Deducing from For. 2 we have a simpler one
E=0.000002222 mV2

in which m is the weight in GRAINS.

For. 3

E=0.000002222×150x2700X2700=2430 f. lbs.

Similarly, E may be computed for any velocity. (One pound avoirdupois=7000 grains)

Problem 3.

Given V, (2700), v (2465), C (.389)

To determine T.

T=CT(v)-T(V)}

For. 4

in which T(v) and T(V) are TIME functions found in Table 1 in the vertical column under T (u), opposite respectively the v and V in column under (u).

Similarly, T may be computed for all ranges, v having first been computed by formula. 1.

*The difference between the time functions of 2470 and 2460 is 0.013, which difference represents an increment of velocity of 10 feet. The difference between 2470 and 2465, the v, is 5 feet; hence the time function difference is 5/10×0.013=0.006, which is to be ADDED to the time function of 2470 velocity.

Problem 4.

Given T (.116)

To determine H, in FEET.

H=(2T)2

H=(2X.116)2=0.054 feet,

For. 5

or, simply stated, H, in feet, equals the square of twice the time, in seconds.

Similarly, H for all ranges for which T has already been computed, may be computed.

Problem 4A.

Given H, generally found in the ballistics given in catalogs. (0.053824) feet.

To determine T.

T=/√H

For. 5A

Hence, the time of flight (in seconds) equals 1⁄2 the square root of H (in feet).

T=1⁄2 √ (0.053824)=0.116 (sec.)

The preceding formulae, illustrated with problems, are all the mathematics needed in computing the ballistics at sea level for any projectile.

Should the rifleman wish to determine the horizontal distance to the foot of the perpendicular, H, the following two formulae are given.

of H.

To determine x, the distance from muzzle to foot

x=CS(v)—S(V) }

S(v°) = 3036.5

For. 7

S(V)

C

X

=2644.8

391.7

.389

== 152.3 ft. 50.8 yards.

Similarly, x for any range may be calculated.

A

CHAPTER III.

Graphs and Curves.

GRAPH is a line symbolizing the relation of

a function and its argument. They are plotted and drawn to show clearly and instantly this relation, also that a comparison of similar elements may be as readily made, that a visible check may be made on calculations or plottings, that any variations not accounted for may develop new facts, etc. For the purpose in this volume 10x10 cross section paper, inexpensive, is used.

To Plot a Velocity Curve.

Lay off on AB, Fig. 2, equal spaces representing, say 500 ft., 1000 ft., 1500 ft., etc., to the desired range. Lay off on the vertical line AC equal spaces representing, say 500 f. s., 1000 f. s., etc., to the muzzle velocity of the projectile.

Compute the remaining velocity, v, formula 1, for 500 ft., 1000 ft., 1500 ft., etc., up to the desired range. On lines perpendicular to AB at these division points lay off the value of the remaining velocity for that distance. Beginning with the point in AC representing the muzzle velocity, using a No. 4, Keuffel and Esser curve, also inexpensive, draw a curve through all the points representing the remaining velocity. Fig. 2.

If the velocity of several projectiles are plotted upon the same sheet, they may be more advan.