444 
ME. C. W. MEERIEIELD ON THE LAW OE THE 
gives m= 2 cos ^ Vi being the initial velocity, s the actual range, and 0 the inclina- 
tion. The time t was that of the range in vacuo due to the supposed initial velocity 
and given elevation. It was assumed, first , that the vacuum time might be taken to 
represent the real time, and, second , that the horizontal resistance might be taken to 
vary as the cube of the horizontal velocity. The result is given in the following Table. 
Calculation of Resistance, supposed to vary as the Cube of the Velocity. 
Initial velocity taken as 1358 feet per second. 
Angle of 
elevation. 
Actual 
range, 
in feet. 
Eange 
in vacuo, 
in feet. 
Reduction 
of range by 
resistance, 
in feet. 
Time 
of flight 
in vacuo, 
in seconds. 
Coefficient 
of resist- 
ance pro- 
portionate 
to 
Departure 
from mean 
value. 
Pinal 
velocity, 
in feet per 
second. 
Velocity 
lost in each 
100 yards, 
in feet per 
second. 
Actual 
range, 
in yards. 
9 30 
300 
316-62 
16-62 
0-23316 
16-620 
-0-018 
1222-4 
135-6 
100 
20 
600 
666-57 
66-57 
0-49085 
16-643 
+ 0-005 
1111-5 
110-9 
200 
31 30 
900 
| 1049-81 
149-81 
0-77309 
16-647 
+ 0-009 
1018-8 
92-7. 
300 
44 
1200 
1466-32 
266-32 
1-07985 
16-647 
+ 0-009 
940-6 
78-2 
400 
57 30 
1500 
1916-02 
416-02 
1-41115 
16-643 
+ 0-005 
873-4 
67-2 
500 
1 12 
1800 
2399-00 
599-00 
1-76695 
16-654 
+ 0-016 
- 815-2 
58-2 
600 
1 27 30 
2100 
2915-04 
815-04 
2-14732 
16-644 
+ 0-006 ! 
764-3 
50-9 
700 
1 44 
2400 
3464-11 
1064-11 1 
2-55206 
16-634 
-0-004 
719-4 
44-9 
800 
2 1 30 
2700 
4046-12 
1346-12 
2-98133 
16-639 
+ 0-001 
679*4 
40-0 
900 
2 20 
3000 
! 4660-92 
1660-92 
3-43504 
16-633 
-0-005 
643-7 
35-7 
1000 
2 39 30 
3300 
5308-37 ! 
2008-37 
3-91317 
l6-6l6 
— 0-022 
611-5 
32-2 
1100 
These two columns 
Mean ...... 
16-638 
contain the data. 
Resulting Coefficient of resistance =0-00000 02723. 
The coefficient of resistance, so determined for each range, has no sensible variation, 
thus proving that the facts are exactly met by the law that the resistance varies accord- 
ing to the cube of the velocity, with a coefficient of resistance, for this particular bullet, 
of 0-00000 02723. This is subject to the assumptions previously mentioned. It is 
further either involved or assumed that the bullet presents an invariable aspect in a 
horizontal direction. 
These assumptions are sufficiently right for such a very low trajectory as is given by 
2° 40' for 1100 yards, giving a vacuum height of 64 feet. I got out a graphical solution 
of the resisted time of a bullet thrown with a velocity of 64 feet per second (which cor- 
responds to that height) and with a coefficient of 0-000001, and I found the variation in 
time too small to detect in fine curves carefully drawn with ordinates of nearly 2 feet 
in length. I consider this as amounting to proof that the difference between real and 
vacuum time is insignificant in this problem. The second assumption, as to the hori- 
zontal resistance varying as the cube of the horizontal velocity, is justified by the low 
trajectory. On the question of aspect, my present knowledge does not authorize me 
to form any decided opinion. 
