Major J. G. Barnard on Elongated Projectiles. 195 
and from this results the conical motion of the axis to the right, 
if the rotation is to the right—to the /eft in the contrary case.* 
Before attempting to apply the foregoing to the real case, it 
will help us to consider a more simple one. 
Suppose the rotating projectile with its axis inclined to its 
trajectory to be propelled through the air, and that the centre of 
inertia is confined to a rectilinear path (as if it slid along an ex- 
pues wire, AB, for example), and that the force of gravity 
oes not act. 
6: 
PF. canes Senne 
- Pn a = > =. 
oy Ba ome - 
- ~ - 
=. a besied a 
= 
= ral Na _ 
™ “" ~. - 
RR Re Rig whe tw we oor 
ig PT aad Pe annenn nee” 
Sf ss 
4 
a] 
oo 
ct 
= 
(2) 
mt 
or 
mo 
oO 
Q 
is?) 
=) 
at 
y. 
ia) 
2} 
Lear) 
~~ 
p 
°) 
La | 
et, 
a 
Let now all the circumstances be as above except the confine- 
ment of the centre of inertia. 
eaeerete teen nee, 
s - on 
pa Rn a, Rg ES ls ee ne, ayia ai lebron. . 
¢ Ss 
The resistance R, acting obliquely to the axis of figure, will 
(as in the familiar case of t ili on the wind) 
give the projectile a component of motion in the direction of its 
s, and the centre of inertia cannot remain on its rectilineal 
Ps ty AB. But, owing to the conical motion of that axis 
at a line parallel to the resistance R, (a direction, itself, 
lmece changing) the result will be that the Project itself will 
mibe a helix, sss, about the line of original direction A B.t 
direct} ye results have been exhibited experimentally by Prof. Magnus; they flow 
} ~ Peta my analysis made without experiment of any kind. : 
Vehiew period of these conical, or rather helical revolutions, could be computed if 
exact intensity of the force R; the distance Om, (or y) from the centre 
8. of inertia, at which it cuts the axis of figure; the 
value &, of its radius of gyration about its axis of 
figure ; and the velocity, 2, of rotation. 
The peri deduced from my treatise on the 
in seconds thus— 
Ia why : 
_— rae total resistance of the air +mass of the projectile. The value 
jn ordinary musket ball would be about 100. Assurhing it at 30 for the 
i ball with more mass and J istance—and assuming 7 but +5 inch, put- 
+ 2nX 150, and k*=°15 inch, we should get T=}’’ or three-fourths of a second. 
t 
