THE EOYAL ARTILLEEY INSTITUTION. 
187 
on 
Whence we have, putting K — (1Q00) 3 , 
500 <yiooo \ 3 /loooYl 
» X l{ - Kir)) 
.(1) 
2nd. v ^ = 
as 
2fo> 3 ; 
-* = 25*, 
tf 3 
.*. (integrating ), i — i ^ or v ~ ^ when s = 0. 
Whence = (W/IOOO _ 1000^. 
w 
K 
V / 
.( 2 ) 
In order to obtain the relation between s and t } we must substitute 
for v in some one of the foregoing equations which will answer the 
ds 
dt 
purpose 
Take ~ - ], = 25 s, 
V V 
dt 1 0 , 
.-. t - 4 + 5s 3 . 
dt 
_ (i + 25s 
j *, 
■(*) 
Again, dividing (1) by (2), we have 
1 1 _ 25 
v + V~ s 
(4) 
(ft* dP 
Values of — t and — s —from equations (1) and (2)—-have been tabu- General 
w W 1 Tables 
lated for all velocities— VUl.toXl. 
from 500 to 1900 f.s. for elongated projectiles, 
„ 540 „ 1700 „ spherical „ 
d l 
$0 
The numbers against each velocity (read as in log. tables), represent 
multiplied by the space or time passed by the projectile whilst the 
velocity is reduced from the highest velocity given, to the one corres-* 
ponding to the number taken. 
The difference between any two numbers in the same table gives the 
result for the reduction of the higher velocity to the lower. 
An idea may be obtained of the amount of accuracy to be looked for 
by comparing some calculation by the General Tables with a trajectory 
carefully worked out. 
As an example, take the 16-pr. and the horizontal distances to the § 14* 
vertex—already calculated to be 2899*56 ft. 
The velocity is reduced from 1355 to 1016*46, 
s = % x (8952 - 1574) = x 2378 = 3030ft. 
& ■ 3-541* 
This result, being the length of the arc, is—as was to be expected— 1 
greater than the true one, but only by 1364 ft. 25 
Table 
VIII.' 
