4\^'^»a ^Y\()mi'%^dk the Flight of a Projectile, ^ ' 389 



Adiythdt pointi^ is the tangent to another great circle passing 

 through the place at right angles to the former, and may be re- 

 presented by the two lines NS, WE ; these lines always of course 

 remaining at right angles to each other. We will suppose that 



K 



B' 



^sr 



^. 



E 



two guns are placed at P, which is 52° lat., the one pointing due 

 south and the other due west, at two objects 5600 yards distant 

 from P in these directions, and that they are both fired at the 

 same moment. Now the directions in which the balls are fired 

 are at right angles to each other, and there is nothing in the 

 rotation of the earth to alter the relative positions of the two lines 

 drawn from the guns to the shot during any moment of their flight. 



It has been shown that the shot fired due south will be 

 deflected 10-914 yards to the right of the object in 34'^ Let the 

 above figure represent the north and south, and east and west 

 lines, at the end of 34". Now the position of the ball fired due 

 south will be B, SB being equal to 10*914 yards ; join PB, and 

 draw B'P at right angles to PB ; then if PB and PB' be equal, 

 WB' will be 10*914 yards. This perhaps may not be rigorously 

 correct, as the correction necessary to be made on account of 

 the horizontal curved motion of the point where the gun stands 

 would not be so great in the one case as in the other. 



By the same reasoning, it can be shown that the deviation of 

 the shot will be the same in amount in the same latitude, or 

 nearly so, whatever may be the direction of the range, and that 

 the deviation will in all cases be to the right of the object. 



In difierent latitudes, it appears, from what has been stated, 

 that the amount of deflection depends upon the length of range, 

 the time of flight, and the cosine of the latitude of the gun ; it 



