1620 Chess 



Knight's move, solution by geometry of posi- 

 tion. Volpicelli, P. Em. At. E. Ac. 25 



(1872) 87-, 364-; 26 (1873) 49-, 241-. 

 , (Volpicelli) . Tarry, H. Les Mondes 



28 (1872) 60-. 

 moves over squares of 5, 6, 7, 8, and 



extension to higher squares. Frost, A. H. 



QJ. Mth. 14 (1877) 354-. 

 Mathematical analysis applied to chess. 



(Brief resume.) Janisch, . St Pet. Ac. 



Sc. Bll. 6 (1863) 473-. 

 Problem, solution by aid of numerical functions. 



Bugaev, N. V. (xn) [1878] Eec. Mth. 



(Moscou) 9 (1878-81) (Pt. 1) 355-. 

 8 queens problem. Glaisher, J. W. L. Ph. 



Mg. 48 (1874) 457-. 

 . Eohn, K. Dresden Isis Sb. (1889) 



(Ab.) 89-. 

 . Sprague, T. B. Edinb. Mth. S. P. 



8 (1890) 30- ; 17 (1899) 43-. 

 , generalisation. Gunther, S. Arch. 



Mth. Ps. 56 (1874) 281-. 

 n queens problem. Parmentier, T. As. Fr. 



C. E. (1883) 197-. 

 Sylvester's anallagmatic chess-board pattern. 



Lucas, E. As. Fr. C. E. (1877) 213-. 



Class of numbers arising in certain expansions. 



Ocagne, M. d'. Am. J. Mth. 9 (1887) 353-. 

 Classes, division into. Harding, P. J. Mth. 



Gz. No. 6 (1895) 59. 

 Coefficients in expansion of (x + y) n . Laisant, 



. As. Fr. C. E. (1888) (Pt. 2) 72-. 



._ f ?fz*Y*. Mathieu, J. J. A. N. 

 A. Mth. 2 (1863) 509-. 



COMBINATIONS. 

 Kirkman, T. P. (n Adds.) Ph. Mg. 5 (1853) 



Buniakovskij, V. Ja. St. Pet. Ac. Sc. Mm. 



(Es.) 21 (*1872) 261-. 



Mantel, W. N. Arch. Wisk. 11 (1884) 190. 

 Thiele, T. N. Kjtfb. Ov. (1895) 415-, xv-. 

 application to explanation of Arbogast's method. 



De Morgan, A. Camb. and Dubl. Mth. J. 6 



(1851) 35-. 

 of a certain number of successive integers 



having a sum below a given limit, number 



of. Marsano, G. B. G. Mt. 19 (1881) 156- ; 



20 (1882) 249-. 



complete. Levret, . N. A. Mth. 1 (1842) 87-. 

 . Melon, A.G. N. A. Mth. 8 (1869) 168-. 

 . Niewenglmvski, G. H. N. A. Mth. 13 



(1874) 285-. 

 compound. Cayley, A. Manch. Lt. Ph. S. 



P. 16 (1877) 113-. 

 Crocchi's theorem (on sums of combinations 



of powers and homogeneous products). 



Sylvester, J. J. (xn) [1882] J. H. Un. 



Cir. [2] (1883) 2. 

 ( ) proof. 



Franklin, F. (xn) [1882] J. H. Un. Cir. 



[2] (1883) 24. 



Combinations 1620 



of 28 dominoes. Eeiss, M. [1859] A. Mt. 5 



(1871-73) 63-. 

 of elements dispersed in a plane. Mantel, . 



As. Fr. C. E. (1883) 171-. 

 and factorial numbers, theorems. Catalan, E. 



Brux. Ac. Bll. 25 (1893) 238-, 430-. 

 formula. Catalan, E. C. Liouv. J. Mth. 7 



(1842) 511-. 

 , new. Studnicka, F. J. Prag Sb. (1879) 



295-. 

 formulae. Grand, , & EocJiat, . Gergonne 



A. Mth. 3 (1812-13) 213-. 

 for expanding power of binomial. Gergonne, 



J. D. Gergonne A. Mth. 17 (1826-27) 



356-. 

 a game of. Brianchon, C. J. Par. EC. Pol. 



Cor. 3 (1814-16) 387-. 

 number of given class having a given sum. 



Boschi, P. Bologna Ac. Sc. Mm. 5 (1883) 



805-. 

 probabilities and life contingencies. Hardy, 



P. Assur. Mg. 2 (*1852) 151-, 259-. 

 problem. Euler, L. [1779] St Pet. Ac. Sc. 



Mm. 3 (1811) 57-. 

 . Durrande, J. B. Gergonne A. Mth. 7 



(1816-17) 334-. 

 . Catalan, E. C. Liouv. J. Mth. 3 (1838) 



111- ; 5 (1840) 264 ; 6 (1841) 74. 

 . Chevillard, A. J. N. A. Mth. 3 (1844) 



537-. 

 . Kirkman, T. P. Camb. and Dubl. Mth. 



J. 2 (1847) 191- ; 5 (1850) 255-. 

 . Anstice, E. E. Camb. and Dubl. Mth. J. 



7 (1852) 279- ; 8 (1853) 149-. 

 . Prouhet, E. N. A. Mth. 12 (1853) 85-. 

 . Kelland, P. [1855] Edinb. E. S. T. 21 



(1857) 359-. 

 . Polignac, (Prince) C. de. [1868] L. Mth. 



S. P. 2 (1869) 69-. 

 . Robertson, A. Edinb. Mth. S. P. 4 (1886) 



78-. 

 . Hertzsprung, S. Ts. Mth. 5 (1887) 13- ; 



Fschr. Mth. (1887) 198-. 

 . Brunei, . Bordeaux S. Sc. Mm. 5 



(1895) xiv-. 

 problems. Encontre, D. Mntp. Eec. Bll. 2 



(1805) 68-. 

 . Anon, (vi 538) Gergonne A. Mth. 11 



(1820-21) 165-. 

 . Weiss, A. Crelle J. 34 (1847) 255-; 38 



(1849) 107-. 



. Sinram,T. Arch. Mth. Ps. 63 (1879) 445-. 

 . Holtze,A. Arch. Mth. Ps. 11 (1892) 284-. 

 proof for number of combinations of n things 



taken r at a time. Scott, W. H. Mess. 



Mth. 5 (1876) 18-. 

 of theorem. Forstemann, W. A. Crelle J. 



13 (1835) 237-. 

 . Crone, C. (xn) Ts. Mth. 1 (1877) 



153-. 

 questions in. De Morgan, A. Assur. Mg. 5 



(*1855) 93-. 

 regular, and applications. Ai\dre, D. Par. EC. 



Norm. A. 5 (1876) 155-. 

 with repetition. Martynowski, J. Liege Mm. 



S. Sc, 16 (1861) 53-. 

 . Catalan, E. C. Li^ge Mm. S. Sc. 2 



(1867) 1-. 



82 



