PRINCIPLES OF GUNNERY. 
247 
The units employed are distance in feet, time in seconds, and velocity 
in feet seconds. 
In Tables I. and II. the left hand vertical column (v) denotes velo- Expiana- 
cities from 500 f.s. to 1700 f.s., at intervals of 10 f.s., and by means offfif M 
the top horizontal column these velocities are subdivided into intervals aud n » 
of 1 f.s. 
The figures in the vertical columns under 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 
(Table I.), express the distance in feet corresponding to the velocities, 
and may be denoted by the abbreviation S v . 
Similarly, the figures in the vertical columns under 0, 1, 2, 3, 4, 5, 6, 
7, 8, 9 (Table II.), express the time in seconds corresponding to the 
velocities, and may be denoted by the abbreviation T v . 
For example: in Table I., suppose it required to find the distance 
corresponding to the velocity 601 f.s.— i.e., S v = S m = 14384*8 ft.; or, 
conversely, if S v — 14384*8 ft., v — 601 f.s. 
Also, in Table IT., suppose it required to find the time corresponding 
to the velocity 705 f.s.— i.e., T v = T^=. 11*0732 secs. ; or, conversely, 
if T v = 11*0732 secs., v = 705 f.s. 
Table I. is obtained by calculating the integral in the left-hand Equation 
member of the equation Sting 1 ’ 
A 2 
to 
-/ 
(1000) 8 <fo 
Kip ' 
distance 
and velo¬ 
city. 
and when the integral is taken between the limits of velocity v and V 3 
it may be expressed in the notation adopted in Table I. thus : 
d 3 f r (lOOOfdv 
to J v ~ Kv » 
(I.) 
In the same way, Table II. is obtained by calculating the integral Equation 
in the right-hand member of the equation 
df 
w 
/Tiooo) 3 ^ 
J Kv 3 ; 
iuquat 
(II.), con¬ 
necting 
time and 
velocity. 
and when the integral is taken between the limits of velocity v and V 3 
it may be expressed in the notation adopted in Table II. thus: 
df = f v (lOOO) 3 ^ 
to J v Kv z 
= T V - Tv. 
(II.) 
In order to make use of Tables I. and II. in the solution of problems 
in practical gunnery, it must be remembered that they apply rigidly 
only to elongated projectiles with ogival-shaped heads, and under 
conditions of atmosphere mentioned in the note on the Table of 
Values of A, and that 
V = the velocity of the projectile at the beginning of the distance or 
time under consideration, 
v = the velocity at the end of the distance or time under consideration, 
S = the distance or range in feet , 
T= the time in seconds , 
d = diameter of projectile in inches , 
w = weight of projectile in lbs. 
