Now that we know something about the parallelogram of forces we may return to the problem of sailing across and against the wind. In Fig. 60 we are looking down on the deck of a ship and the wind is represented by the arrow. The dotted line _A B_ represents the direction in which the boat is traveling and the line _C D_ represents the plane of a sail. If the line _E F_ represents the magnitude and direction of the force of the wind at the center of the sail, then we can tell how much pressure is being exerted directly against the sail, by drawing the line _g F_ perpendicular to the sail and completing the parallelogram by drawing from _E_ a line parallel to the sail intersecting _g F_ at _G_ and another line parallel to _g F_ intersecting the plane of the sail at _H_. Then the length of the line _G F_ represents the pressure against the sail. If the line _G F_ is half as long as the line _E F_, then only half of the force of the wind is exerted in the direction _G F_. In other words, a wind pressure of one pound per square foot blowing in the direction of _G F_ will do as much work as two pounds in the direction _E F_. The force of the wind has been broken up into two “components,” one (_G F_) at right angles to the sail, and the other (_H F_) edgewise to the plane, and of course the latter has no effect upon the propulsion of the boat. [Illustration: FIG. 60.--FORCES THAT MOVE A SAILBOAT] If there were nothing to prevent it, the boat would sail in the direction _G F_; but the keel of the boat offers resistance to motion in this direction, and we must construct another parallelogram around the force _G F_ to find the magnitude of the force exerted in the direction _A B_. The line _K F_ is drawn at right angles to _A B_, and then the parallelogram is completed by drawing a line from _G_ to _K_ parallel to the line _A B_ and another from _G_ to _M_ parallel to _K F_. We have then resolved to force _G F_ into two components _M F_ and _K F_. The former tends to push the boat along its course while the latter tends to make it drift to leeward. The length of the line _M F_ is little more than a quarter of the length of the wind force _E F_ and the leeward acting force _K F_ is actually considerably greater than the forward acting force _M F_. Even with a deep keel there will be some drift to leeward. This is corrected by means of the rudder of the ship which is turned to head the ship further into the wind so that although the boat does not actually travel in the direction of its axis it may be made to travel along the course _A B_. Of course the boat cannot sail directly against the wind, but it can accomplish the same result by tacking alternately to port and starboard so that eventually it can reach a port that lies in the direction from which the wind comes. THE SPEEDY CLIPPER