It may be noted that, following the author's solution, the 4th move, sacrificing Q, is unnecessary. White can play at once 4 B takes Kt discover ch, Black is forced to take the B with his K, when White can mate by Q to K B 2, or Kt to B 5, as he pleases.

The following letter, from Mr. James Pierce, refers to our comment upon the two-move problems, which was confined to the bare assertion that a majority of them are afflicted with "dual mates."

To the Editor of the WESTMINSTER PAPERS.

DEAR SIR,-I have carefully gone through the 2-movers, to which you object on account of their dual mates, and I find that without doubt there are some liable to the charge; but they are very few, unless the assumption is made that to any move of Black, however inane, there should be only one answer of White. I doubt if any collection of 2-move Problems will stand such a test as this. I have just been through Mr. Healey's, and I find the following (on this theory) have dual solutions out of the twenty-seven in his collection, Nos. 23, 27, 32, 33, 36, 37, 38, 39, 40, 43. It is evident, therefore, that that master of Chess strategy never contemplated such a test. The right view, in my opinion, is that those moves of Black should only be considered which are really

I

defensive—that is, which tend to thwart some threatened mate of White's. If this view be sound, you will find on re-examination that most of the 2-movers in our book are sound. Take, for instance, No. I. A critic has objected that if B to Kt 6 or 1 B to R 7, there are two mates; but how can such moves in any sense be considered defensive? I trust that you will consider what I have urged, and should you think it sound, kindly re-examine the positions in question, and I believe you will find only four or five troubled with the epidemic you complain of; and should this be so, I am sure that your sense of justice will lead you to state this in a future number.

I wish to say one word respecting No. 28. You say, "Of the 3-movers, at least one (No. 28) has three solutions." You have fixed on a most unfortunate one, as it certainly has not three solutions, but only my own. I feel confident that you will also retract that damaging assertion.

As regards the frontispiece Problem, I have not had time to examine properly what may be the ground of the very grave charge you bring against it; but this I hope to do as time permits, requesting others also to give it a most exhaustive analysis, and the results must be published. I cannot help thinking that it would have been more satisfactory had you given some proof of the severe statements you have made. I am, Dear Sir, yours faithfully,

COPTHILL HOUSE, BEDFORD, 19th January 1874.

JAMES PIERCE.

The whole truth of the charge complained of appears to us to be conceded in the passage"I find that without doubt there are some liable to the charge; but they are very few, unless the assumption is made that to any move of Black, however inane, there should be only one answer of White." Of course the " assumption is made," and moreover we have never yet seen adduced any convincing reason why it should not be made. How can any one move of Black in a two-move problem be considered less "inane" than another? Whatever move he makes, his fate is sealed-he dies on the next stroke; and it is too much to expect that he shall choose the manner of death most pleasing to his adversary. If composer and solver be substituted for Black and White, our meaning will be clearer. The solver is the composer's adversary, and if he produces a solution in exact accordance with the author's conditions, the latter has no right to complain that he did not mean to effect it in that way. Composers of problems know that well enough, and we doubt if there is one among them who, if he detects a dual mate in his problem, will not do all in his power to prevent it before submitting his problem to the public. But this is neither the time nor place to discuss the question of "dual mates," or the merits of Mr. Healey's problems, although we know that, since the publication of his book, that gentleman's views about dual mates have been materially changed, and so far, at least, as two-move problems are concerned, are precisely the same as our own.

Our present business is simply to show that our remark upon Messrs. Pierce's two-move problems was not made without warrant. We find then dual mates in all of the following problems:-Nos. 1, 4, 6, 7, 10, 11, 13, 14, 15, 17, 18, 20 and 22, or thirteen out of the twenty-two which appear in the book. We have no space to dilate upon the importance or otherwise of these dual attacks.

On some other occasion we shall advert to that part of the subject without reference to this book; here they are given as facts, which we believe to be beyond controversy, and in support of our charge that a majority of the two-move problems are afflicted with the prevailing epidemic, dual mates.

No. 1. If Black plays 1 B to Kt 4 or R 6, White can mate by 2 R takes Kt, and by Kt to Kt 3.

No. 4. White's first move threatens Q takes K B P; if Black defends the Pawn by Kt to R 4, White can mate by Q takes Kt, and by Q to R 4.

