2-4 S. VI. 152., Nov. 27. '58.] 



NOTES AND QUERIES. 



435 



Old Romney and Broohland. — I have in my 

 possession three small volumes of Sermons in MS., 

 preached in the above two places between the years 

 1691 and 1694. Can any of your readers tell me 

 the author's name ? Sampson. 



[Perhaps our correspondent maj' obtain a clue to the 

 author if we state that the Rev. John Defray was Rector 

 of Old Romney from 1690 to 1738; and that the Rev. 

 Thomas Johnson was Vicar of Brookland from 1C77 to 

 1727.] 



JicpItCS. 



CHESS CALCULUS. 



(2"'i S. vi. 347.) 



The question asked is whether it be " practica- 

 ble to construct a Chess Calculus, so that every 

 position in a game may be expressed by a func- 

 tion of the positions and powers of the pieces, by 

 operating on which the best move for the next 

 player might be evolved." The following pre- 

 sumptions in favour of the practicability are 

 raised : — First, that chess is evolved from axioms 

 and definitions ; secondly, that the power of a 

 piece may be expressed by coordinates. 



To say that such a calculus must be impossible, 

 would be to speak beyond knowledge ; and more- 

 over would not be conclusive : for impossible 

 things are done from time to time. A very sim- 

 ple game might be proposed of which the calculus 

 is not impossible : and if a simple game admit of 

 such treatment, in what should a more compli- 

 cated game differ from it except in complication ? 

 Take the common game which in my school days 

 used to be called by some noughts and crosses, 

 and by others tit-tat-toe, which were the formular 

 words of victory, just as check-mate are those of 

 chess. There are nine squares in rank and file, in 

 one of which the first player enters a nought, the 

 second player enters a cross in another, and so on ; 

 the game being won when either player can point 

 out his marks three in a row, whether horizontal, 

 vertical, or diagonal. Now the number of pos- 

 sible games must very considerably fall short of 

 362880, the product of the first nine numbers, the 

 total number of orders in which the squares can 

 be filled up. The number of rationally played 

 games probably" does not'exceed a few hundreds. 

 A calculus is conceivable : but it would be of very 

 intricate expression. Given the state of things at 

 the Kth move, it is possible that a formula might, by 

 inserting the value of n, give out all the ways in 

 which a player might afterwards win, distinguish- 

 ing the few in which the new move reduces his 

 winning to a certainty.* 



But the chess calculus is beyond human ima- 

 gination. In the first place chess is not entirely 

 evolved from definitions and postulates. A geo- 

 meter who plays with these things as he finds 

 them in Euclid, must play every proposition of 



every book : but the chess player is dictated to by 

 an adversary. Suppose all possible rational games 

 to be, one with another, of 30 moves on each side, 

 60 moves in all, which is rather low. Suppose that 

 at each of 50 moves the player in action has two 

 good choices, which is not much, considering how 

 many choices he frequently has. 



This supposes more than eleven hundred mil- 

 lions of millions of games, and a calculus supposes 

 a formula containing in its structure an implicit ac- 

 count of the progress of every one of these games. 

 For a formulary contains not merely what shall 

 emerge in any case ; but all that by possibility 

 might emerge. That the use of such a formula 

 should involve the solutions of equations of the 

 ten- thousandth degree is probably very much be- 

 low the mark. 



Again, how are we to express thQ poioers of the 

 several pieces? I rememlaer seeing an attempt 

 which was based on the number of squares com- 

 manded : but the proposer acknowledged himself 

 incapable of representing the additional power 

 derived by a knight from his not being stopped 

 by other pieces. This, however, would be far 

 from enough, even if it could be satisfactorily 

 done. The power of a piece depends upon the 

 neighbours it may have, and the opponents who 

 check it. A protected pawn immediately before 

 a castle limits its power and value, except in those 

 rare cases in which it will be worth while to sacri- 

 fice the castle for the pawn. Whether or no the 

 sacrifice would be worth while depends upon the 

 prospects of the game. Hence the power of the 

 pieces, in any given position, will depend upon the 

 whole structure of the game ; while the formula 

 for the game will depend upon the mode of ex- 

 pressing the power of the pieces. Such compli- 

 cations of the ignotum per ignotum it is the daily 

 business of mathematical analysis to unravel : but 

 I confess that I should expect, in the expression of 

 the chess problem, a complexity far exceeding that 

 of any problem which was ever successfully dealt 

 with up to this time. A. De Moegan. 



WARSTON S WORKS. 



(2°"i S. vi. 368.) 



I have just seen in " N. & Q." some rather 

 severe strictures on Mr. Halliwell's late edition 

 of this poet. I do not think they are merited ; 

 for Mr. Halliwell's object was, as he says, to give 

 these pieces " as nearly as possible in their ori- 

 ginal state," and thus to give people who, like 

 myself, cannot or will not lay out large sums in 

 the purchase of old and scarce books, or spend 

 days in the Museum, an opportunity of seeing 

 how books came out of the hands of the old prin- 

 ters, even when, as was evidently the • case with 

 Marston, the proofs were read by the author, 



