nce to the middle velocity will be 2 Ibs, 10 oz. avoir- 
lapois, whereas the theoretical resistance will be only 
ihe of thias 6 | ole OUP 
_ From these experiments, it is manifest, that the 
theory of the resistance of air in slow motions, as esta- 
_blished by Sir Isaac Newton and others, is quite in- 
correct when applied to the rapid motions of military 
_ projectiles. The parabolic theory of gunnery is, there- 
in every respect erroneous. The path of military 
iles is neither a bola, nor approaching to a 
parabola, unless when their velocities are very small ; 
_and instead of their path lying in the same place, it is 
‘in reality doubly incurvated, the ball being frequently 
driven to the right and left of its original direction by 
the action of some force acting obliquely to the pro- 
gressive motion of the body, occasioned no doubt by the 
whirling motion of the shot about its axis. 
In computing the paths of bodies moving rapidly 
“through air, Mr Robins lays down the following 
principles which he has deduced from numerous experi- 
‘ments. 
First, That the resistance varies as the squares of the 
velocities, when the velocities do not exceed 1100 feet 
_ per second ; and that a 12 pound shot, moving with a 
velocity of 25 feet per second, is half an ounce avoir- 
dupois. Hence we shall have its resistance for different 
velocities thus: 
Velocity. Resistance. 
‘25 feet persecond . . 5... . Jon 
160 uF ASF weiss. 6 . 8 02. 
UeSOGe omg indy iunge? phe Yi (agp, 
1000 . . . . * . . . . . 50 b. 
cigs Ree eB he riage Pg 
Second, That if the velocity be greater than 1100 
- ®r 1200* feet per second, then the resistance will be 
 threé times as great as it should have been by a compa- 
rison with the smaller velocities. Thus the 12 lb. shot 
above-mentioned, instead of being resisted by 144 Ibs. 
will now suffer triple that resistance, or 4534 Ibs. 
_ In proceeding to give an account of Mr Robins me- 
thod of com 
the terms which he émploys. 
© 91. The potential random of a projectile is the horizon- 
tal distance to which it would be thrown in a non-re- 
sisting medium, at an angle of 45°. If’ v be the initial 
velocity of the projectile in a second, in feet, then the 
potential random or p= ae ae atwess fe B die 
T 
_ the potential random is given. 
2. The potential range is the horizontal distance to 
which the projectile would be thrown at any angle dif- 
ferent from 45°. 
~ $. The «erual range is the horizontal distance to 
which the projectile is actually thrown. 
- In computing the effects of resistance, he assigns a cer- 
_tain quantity F, adapted to the resistance of the particu. 
lar projectile | This quantity F expressed in yards, in 
iron shells, or bullets, is d ~ 300 when d is the bullet’s 
diameter in inches. When the bullet has a different 
fie gravity from iron, then F must be increased or 
iminished in the ratio of the specific gravities. Mr 
Robins then gives the three following, propositions, 
which are suited to velocities below 1100 or 1200 feet 
GUNNERY. 
ting the resistance, we must first explain . 
581 
lication of the principle to great- 
’ er tte corallety'te Phe in oaede 
Prop, I. nag 
To determine the potential range, and consequently : 
the potential random and initial velocity of a given 
shell or bullet, when its actual range is given, and when 
its elevation does not exceed 8° or 10°. 
Enter the following Table with the quotient arisi 
from dividing theactual range by F, and the correspond 
ing number in the 2d column, multiplied by F, will 
be the potential range required ; and as the at 
different elevations are proportional to the sines of 
twice the angle of elevation, (see Chap. 1. p. 574. col. 
in arecond, The: 
er velocities will be sh 
Pesce 
2.) the range at 45°, the potertial random is also given. 
Then, as the velocity is chat which is due to a height 
equal to one half of the potential random, (See p. 
574.) the initial velocity is likewise given, us we 
t 
haveo= SAP . 
2 
wi] Be e Su Ps « 
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2s BR | € 3 £5 z 
£5| S25 |23| 6a5 |45| 623 
“| 0.01} 0.0100 1.55) 2.7890 || 3.3 | 13.8258 
0.02] 0.0201 | 1.6 | 29413 || 3.95] 14.4105 
0.04) 0.0405 1.65} 3.0994 || 3.4 | 15.0377 
0.06} 0.0612 1.7 8.2635 || 3.45) 15.6814 
0.08 | 0.0822 1.75) 3.4338 || 3.5 | 16.3517 
0.1 | 0.1034 1.8 $.6107 || $.55| 17.0497 
0.12} 0.1249 1.85] 3.7944 || 3.6 | 17.7768 
0.14) 0.1468 1.9 3.9851 | 365| 18.5341 
0.15] 0.1578 1.95} 4.1833 || 3.7 | 19.8229 
0.2 | 02140 | 2. | 4.3890 | 3.75} 20.1446 
0.25 | -0:2722 2.05| 4.6028 | 3.8 | 21.0006 
0.3 | 0.3824 21 4.8249 | 3.85] 21.8925 
0.35 | 0.3947 2.15| 5.0557 || 3.9 | 22.8218 
04°) 0.4591 22 5.2955 || 3.95) 23.7901 
0.45| 0.5258 2:25) 5.5446 | 4.0 | 24.7991 
0.5 | 0.5949 2.3 5.8036 |} 4.05] 25.8506 
0.55| 0.6664 235| 6.0728 | 4.1 | 26.9465 
0.6 | 0.7404 | 24 |. 6.3526 | 4,15] 28.0887 
0.65} 0.8170 | 2.45) 6.6435 } 4.2 | 29.2792 
0.7 | 0.8964 | 2.5 6.9460 | 4.25| 30.5202 
0.75| 09787 | 2.55) 7.2605 || 4.3 | 31.8138 
0.8 1.0638 2.6 7.5875 || 4.35) 33.1625 
0.85] 1.1521 | 2.65] 7.9276 | 4.4 | 34.5686 
0.9 | 1.2436 2.7 8.2813 | 4.45| 36.0346 
0.95} 1.8383 } 2.75] 8.6492 | 4.5 | 37.5632 
1.0 | 14366 | 2.8 9.0319 || 4.55) 39,1571 
1.05] 1.5984 | 2.85] 9.4800 || 4.6 | 40.8193 
11 1.6439 | 2.9 9.8442 || 4.65) 42.4527 
1.15] 1.7534 | 2.95) 10.2752 || 4.7 | 44.3605 
12 | 1.8669 | 3.0-| 10.7287 || 4.75) 46.2460 
1.25] 1.5845 | 3.05] 11.1904 | 48 | 48.2127 
18 | 2.1066 | 3.1 | 11.6761 | 4.85} 50.2641 
1.35] 2.2332 | 3.15} 12.1816 | 4.9 | 52.4040 
1.4 | 2.8646 3:2 | 12.7078 |} 4.95) 54.6363 
1.45] 2.5008 3.25] 18.2556 || 5.0 | 56.9653 
1.5 | 2.6422 
' * Mr Robins has noticed the remarkable fact, that the velocity at which the projectile begins to follow a new law of resistance, is 
“nearly the seme as the velocity of sound: It follows, however, from Dr Hutton’s experiments, that there is no such saltus from 
the law of the equares of the velocities ; but that the increase of 
the resistance above this law takes place gradually frem the slows 
€st motion, and never rises so high as to be three times that quantity. 