No. 6. If either Pawn moves, White can mate by Kt takes B, or Kt to K 5; and if B moves to any square except Q 3, White can mate with Kt at either Kt 2 or K 5 as he pleases.

No. 7. The author's leading idea appears to be founded upon Black's move I Q takes Kt. In reply to that move, White can mate by B to B 5, B to K 5 and Q takes B.

No. 10. The first move of White threatens mate with Q at K B 4. If Black plays the natural move R to K B 3, White can mate by Q to R 5 and by B to R 4.

No. 11. If Black moves the K or Q Pawns or R to Kt 3, White can mate by the double check of R and B, or with the discover check to the B alone, and if R at R 3 takes R, White can mate by R to Kt 7, and by R to B 8.

No. 13. If Black plays Q takes P, Q to Q 6, or Q to B 7, White can mate by Q to K 6 or R to K B 4 double check; and if he moves the K B to any square, except Kt square or to capture the Pawn, White can mate by the double check R to B 4 and by P takes R, claiming a Kt mating.

No. 14. If Black plays 1 K to K 5, White can mate by Kt to B 6, and by Q to K R square.

No. 15. If Black plays B to K square, White can mate by Kt to K 6, Q takes Q, and R takes Q.

No. 17. If Black plays B to B 2, or K square, White can mate by R to B 5, and by R takes P; and if he plays P to Kt 3, or Q away from the rank on which she stands in the Diagram, White can mate by Kt to K 6, and by Kt takes B ; if.in moving the Q, K 6 is defended, White can then mate by Kt to K 2 and Kt takes B.

No. 18. White's first move threatens mate with Kt and with R. If Black captures the Kt, White can mate by Q to K 3, and by Q to Q 4; and if he attempts to prevent the mate with Q by Q to R 3, White can mate with Kt, R or Q as he pleases; and if he attempts to prevent the mate with R by B to Kt 2, R to R 6, or Q to Kt 2, White can mate with either Q or Kt.

No. 20. If Black plays B takes Kt, or R takes Kt, White can mate by Q takes Q, and by Q takes B; if the Black Kt is moved to any square but K B 4, White can mate by Q takes B, and by Kt to K B 7.

No. 22. White's first move threatens B takes R mate.

If Black attempts to defend the R, by K to Q 6, White can mate by
The possible moves of the Kt at K B 2, which leave dual mates

Q to K 3, and by Kt takes Kt discover check.
open, are too obvious to require special mention.

If there are any mistakes in the foregoing analyses we shall be happy to correct them. Our columns are at all times open to Messrs. Pierce or their friends for contradiction of our assertions, or for discussing their importance. We regret that they appear to have deemed otherwise, and, if we may judge from the correspondence of our contemporaries, have even appealed to them against us, before addressing ourselves upon the subject. Such a course was obviously unnecessary.

If we make blunders, there are plenty of kind friends willing to remind us of our errors, without any suggestion from Messrs. Pierce. It is something remarkable however, that although the book has now been before the public for nearly a month, only one Metropolitan Chess column has expressed an opinion about it. That opinion (in the English Mechanic) in no way controverts ours regarding the two move problems.

There is one charge contained in our notice of last month, for which we owe the authors an apology. Writing of the three move problems, we stated that No. 28 admitted of three solutions. This is not so, and we admit the blunder.

The three move problems are the best in the whole collection, and a fair proportion of them are of more than average merit. But what could have induced the authors to publish Nos. 35 and 36? The position of No. 35 is as follows :

:

3

White-K at Q 4; B at Q 8; P's at Q Kt 7; and K B 7. Black-K at Q 3. The author's solution is-1 P Knights. 2 P Rooks. R mates, but White, on his first move, may promote either Pawn to a Knight, or either Pawn to a Queen. The latter, we believe, has been entirely overlooked by the authors, but in any case the position is not worthy of a diagram. In No. 129 we see no mate after 1 Kt to K Kt 8, if Black plays 1 K to Q B 4.

In No. 132 there is a second solution, commencing 1 Kt to R 5, and in No. White may play 1 Q to Q B 4 ch (1 K takes Kt) 2 B to K sq, and 3 Q mates. then White plays 2 B to B 3 ch, and Q mates.

