186 
MINUTES OF PROCEEDINGS OF 
use to the reader, but they must not be relied upon as being absolutely 
correct; correct values could only be obtained by actual experiments:— 
V. 
| 
log- 
9 
800 
1-921 
•2835 
810 
1-926 
•2847 
820 
1-932 
•2860 
830 
1-938 
•2873 
840 
1-944 
•2887 
850 
1-951 
•2903 
860 
1-959 
•2920 
870 
1-968 
•2940 
880 
1-978 
•2962 
890 
1-989 
•2986 
15. Derivation op Elongated Projectiles. 
(Articles 73, 74.) 
These articles are at the end of the chapter on the motion of a pro¬ 
jectile in a resisting medium. Attention is therefore drawn to them, 
lest they should be overlooked. 
Chap. v. 16. Rectilinear Motion in a Resisting Medium. 
By considering the motion of a projectile to take place in a straight 
line, very close approximations can be obtained for the time of flight 
and horizontal range in terms of the velocities. The error is repre¬ 
sented by the difference between the lengths of the arc and chord of 
the trajectory. 
We have the differential equations 
„ dh dv dv 
w J -dTr m dt’ mv ds- 
Also / = — 2 bv*. 
We want to obtain relations between t and v, s and v, s and t; and 
must choose our differential equations accordingly. 
1st. ~=- Z6v s ; = Zbdt, 
dt v 6 
••• integrating), _ _1_ _ 2 U-* 
for when t = 0, v = V (the initial velocity). 
* Misprint in Bashforth, p. 67, 6th line from bottom C = §F 2 ” should be “ C = -h_. 
