once.

6...K - Kt 1; 7 R - Q B 7, K - R 1; 8 K - B 6, K - Kt 1; 9 K - Kt 6, K - R 1; 10 R - B 8 mate.

It has taken exactly ten moves to mate from the original position. On move 5 Black could have played K - K 1, and, according to principle, White would have continued 6 K - Q 6, K - B 1 (the Black King will ultimately be forced to move in front of the White King and be mated by R - R 8); 7 K - K 6, K - Kt 1; 8 K - B 6, K - R 1; 9 K - Kt 6, K - Kt 1; 10 R - R 8 mate.

Example 2.

Since the Black King is in the centre of the board, the best way to proceed is to advance your own King thus: 1 K - K 2, K - Q 4; 2 K - K 3. As the Rook has not yet come into play, it is better to advance the King straight into the centre of the board, not in front, but to one side of the other King. Should now the Black King move to K 4, the Rook drives it back by R - R 5 ch. On the other hand, if 2... K - B 5 instead, then also 3 R - R 5. If now 3... K - Kt 5, there follows 4 K - Q 3; but if instead 3... K - B 6; then 4 R - R 4, keeping the King confined to as few squares as possible.

Now the ending may continue: 4...K - B 7; 5 R - B 4 ch, K - Kt 6; 6 K - Q 3, K - Kt 7; 7 R - Kt 4 ch, K - R 6; 8 K - B 3, K - R 7. It should be noticed how often the White King has moved next to the Rook, not only to defend it, but also to reduce the mobility of the opposing King. Now

White mates in three moves thus: 9 R - R 4 ch, K - Kt 8; 10 R -  any square on the Rook's file, forcing the Black King in front of the White, K - B 8; 11 R - R 1 mate. It has taken eleven moves to mate, and, under any conditions, I believe it should be done in under twenty. While it may be monotonous, it is worth while for the beginner to practice such things, as it will teach him the proper handling of his pieces.

Example 3.—Now we come to two Bishops and King against King.

Since the Black King is in the corner, White can play 1 B - Q 3, K - Kt 2; 2 B - K Kt 5, K - B 2; 3 B - B 5, and already the Black King is confined to a few squares. If the Black King, in the original position, had been in the centre of the board, or away from the last row, White should have advanced his King, and then, with the aid of his Bishops, restricted

the Black King's movements to as few squares as possible.

We might now continue: 3...K - Kt 2; 4 K - B 2. In this ending the Black King must not only be driven to the edge of the board, but he must also be forced into a corner, and, before a mate can be given, the White King must be brought to the sixth rank and, at the same time, in one of the last two files; in this case either K R 6, K Kt 6, K B 7, K B 8, and as K R 6 and K Kt 6 are the nearest squares, it is to either of these squares that the King ought to go. 4...K - B 2; 5 K - Kt 3, K - Kt 2; 6 K - R 4, K - B 2; 7 K - R 5, K - Kt 2; 8 B - Kt 6, K - Kt 1; 9 K - R 6, K - B 1. White must now mark time and move one of the Bishops, so as to force the Black King to go back; 10 B - R 5, K - Kt 1; 11 B - K 7, K - R 1. Now the White Bishop must take up a position from which it can give check next