280 OUTLINES OF NATURAL PHILOSOPHY. 



is stretched out a plain of considerable extent ; and 

 if the same piece of artillery be carried successively 

 to these stations, and fired at the same angle, and 

 in the same circumstances in all respects, and the 

 points marked where the shot in all these cases strikes 

 the plain, it is evident, that all these are points in 

 the curve described by the same shot. 



The same might be done still more easily, by remo- 

 ving the gun from one distance to another in the 

 plain, and firing against the side of the hill. If the 

 points from which the shot were fired, and those 

 which they struck, were all marked on an accurate 

 profile of the ground, they would enable us to de- 

 termine as many points in the path of the pro- 

 jectile as there were experiments made. It is 

 unnecessary to observe, that at each station a 

 great number of shot might be fired at different 

 elevations, so that many curves might be determi- 

 ned from the same set of experiments ; and that at 

 each particular elevation many shots ought to be fired, 

 and a mean taken among the points where the balls 

 struck. 



376. The ranges of the same ball, with the same 

 elevation, but different charges, are nearly as the 

 square roots of the initial velocities ; and the times 

 of flight are nearly as the ranges. 



HUTTON^S 



