238 Wisconsin Academy of Sciences^ 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 gnn, 

 and in making calculations reliable, was the axial rotation, which 

 was attained by grooving the interior 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 beiog 

 retarded on that side next the tangent barrel. The last touch 

 imparted the final rotation, or that which continaed 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 b}' the 

 touch on the right side. But while the left side of the ball is 

 moving forward at a much greater velocity 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 



