OF SEVENTY-FIVE-MILE RANGE. 377 



The nvimber of the chord is denoted by r; the velocity of the 

 projectile is denoted by v; and its A'-component, by Vx. The in- 

 clination of the tangent at the beginning of the arc is dr. The drop 

 away from the tangent, due to gravity, which is of the second order 

 of smallness with respect to the length of the arc, is denoted by Ay. 

 The mean ordinate of a given element is indicated by y. The re- 

 sistance R is found from the graphical table (Fig. 2). The change 

 in the horizontal component of the velocity is Avx, the time taken 

 for the projectile to traverse one arc is A^. Dx represents the " set- 

 back " computed from the resistance, representing the amount by 

 which the projectile falls short of the assumed horizontal distance 

 owing to the resistance of the air. The height reached at the end 

 of the arc is 



y={A' — Dx) t3.nO — Ay, 



The most important thing in a ballistic calculation is the knowl- 

 edge of the ballistic, or resistance, function f{v). We have here 

 made use of the famous result of the greatest of recent ballisticians, 



1 Air Resistance Curve of StdCCL 



1 /c' K(v) - lo'-M 



3 Air Resisiance Curve of F. Hrupp 



Ve/ociiy in Meters pe.r Second 

 Fig. I. 



General Siacci, in his papers in the Rivista di Artiglieria e Genio 

 (1896), from which it appears from the results of thousands of 

 shots made by Bashforth in England, Mayevski in Russia (shots 



