problem, often stated by writers on Chess, shows how the Knight may pass on to every square on the board without stepping on one square twice. The simplest way of effecting this object is that invented by M. Demouvre, which is as follows:The Knight starts from the top right-hand corner, and passes completely over the board in a series of jumps, by which the outer squares are first filled.

Several other ways of effecting this object are known, but the above will suffice.

KING, KNIGHT, AND BISHOP AGAINST KING.

This is one of the most difficult and interesting endings of games that I know of. As it is impossible to checkmate with two Knights, so the mate with Knight and Bishop is seldom accomplished by inferior players within the

given fifty moves. The secret, as in the mate with two Bishops, is not only to drive the adverse King into a corner, but it must be the corner commanded by your Bishop. Suppose you start with the pieces on their several squares, your first efforts must be to drive the single King on to the last line, whence, by a series of ingenious moves, you force him into the fatal corner, from which there is no escape. But a more difficult position still occurs in the " Palamède," and is quoted by Mr. Staunton. Here the King is in the corner not commanded by your Bishop. You have therefore to drive him into a white corner. That the student may better understand the position, I subjoin it in a diagram.

Now, what the player has to do in this case is to keep close to his adversary and drive him

round. Thus :

White.

1 Kt. to K. B.'s 7 (ch.)

2 B. to K.'s 4

3 B. to K. R.'s 7

4 Kt. to K.'s 5

5 Kt. to Q.'s 7

6 K. to his 6

7 K. to Q.'s 6 8 B. to K. Kt.'s 6 (ch.) 9 Kt. to Q. B.'s 5 10 K. B. to his 7 11 Kt.to Q.Kt.'s 7 (ch.) 12 K. to Q. B.'s 6 13 K. to Q. Kt.'s 6. 14 B. to K.'s 6 (ch.) 15 Kt. to Q. B.'s 5 16 B. to Q.'s 7 17 Kt. to Q. R.'s 6 (ch.) 18 B. to Q. B.'s 6 (mate)

Black.

1 K. to Kt.'s sq. 2 K. to B.'s sq. 3 K. to his sq. 4 K. to K. B.'s sq. 5 K. to his sq. 6 K. to Q.'s sq. 7 K. to his sq. 8 K. to Q.'s sq.

9 K. to Q. B's sq. 10 K. to Q.'s sq. 11 K. to Q. B.'s sq. 12 K. to Q. Kt.'s sq. 13 K. to Q. B.'s sq. 14 K. to Q. Kt.'s sq. 15 K. to Q. R.'s sq. 16 K. to Q. Kt.'s sq. 17 K. to Q. R.'s sq.

If, at his fourth move, Black King had moved to his Queen's square, White would have answered with Bishop to Queen's third, and so have prolonged the mate by a move or two. But if the White play well, observing always the rule of the above moves, and allowing the Black King never to get away into the middle of the board, mate is inevitable. But the greatest care must be observed, or the sable monarch will escape, and you will have all your work to do over again, and so perhaps allow your opponent to gain the fifty moves that entitle him to claim

C

a draw. Not to weary the student with too much teaching, let him practise and conquer, the principle of the above moves.

CHECKMATE WITH THE BISHOPS.

In ordinary games between ordinary players the endings are usually confined to a few simple and well-understood methods. We have seen how a Queen, opposed to inferior pieces, wins. In the majority of cases, a Queen would win against two Rooks from her power of checking and forking at the same move; though if the Rooks, with the move, can support each other, they may certainly force an exchange and win. The Queen may generally be said to win against two Bishops; but numerous instances occur in actual play in which the Bishops draw the game. Mr. Walker gives the following position as one in which Black must submit to a draw.

White,
K. at K. Kt. 4
Q. at Q. R. 4

K. at Kt. 2

Black.

Bs. at K. Kt. 3, and K. B. 3 With the Queen or Rooks on the board, mate is comparatively easy, but when you are left with two Bishops opposed to a single King or a King and Pawn, the mate within the stipulated fifty moves becomes a matter of difficulty. But, conquer the principle of this checkmate, and its practice is easy enough. The whole philosophy of the matter is this, the King must be forced into one of the corners, or certainly into a square adjoining, when mate follows as a matter of course. But beware of giving a number of useless checks; support your Bishops with the King,

and then you may give mate with two, or at most, three checks. So long as you continue to check with one or other of the Bishops, so long may your adversary keep in the centre of the board. Place the pieces on their own squares, and gradually advance your King, while at the same time you draw a line of demarcation with your Bishops, across which the opposite King cannot pass. In less than twenty moves you will be able to mate. Instead, however, of giving the actual moves, I leave my young readers to work out the solution for themselves. But let them remember that the power of the Bishops is just as great at a distance as when close to the adverse King.

Take also the following position and try. Mate may be given in about eight moves.

ENDINGS OF GAMES WITH PAWNS AGAINST
PAWNS.

It will have been seen by the intelligent student that the successful ending of a game often depends on the proper management of the generally despised Pawns. It cannot be too often impressed upon the attention of the tyro that the reckless sacrifice of a Pawn in the beginning of a game is fatal, in particular situations; while, on the other hand, the judicious gambit leads to fortune. Numerous games by fine players illustrate this; I shall now show you how and in