'SZ MECHANICS. 



if it undertake to fly against such a wind, it will not 

 advance at all, but remain stationary, A similar re- 

 sult will take place if a steam-boat, having a speed of 

 ten miles an hour, should first run down a river with a 

 current of equal velocity, and then upward against the 

 current ; in the first case it would move twenty miles 

 an hour, and in the latter it would not move at all. 

 Where forces act neither in the same nor in opposite 

 Fig. 7. directions, but obliquely, the re- 



j suit is found in the following 

 ~7 manner : If a ball, placed at the 

 / point a {Fig-. 7), be struck by 

 ■' two different forces at the same 

 moment, in the direction shown 

 by the two arrows, and if one 

 force be just sufficient to carry it from a to c, and the 

 other to carry it from a to b, then it will move inter- 

 mediate between the two, in the direction of the diag- 

 onal of the parallelogram a d, and to a distance just 

 equal to the length of this diagonal or cross-diameter. 

 "When the forces act very nearly together, the paral- 

 lelogram of the forces will be very narrow and quite 



long, with a long di- 



agonal [Fig: 8) ; but 



^^ ^"^"--^^^^^I-! _^ if they act on nearly 



opposite sides of the 

 ball, they will very nearly neutralize each other, and the 

 Fig. 9. diagonal or result will be 



**^ " " ' ""^ very short, showing that 



"^ the motion given to the ball 

 will be very small {Fig: 9.) 

 These examples show the importance of having 



