Notices of the proceedings at the meetings of the members of the Royal Institution of Great Britain with abstracts of the discourses . me to time engaged the atten-tion of mathematicians, perhaps the most isolated has been the subjectof these chess-board arrangements. This isolation does not, I believe,any longer exist. The whole series of diagrams formed according toany given laws must be regarded as a pictorial representation, ingreatest detail, of the manner in which a certain process is performed,We have to exercise our wits to discover what this process is. To saynnd to establish that pro
Notices of the proceedings at the meetings of the members of the Royal Institution of Great Britain with abstracts of the discourses . me to time engaged the atten-tion of mathematicians, perhaps the most isolated has been the subjectof these chess-board arrangements. This isolation does not, I believe,any longer exist. The whole series of diagrams formed according toany given laws must be regarded as a pictorial representation, ingreatest detail, of the manner in which a certain process is performed,We have to exercise our wits to discover what this process is. To saynnd to establish that problems of the general nature of the magic 62 Major P. A. MacMahon [Feb. 14, square are intimately connected with the infinitesimal calculus andthe calculus of finite differences is to sum the matter up. Much,however, remains to be done. The present method is not able to dealwith diagonal properties, or with arrangements which depend uponthe knights move. The subject is only in its infancy at workers are required who will, without doubt, introduce newideas and obtain results far transcending those we are in possession. 16 19 = 7 + 12 = 14 + 5 = 4 + 15 = 6 +13 = 17+ 2= 9+10 = 16+ 3= 1 + 18= 8 + 11 38= 7 + 11 + 14+ 6 = 11+ 2+15 + 10=15 + 16+ 6+ 1 = 11 + 10+ 3 + 14 = 10+15+ 1 + 12= 1+ 6+14+17 = 14+ 3+ 4 + 17= 3+10 + 12 + 13=12+ 1 + 17+ 8 = 3 + 13+18+ 4=13+12+ 8+ 5= 8+17+ 4+ 9 57= 7 + 14+ 4+ 5 + 12 + 15= 6 + 17+ 9+13+10+ 2 = 16+ 1+ 8 + 18+ 3+11 = 7 + 11 + 2 + 15 + 16 + 6 = 11 + 10+15+ 1 + 6 + 14 = 14 + 3 + 10 + 12 + 1 + 17 = 3 + 13 + 12+ 8 + 17+ 4= 4 + 18+13+ 5+ 8+ 9 = 9 + 4+ 3 + 10 + 15 + 16 = 18 + 13+12+ 1+ 6+ 7= 5+ 8 + 17 + 14 + 11+ 2 = 9+ 8 + 12 + 10 + 11+ 7 = 18+ 4 + 17+ 1 + 15+ 2= 5 + 13+ 3 + 14+ 6 + 16 Fig. 15. of now. The latest work has shown that the method is applicable toboards of triangular and trapezoidal shapes, and also to solid boardsin three dimensions, so that the remote ground occupied by magicand Nasik cubes will soon be invaded. In conclusion, I bri
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