152 instead of 1 B to KR 5 If Black plays 1 K to K 4

In the partnership problems Nos. 277 and 279 are identical. The "Chess Studies" are really end games, and many possess no special merit that we can discover. But, it may be asked, are there no good problems in the book? Yes, there are; but they are so completely outnumbered that, as we stated last month, time and patience are required to discover them. The one mistake on the part of the authors is their omission to make the selection themselves.

A selection of Messrs. Pierce's problems might challenge comparison with those of any author. The collection will not bear either comparison or criticism.

In venturing to speak our mind about this book we were not without forebodings of the trouble our candour would entail upon us. Chess players and Chess authors have become so accustomed to the ridiculous platitudes which used to pass for "Chess literature" that they cannot stomach an honest opinion about their productions, and when they get it, cry out as children do against the medicine intended to correct a repletion of sweets. Although willing enough to attract the attention of the public, they resent the consequences that sometimes ensue upon gaining that end. Some are even disposed to ascribe every description of uncharitable motive to the unlucky critic who sees any demerit in their works. Such flabby platitudes as a "Welcome addition to the literature of Chess," "A book by this distinguished author (or composer) cannot fail to interest," is much more to the taste of Chess authors than an impartial verdict upon the contents of their books. It goes with saying that that is a much easier way of discharging critical functions than ours. If we considered authors and our own ease only, we believe we could ring the changes about "welcome additions" and "distinguished composers" as glibly as others, but we prefer discharging our duty to the public, that buys and reads our journal, to the good opinion of any Chess author under the sun. It says little for what is called the literature of Chess that such a declaration should be necessary, but Chess authors (possibly all authors) appear, like so many Alexanders, to live in little worlds of their own, and are slow to credit the existence of any excellence outside of them.

OUR PROBLEMS REVIEWED.

No. 361, by I. O. H. TAYLOR.-"Spoiled by a dual mate in one variation. Otherwise pretty," H. J. C. Andrews." A good problem, although the style is old," C. W. M. Dale.-" Very well constructed," J. N. K.—“A good idea; some of the dual mates should have been avoided,' Othello." Easy," J. A. Miles." Very pretty, H. E. B. R.—"Interesting and instructive," W. Nash. "The best of the two moves,' R. W. Johnson." Delightfully complex," C. Puller. "It is obvious the R must move," L. M. C.-"Good," W. Brown.-"Deceptive," T. R. H.

No. 362, by Dr. S. GOLD.-"Here, again, are dual mates. Surely two movers ought, at any rate, to be exempt from this fault," H. J. C. Andrews.-" An improvement on Dr. Gold's last," C. W. M. Dale.- -"Easy," J. N. K.-" Fair," Othello. -"Class B, poor," J. A. M.- "Easy," H. E. B. R.-"Poor; dual mates are too plentiful," W. Nash. "Very easy, R. W. Johnson.-"The best of the set," C. Puller." Very simple," L. M. C. "Ingenious," W. Brown. Simple," T. R. H.

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No. 363, by G. E. BARBIER.-"Very pretty; the best three mover in this number," H. J. C. Andrews.-"The best in the number," C. W. M. Dale.-" Elegantly designed," J. N. K."Class A, a fine and elegant problem," J. A. M.-"Very fine," H. E. B. R.- Although simple, it is one of the best in this number," W. Nash.-"A very pretty position; the best of the three movers," L. M. C.-" Interesting and pretty," W. Brown ; solved by T. R. H.

No. 364, by J. A. MILES.-"A neat little end game, and not so easy as one thinks at first sight," H. J. C Andrews.-— "The construction is neat," C. W. M. D.-"Easy," J. N. K. "Pretty and pleasing; the BP at Kt 4 is not wanted," Othello. Ingenious,' H. E. B. R.-"Easy; the B Pat Kt 4 is unnecessary," W. Nash.—“ Very neat and ingenious," R. W. Johnson.-"Pretty," C. Puller.- Easy," L. M. C."One of the best," W. Brown.-"No variations," T. R. H. No. 365, by J. GOCHER.—“Very good," H. J. C. Andrews. Very fair," C. W. M. D.- "A hackneyed device," J. N. K. "Good; the B P's on B's file are not wanted," Othello.Very poor," J. A. M.-"Easy, H. E. B. R.; the position is inelegant, but it is not without merit," W. Nash.-" A very unnatural position," R. W. Johnson." Simple,' C. Puller."Easy," L. M. C.-" Unnatural position," W. Brown.—— 66 Clumsy," T. R. H.

