(85.) The action of wind upon the sails of a vessel, and the force thereby transmitted to the keel, modified by the rudder, is a problem which is solved by the principles of the composition and resolution of force; but it is of too complicated and difficult a nature to be introduced with all its necessary conditions and limitations in this place. The question may, however, be simplified, if we consider the canvass of the sails to be stretched so completely as to form a plane surface. Let A B, _fig. 14._, be the position of the sail, and let the wind blow in the direction C D. If the line C D be taken to express the force of the wind, let D E C F be a parallelogram, of which it is the diagonal. The force C D is equivalent to two forces, one in the direction F D of the plane of the canvass, and the other E D perpendicular to the sail. The effect, therefore, is the same as if there were _two winds_, one blowing in the direction of F D or B A, that is against the edge of the sail, and the other, E D, blowing full against its face. It is evident that the former will produce no effect whatever upon the sail, and that the latter will urge the vessel in the direction D G. Let us now consider this force D G as acting in the diagonal of the parallelogram D H G I. It will be equivalent to two forces, D H and D I, acting along the sides. One of these forces, D H, is in the direction of the keel, and the other, D I, at right angles to the length of the vessel, so as to urge it _sideways_. The form of the vessel is evidently such as to offer a great resistance to the latter force, and very little to the former. It consequently proceeds with considerable velocity in the direction D H of its keel, and makes way very slowly in the sideward direction D I. The latter effect is called _lee-way_. From this explanation it will be easily understood, how a wind which is nearly opposed to the course of a vessel may, nevertheless, be made to impel it by the effect of sails. The angle B D V, formed by the sail and the direction of the keel, may be very oblique, as may also be the angle C D B formed by the direction of the wind and that of the sail. Therefore the angle C D V, made up of these two, and which is that formed by the direction of the wind and that of the keel, may be very oblique. In _fig. 15._ the wind is nearly contrary to the direction of the keel, and yet there is an impelling force expressed by the line D H, the line C D expressing, as before, the whole force of the wind.