THE SMALL-ARMS OP EUROPE. 
3 
x a = oo or when m — 0; the quantity x a is thus small in proportion as 
the effect of the air resistance is great, and consequently as m itself is 
proportionally great. 
It is conceivable also that, given the equation of the trajectory, the 
parametres x a and m are obtainable by means of more or less long and 
complicated calculations with the practical data got from two series ot 
rounds corresponding to two different distances, by a method similar 
to that indicated in Graphic Ballistics .* 
Take, for example, the Werndl, converted for the use of the 
strengthened cartridge of 1877. The angles of elevation for 600 and 
1600 paces (500 and 1333 yds.) are respectively 
0! = 1° V 58", and 0 2 = 4° 37' 58". 
The mean values are then calculated to be 
x a — 12ol w , and m = 1*46 ; 
quantities which may be taken as constant when the range does not 
exceed 1200 paces. 1 or greater distances x a and m must be recalculated 
with suitably selected experimental data. 
This settled, the tables were calculated by means of the following 
formulas :— 
(a) Ordinates of the trajectory: 
y = *tan»- ( ^ X .(2) 
r 2F 2 cos 2 0 \£ a — x) 
(b) Angle of elevation for range X: 
,in2o = ^(^ J.(3) 
( c ) Angle of drop: 
tan 0 = — tan 0 Xa Xh “hAl —...(4) 
x a X 
(d) Remaining velocity: 
» = r ^4 ( x " ~~X .(5) 
sin 0 \ x a ) 
(f) Dangerous zone , to catch the height (h) of a man—viz. 6 ft.: 
X /X 2 hX 
* = ¥ “ V.T . (6) 
* See “Revue d’Artillerie,” XI., Feb. 1878* 
