move along the White diagonal, when the Black King moves back to Kt 1. 12 B - K Kt 4, K - Kt 1; 13 B - K 6 ch, K - R 1; 14 B - B 6 mate.

It has taken fourteen moves to force the mate and, in any position, it should be done in under thirty.

In all endings of this kind, care must be taken not to drift into a stale mate.

In this particular ending one should remember that the King must not only be driven to the edge of the board, but also into a corner. In all such endings, however, it is immaterial whether the King is forced

on to the last rank, or to an outside file, e.g. K R 5 or Q R 4, K 1 or Q 8.

Example 4.—We now come to Queen and King against King. As the Queen combines the power of the Rook and the Bishop, it is the easiest mate of all and should always be accomplished in under ten moves. Take the following position:

A good way to begin is to make the first move with the Queen, trying to limit the Black King's mobility as much as possible. Thus: 1 Q - B 6, K - Q 5; 2 K - Q 2. Already the Black King has only one available square 2...K - K 4; 3 K - K 3, K - B 4; 4 Q - Q 6, K - Kt 4. (Should Black play K - Kt 5, then Q - Kt 6 ch); 5 Q - K 6, K - R 5 (if K - R 4, K - B 4 and mate next move); 6 Q - K Kt 6, K - R 6; 7 K - B 3, K moves; 8 Q mates.

In this ending, as in the case of the Rook, the Black King must be forced to the edge of the board; only

the Queen being so much more powerful than the Rook, the process is far easier and shorter. These are the three elementary endings and in all of these the principle is the same. In each case the co-operation of the King is needed. In order to force a mate without the aid of the King, at least two Rooks are required.

2. PAWN PROMOTION

The gain of a Pawn is the smallest material advantage that can be obtained in a game; and it often is sufficient to win, even when the Pawn is the only remaining unit, apart from the Kings. It is essential, speaking generally, that

the King should be in front of his Pawn, with at least one intervening square.

If the opposing King is directly in front of the Pawn, then the game cannot be won. This can best be explained by the following examples.

Example 5.

The position is drawn, and the way to proceed is for Black to keep the King always directly in front of the Pawn, and when it cannot be done, as for instance in this position because of the White King, then the Black King must be kept in front of the White King. The play would proceed thus: 1 P - K 3, K - K 4; 2 K - Q 3, K - Q 4. This is a very important move. Any other move would lose, as will be shown later. As the Black King cannot be kept close up to the Pawn, it must be brought as far forward as possible and, at the same time, in front of the White King.

3 P - K 4 ch, K - K 4; 4 K - K 3, K - K 3; 5 K - B 4, K - B 3. Again the same case. As the White King comes up, the Black King must be kept in front of it, since it cannot be brought up to the Pawn.

6 P - K 5 ch, K - K 3; 7 K - K 4, K - K 2; 8 K - Q 5, K - Q 2; 9 P - K 6 ch, K - K 2; 10 K - K 5,