The State of Wisconsin Collection

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Transactions of the Wisconsin Academy of Sciences, Arts and Letters
volume IV (1876-1877)

McMurphy, J. G.
Rotation as a factor of motion,   pp. [235]-240 PDF (1.5 MB)

Page 238

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238     Wisconsin Academy of &iences, Arts, and Letters.
one nor the other, but upon a new axis intermediate between the
vertical and horizontal axes, pointed out by the resultant of the
parallelogram of angular forces. This is the principle illustrated
by the Gyroscope. The ball will describe a curve upon the plane
in the same way that a truck rolled upon the ground when the
axes cease to be level, begins to curve its path; of course the two
cases are quite different, because the curve made by a ball is much
less marked than that made by a truck or wheel.
There is something of a similar nature seen when a ball is pro-
jected from a gun or cast from the hand.  Since the middle of
the sixteenth century, it has been known that the path of a pro-
jectile is a parabola, if no account is taken of the resistance of the
air. Templehoff was the first to take into consideration this ele-
ment in calculating for projectiles. The resistance of the air in-
creases with the square of the velocity until the velocity exceeds
1,300 feet per second, when the resistance is much greater.
In experimenting with smooth-bored guns, it was found that
rotation had much to do with the motion of the projectile from
the muzzle. The only rotation which aided in aiming the gin,
and in making calculations reliable, was the axial rotation, which
was attained by grooving the-in~terior of the barrel.
In the practice of gunnery with a smooth-bored gun there was
allowed enough space around the ball for free and easy motion. It
was called windage. This windage allowed the ball to ballot
slightly from side to side as it passed through the barrel. At
each point of balloting the ball received a rotary motion by being
retarded on that side next the tangent barrel. The last touch
imparted the final rotation, or that which -continued through the
space traversed by the ball. If the last ballot was upon the right
side of the barrel the ball received a right hand rotation. It also
received an impulse toward the left of the mark aimed at by the
touch on the right side. But while the left side of the ball is
moving forward at a much greater velocitv than the center on ac-
count of the right hand rotation, the right side is moving much
slower than the center on account of the same rotation. The left
side, therefore, encounters a greater resistance than the right side.
The air in front and to the left is compressed, and accumulated

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