466 Mr. J. W, L. Glaisher on the Problem of the Eight Queens. 



(not seven), so that we have a reduction of 4, and the number is 

 96—4 = 92. As the symmetrical solution is unique, it is per- 

 haps worth giving it here : — 



1 



1 . .. 



It will be noticed that on the chessboard all the uneven suf- 

 fixes correspond to white squares, and the even suffixes to black 

 squares ; every solution thus involves four white and four black 

 squares. 



In developing the determinants I found it most convenient to 

 replace the zero constituents by crosses, and to write down the 

 terms not previously obliterated and scratch them through with 

 the pen—thus, e. g., to write the right-hand side of (2), 



x 



c 5 



a 7 



96 



+ e s 



u 3 

 X 



96 



fe h 



and erase by a stroke the constituents which are printed as 

 points in (2). But a little practice soon indicates the most rapid 

 course of procedure, and suggests several artifices which abbre- 

 viate the work. The fact also that the signs of the terms are 

 not required and may all be taken as positive, renders the process 

 of development much less troublesome than it would otherwise 

 be. I performed the whole work twice independently, and found, 

 on comparing the two calculations (which were very different in 

 many respects), that all the results were the same; so that I feel 

 very little doubt of their accuracy. I also verified that every 

 solution contained one square from each row and one from each 

 column. 



It is worth while, in conclusion, to place here together th 

 final results for the different boards. 