66

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No. 366, by J. H. FINLINSON.- "A Christmas plum for juveniles," H. J. C. Andrews.-" Very neat," C. W. M. D.— "Ingenious," J. N. K.--“ Fair,” Othello.-"Sweet simplicity,' J. A. M.-"Very poor," H. E. B. R.-"Nothing original about this idea," W. Nash.-"Neat, but simple," R. W. Johnson.— "Not easy," C. Pullen. "Neat and pretty," L. M. C."Pretty, but obvious," W. Brown.—“No variations," T. R. H. No. 367, by J. N. KEYNES, "The idea is of course excellent, being almost identical with that of the famous Indian Problem,' H. J. C. Andrews. "This so nearly resembles the Indian

"Fair,"

Problem that criticism is unnecessary,'
"C. W. M. D.-
Othello." Pretty," H. E. B. R.--“ An old bone, picked pretty
clean before now," W. Nash.-"The idea has been worked to
death," R. W. Johnson.-"Lo ! the poor Indian," J. A. M.-
"The most difficult problem of the set," C. Puller." Based on
the Indian problem," L. M. C.—"A fair problem," W. Brown.
-“No variations," T. R. H.

No. 368, by G. B. STOCKER." The position is ungainly, but
the solution is neat," H. J. C. Andrews." Rather obvious, but
the construction is neat," C.W. M. D.- "The arrangement of the
White Pawns is not inartistic," J. N. K.-
"Good and beautiful,"
Othello.-Class A, a gem,” J. A. M.- "Good; the use of the
White Knight is perfection," H. E. B. R.
"Another very
pleasing, though simple position," W. Nash.-Very neat," R. W.
Johnson." Perfect," C. Puller.-"The second best," L. M. C.
"Pretty; the best three-mover," W. Brown. Solved by

T. R. H.

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No. 369, by F. W. LORD.-"Pretty, well constructed," H. J. C. Andrews.-"Remarkably neat, C. W. M. D.'Easy," J. N. K.-Othello solves this problem by 1 Q to Q square, &c.-"Too simple and easy," J. A. M.-"Very pretty,' H. E. B. R. "The weakest in the number," W. Nash. C. Puller, R. W. Johnson and W. Brown solve this problem by IQ to Q square, &c.- Not equal to the last contributions of this composer," L. M. C.-" Poor," T. R. H.

- Solved by

No. 370, by V. GORGIAS and JAMES PIERCE.
Kt takes R P, by H. J. C. Andrews, C. W. M. D., J. N. K.,
Othello, H. E. B. R., W. Nash.- "Not difficult," Č. Puller,
L. M. C., W. T. N. Brown, T. R. H.-Author's solution by
R. W. Johnson.

"For

No. 371, by J. W. ABBOTT.-"A stratagem of the old school," H. J. C. Andrews.-" Very beautiful," C. W. M. D. "Neat, but easy," J. N. K.- "A good and pleasing problem," Othello." Very pretty and curious, but not up to Mr. A.'s standard," J. A. M.- "Ingenious,' " H. E. B. R. beginners," A. Nash.- "A pretty puzzle," R. W. Johnson."Solved at a glance," C. Puller. "A very pretty solution," L. M. C.-"Very neat," W. T. N. Brown." An example for the episcopal bench," T. R. H.

gem,

No. 372, by W. COATES.- "Neat; but the position of the Black Knight tells the tale," H. J. C. Andrews.-"A little ," C. W. M. D.-" There is a run on this species of mate. We have it in Nos. 363, 369 and 371," J. N. K.-"Good," Othello.- "Class A, very fine, and undoubtedly the best in the number," J. A. M.- Easy," H. E. B. R. 'Very neat and well constructed," W. Nash.-"Ingenious," R. W. Johnson. Pretty," C. Puller.-" Very good," L. M. C.-"A good problem," W. T. N. Brown.-"Difficult; but no variations," T. R. H.

66

No. 373, by H. MEYER.-" A subtle and splendid study," H. J. C. Andrews.-"A magnificent study," J. N. K.-" The idea and carrying out are alike admirable," W. Nash.-"The best in this number," W. T. N. Brown.