59] CALCULATING THE TRAJECTORIES OF SHOT. 485 



the theory. The most extensive and accurate series of such experiments 

 which we have are those made by Mr Bashtbrth by means of his chrono- 

 graph, which measures with the greatest precision the times taken by the 

 same projectile in passing over several successive arcs in the course of its 

 flight. In a summary of his results for ogival-headed shot, struck with a 

 radius of l diameters, given in Nature (Vol. xxxm. pp. 605, 606), Mr 

 Bashforth concludes that the resistance may be approximately represented 

 by supposing it to vary, as one power of the velocity when that velocity 

 lies between certain limits, as another power when the velocity lies between 

 certain other limits, and so on. 



Thus, if v denote the velocity expressed in feet per second, 



d the diameter of the shot in inches, 

 and w its weight in pounds, 



d- 

 and if = c, 



w 



then, when v lies between 430 f.s. and 850 f.s., 



the resistance is nearly = 6 l'3c (- 



when v lies between 850 f.s. and 1040 f.s., 



/ v 

 the resistance is nearly = 74'4c (-r-r ; 



when v lies between 1040 f.s. and 1100 f.s., 



the resistance is nearly = 79'2c 

 when v lies between 1100 f.s. and 1300 f.s., 



/ v V 



the resistance is nearly = 108'8c( 1 ; 



and lastly, when v lies between 1300 f.s. and 2700 f.s., 

 the resistance is nearly = 141'5c 



Hence the resistance varies nearly as the square of the velocity both when 

 the velocity is less than 850 f.s., and when it is greater than 1300 f.s., 

 but the coefficient increases from 61'3 in the former case, to 141'5 in the 



