204 Dynamics. 



The greatest elevation is equal to h multiplied by the sing 

 square of the angle of projection, that is, equal to h (sin 45) 3 . 



h = 9937,75ft. log 3,99729 



45 log sin 9,84949 



9,84949 



Greatest elevation = 4969 feet 3,69627 



4969 wants only 31 1 feet of a mile. 



Moreover, according to the case supposed, we have 

 as the expression for t the time of flight. 



h = 9937,75....1og....3,99729 

 g = 32,2 log 1,50786 



2)2,48943 



17",57 1,24472 



2 



t = 35, 14 



On the supposition of a velocity of 1600 feet in a second, the 

 angle of projection being the same, we should have for the hori- 

 zontal range 79503 feet or 15 miles, for the greatest elevation 

 3,7 miles, and for the time of flight 3 minutes and 38 seconds. 

 So great, however, is the resistance of the air, that a cannon 

 ball, under the most favorable circumstances, is seldom known to 

 have a range exceeding 3 miles ; the path described is not strict- 

 ly a parabola or any known curve ; its vertex is not in the mid- 

 dle, but more remote from the point of projection than from the 

 other extremity ; and the path through which the body descends 

 is less curved than that through which it ascends. This resistance 

 increases faster than the velocity ; so that in the slower motions, 

 there is a nearer approach to the foregoing theory, than in those 

 which are more rapid, as is apparent to the eye in the spouting 

 of water, and more especially of mercury from the side of a ves- 

 sel. To treat of this resistance, and to estimate its effects, be- 

 longs to that branch of our subject which has for its object the 

 motion of fluids and that of bodies immersed in them. 



