THE ROYAL ARTILLERY INSTITUTION. 
371 
x d 2 -~-w = *00001619. For values of v from 1700 to 1675 f.s. we have 
1000 = 1000 20 000 6 / m = . 588 235 + -001 591», and ifV, v,, vv., &o., 
denote the values of v corresponding to n — 1, 2, 3, 4, &c., respec¬ 
tively, we have 
i^ = -588 235 +*001 591 = -589 826, or ^ = 1695*4. 
1000 
•588 235 + -003 182 = *591 417, or v 2 = 1690*8. 
1000 
^3 
1000 
= •588 235 + *005 773 = *593 008, or ^ = 1686-3. 
^4 
1000 
= •588 235 + *006 364 = *594 599, or v 4 = 1681*8. 
•588 235 + -007 955 = *596 190, or ^ = 1677*3. 
Here, as v 6 will he less than 1675, we must change the co-efficient 
5', and treat v 5 as the initial velocity, thus 
1000 -596 190 + *001 619 = *597 809, or v 6 = 1672-8. 
V 6 
1000 
&c. = &c. See column headed v in Table 6. 
■596 190 + *003 238 = *599 428, or ^ = 1668*3. 
It must be remarked the value of V for a given velocity varies as 
d 2 -~w, consequently when a table of values of v l9 v 2 , v 3 , &c., has 
been calculated for a given value of d 2 -^-w, that table serves equally 
well for all other shot of similar form which have the same value of 
d 2 ~w. 
If the law of resistance be supposed to be the cubic, and if the 
time over a given distance be measured by a chronograph, then the 
velocity at the middle point of that distance in feet per second will 
be found exactly by dividing the space in feet by the time in seconds. 
Calculation of the Times of Flight of Shot.—In the following tables 
the numbers in the column t denote the time occupied by the shot 
in passing over the distance standing opposite in the column of dis¬ 
tances, the shot being supposed to have started with the velocity 
opposite the distance zero. They have been calculated by the help 
of the formula (2), where s=100w feet. This gives 
t= ( 1C ^° + 100 0006'ra) A 
where the values of V must be varied to agree with the correspond¬ 
ing velocities. Let n — 4 , v = 1700 f.s., t = t v then, as we have seen, 
10005 ' = -00000796 ; t A = (;588 235 + *000 796 ) x *4 = 0"*236 : see 
column t , Table 6, opposite distance 400 feet. 
