AIR TO THE MOTION OF ELONGATED PROJECTILES. 
437 
No. of 
round. 
Weight 
of shot. 
Value of 
bP. 
Difference from 
mean. 
15 
lbs. 
21-92 
•00124 
+•00006 
21 
21-89 
•00121 
+ -00003 
23 
21-94 
•00118 
•00000 
25 
21-97 
•00114 
-•00004 
27 
21-97 
•00118 
•00000 
29 
21-97 
•00119 
+•00001 
31 
21-91 
•00116 
- -00002 
33 
21-94 
•00118 
•00000 
Means 
21-94 
•00118 
•00002 
Since the second differences of 0 , t 2 ,t 3 t l0 are nearly constant in the preceding 
experiments, we are led to the equation 
t=as-\-bs 2 , connecting space and time. 
This shows that if v be the velocity of the shot at time t, and / the retarding force, then 
_ds 1 
V dt a + 2bs i 
and if v=V when s=0, we have V= - ; 
5 a ’ 
1 
and 
/=g=-25»*. 
The values of bl 2 for each experiment were obtained as follows : — 
Since t =as-\-bs 2 
If s—l, then t 2 =al+bl 2 , 
s=2l, „ t 3 =2al+m 2 
s—n—ll, „ t n =n— lal+n— l 2 bl 2 , ; 
or 
\=al+ IP, j 
|=<rf+2iP, I 
=.al-\-n— Ibl 2 . 
Finding, then, the numerical values of 
for each experiment, and taking the difference of two of these quantities, we find 
t„ 
n— 1 
—~=n—Sbl 2 , 
