Major J, G. Barnard on Elongated Projectiles. 191 
air will be identically the same, whether it possesses or not 
rotary motion: for in either case, the surface, considered as a 
whole, advances in identically the same manner—the displace- 
ment of atmospheric particles is the same, and the resulting re- 
sistance, the same. ® 
t the rotation be supposed about a horizontal axis, per- 
pendicular to the line of flight, and in the direction AD. The 
velocity of the individual points, m,n—or if you choose—ele- 
surface, mn, will be the resultant of the rotary and 
translative velocities, and the little surface mn, instead of moving 
(at the instant) in the direction 0, will move in an oblique direc- 
tion np. But the rotary component of velocity lies in the plane 
of this elementary surface, and has, (as in the case of the /ateral 
Velocity AC of the plane, Fig. 1) no agency whatever in dis- 
placing the air, or in affecting the intensity or character of its 
act, 
ese considerations will, perhaps, be rendered more clear by 
reflecting that the resistance of a fluid, is due and due only to the 
t of tts particles—that when the centre of the sphere 
has advanced from C to B, the anterior surface has advanced 
fom FAD to F’ A! D’, and displaced the air-in identically the 
“ame Manner, whether the sphere revolves or not. 
These considerations are so obvious that it seems superfluous 
to insist on them; yet few of the writers on this subject have 
exhibited a clear understanding of them; or rather it may 
‘tid that they exhibit the reverse. 
Pica rejecting friction entirely, or rather considering its 
wah inappreciable, bases his reasoning on the higher velocity 
the which the points of the surface on the side A F wmpinge on 
- 1, Over that belonging to points on the side AD; an idea, 
tile shown, entirely fallacious, Capt, Neumann (Prussian ar- 
Riad in a theory as pretentious as it is unmeaning (Delobel’s 
the de Technologie Militaire, vol. i.), carries this absurdity to 
ore of considering each elementary surface mn, sepa- 
a With its combined motion of translation and rotation, and, 
ete to each the ordinary expression for resistance of 
pone rice impinging obliquely upon an elastic medium, in- 
total through each half of the anterior surface, to obtain the 
action on each side. : 
eb are the conventional expressions for the resistance of 
but th oblique plane surfaces peer most inaccurate in practice, 
form ey lose all a plicability when they cease to be tso/ated, an 
lem, a of another larger surface (not plane); and this prob- 
~'y Of which the knot is so expertly cut by Capt. Neumann, who 
and oth to apply his results to the criticism or test of Magnus’ 
€r theories, is the very “pidce de résistance” which has 
the analysis of d'Alembert, Poisson and Poncelet—per- 
