line. Suppose the sets of duads are com- 

 posed of the letters «, b, c, d, e,f, g, h, i,j, k, /, it does not 

 appear that there is any set of six duads composed of these 

 letters, and situated one duad in each line, other than the 

 single set al, bk, cj, di, eh,fg\ and the same being the case 

 for any twelve letters out of the thirteen, the derivation of the 

 thirteen systems of thirty-five triads by means of the cyclical 

 permutations of thirteen letters is impossible. And there does 

 not seem to be any obvious rule for the derivation of the thir- 

 teen systems from any one of them, or any j^'ima facie reason 

 for believing that the thirteen systems do really exist, it having 

 been already shown that such systems do not exist in the case 

 of seven things. 

 2 Stone Buildings, June 14, 1850. 



V. On some remarkable effects of Lightning, observed in a 

 Farm-house near Moniemail, near Cupar-Fife. Communi- 

 cated by William Thomson, Esq., M.A., Fellow of St. 

 Peter's College, Cambridge, and Professor of Natural Phi- 

 losophy in the University of Glasgow*. 



THE following is an extract from a letter, addressed last 

 autumn to me, by the Rev. Mr. Leitch, minister of 

 Moniemail parish : — 



" Moniemail Manse, Cupar-Fife, 

 August 26, 1849. 

 « * * \\T e were visited on the 11th inst. with a violent 

 thunder-storm, which did considerable damage to a farm- 

 * Read before the Philosophical Society of Glasgow, Dec. 5, 1849. 



