COMPOSITION AND RESOLUTION OF FORCE. 



213 



The action of the oars themselves, in impelling the boat, is an example of 

 the composition of force. Let A, fig. 7, be the head, and B the stern of the 

 boat. The boatman presents his face toward B, and places the oars so that 

 their blades press against the water in the directions C E, D F. The resist- 

 ance of the water produces forces on the side of the boat, in the directions G 

 L and H L, which, by the composition of force, are equivalent to the diagonal 

 force K L, in the direction of the keel. 



Similar observations will apply to almost every body impelled by instruments 

 projecting from its sides and acting against a fluid. The motions of fishes, the 

 act of swimming, the flight of birds, are all instances of the same kind. 



The action of wind upon the sails of a vessel, and the force thereby trans- 

 mitted 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 compli- 

 cated 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. 8, be the position of the sail, and let the wind 



Fig. 8. 



blow in the direction CD. 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, there- 

 fore, 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 what- 

 ever 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 parallel- 

 ogram 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 side- 

 wise. 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 leeway. 



From this explanation, it will be easily understood how a wind which is 



