COMPOSITION AND RESOLUTION OF FORCE. 



215 



ual ; it glides off on the surface of the canvass without producing any effect 

 upon the vessel. The part D I produces leeway, and the part D H impels. 



If the wind, however, be directly contrary to the course which it is required 

 that the vessel should take, there is no position which can be given to the sails 

 which will impel the vessel. In this case, the required course itself is resolv- 

 ed into two, in which the vessel sails alternately, a process which is called 

 tacking. Thus, suppose the vessel is required to move from A to E, fig. 10, 

 the wind setting from E to A. The motion A B being resolved into two, by 

 being assumed as the diagonal of a parallelogram, the sides A a, a B, of the 

 parallelogram are successively sailed over, and the vessel by this means ar- 

 rives at B, instead of moving along the diagonal A B. In the same manner 

 she moves along B i, b C, C c, c D, D d, d E, and arrives at E. She thus 

 sails continually at a sufficient angle with the wind to obtain an impelling force, 

 yet at a sufficiently small angle to make way in her proposed course. 



The consideration of the effect of the rudder, which we have omitted in the 

 preceding illustration, affords another instance of the resolution of force. We 

 shall not, however, pursue this example further. 



A body falling from the top of the mast, when the vessel is in full sail, is an 

 example of the composition of motion. It might be expected that, during the 

 descent of the body, the vessel, having sailed forward, would leave it behind, 

 and that, therefore, it would fall in the water behind the stern, or at least on 

 the deck, considerably behind the mast. On the other hand, it is found to fall 

 at the foot of the mast, exactly as it would if the vessel were not in motion. 

 To account for this, let A B, fig. 11, be the position of the mast when the body 



Fig. 11. 

 ... 



Fig. 12. 



at the top is disengaged. The mast is moving onward with the vessel in the 

 direction A C, so that in the time which the body would take to fall to the 

 deck the top of the mast would move from A to C. But the body, being on the 

 mast at the moment it is disengaged, has this motion A C in common with the 

 mast, and, therefore, in its descent it is affected by two motions, viz., that of 

 the vessel expressed by A C, and its descending motion expressed by A B. 

 Hence, by the composition of motion, it will be found at the opposite angle, D, 

 of the parallelogram, at the end of the fall. During the fall, however, the mast 

 has moved with the vessel, and has advanced to C D, so that the body falls at 

 the foot of the mast. 



An instance of the composition of motion, which is worthy of some attention, 

 as it affords a proof of the diurnal motion of the earth, is derived from observ- 

 ing the descent of a body from a very high tower. To render the explanation 

 of this more simple, we shall suppose the tower to be on the equator of the 

 earth. Let E P Q, fig. 12, be a section of the earth through the equator, and 

 let P T be the tower. Let us suppose that the earth moves on its axis in the 



