COMPOSITION AND RESOLUTION OF FORCE. 



When a boat is rowed across a river, in which there is a current, it will not 

 move in the direction in which it is impelled by the oars. Neither will it take 

 the direction of the stream, but will proceed exactly in that intermediate direc- 

 tion which is determined by the composition of force. 



Let A, fig. 6, be the place of the boat at starting ; and suppose that the oars 

 are so worked as to impel the boat toward B with a force which would carry 

 it to B in one hour, if there were no current in the river. But, on the other 



Fig. 6. 



hand, suppose the rapidity of the current is such that, without any exertion of 

 the rowers, the boat would float down the stream in one hour to C. From C 

 draw C D parallel to A B, and draw the straight line A D diagonally. The 

 combined effect of the oars and the current will be, that the boat will be car- 

 ried along A D, and will arrive at the opposite bank in one hour, at the 

 point D. 



If the object be, therefore, to reach the point B, starting from A, the rowers 

 must calculate, as nearly as possible, the velocity of the current. They must 

 imagine a certain point, E, at such a distance above B that the boat would be 

 floated by the stream from E to B in the time taken in crossing the river in the 

 direction A E, if there were no current. If they row toward the point E, the 

 boat will arrive at the point B, moving in the line A B. 



In this case the boat is impelled by two forces, that of the oars in the direc- 

 tion A E, and that of the current in the direction A C. The result will be, 

 according to the parallelogram of forces, a motion in the diagonal A B. 



The wind and tide acting upon a vessel is a case of a similar kind. Sup- 

 pose that the wind is made to impel the vessel in the direction of the keel, 



Fig. 7. 



while the tide may be acting in any direction oblique to that of the keel. The 

 course of the vessel is determined exactly in the same manner as that of the 

 boat in the last example. 



