Now, it is almost impossible to project a spherical ball from a smooth-bore gun without giving it a rotation the direction of which it is difficult to predict; hence the inaccuracy of that kind of fire. Spherical balls are not homogeneous, as a rule. If the center of figure and center of inertia do not coincide, the ball will rotate when fired—unless so placed in the gun that these points are both in the axis of the piece. Taking advantage of these principles, Major Wade, of our army, years ago managed to make an eccentric shell curve so as to fall fifty yards to the right or left of the plane of fire. The “curving” due to rotation is in the direction in which the _front of the ball rotates_. Perhaps the explanation accepted by artillerists can be best understood by the aid of a figure. Let the ball be moving in the direction AE and be rotating at the same time in the direction BCD about an axis vertical to the plane of the paper. AE will be the projection of the plane of fire—which plane will divide the ball into two hemispheres. Now, the half of the ball on the side B will be moving forward by the rotation, or in the same direction as the center, while the other half D will be moving backward, or in opposition to the motion of the center. The side B will have a greater velocity than the side D. The resistance of the air upon any surface moving through it varies with the amount and form of the surface. In these regards, the two sides are alike, but the resistance also varies with the velocity of the moving surface, increasing with some power greater than the square, and in this regard the two sides are different. The side B will experience a greater resistance than the side D, or, what is the same thing, the resultant of all the pressures on all points of the hemisphere. B is greater than the corresponding resultant on D, and the ball will yield toward the side D, describing a curve C F. [Illustration] The deviation of oblong rifle projectiles which rotate about their axes of figure is called “drift.” This is a very interesting phenomenon, but it should not be confounded with the “curving” or deviation by rotation of spherical projectiles, as it is to be explained very differently. Yours truly, W. R. QUINAN. The next letter is sent from Chicago, and the writer’s theory is comparatively a simple one: CHICAGO, 1886. DEAR ST. NICHOLAS: I have been much interested in the letters on the subject of curve-pitching, and since I have taken you for eleven years, I hope you will publish my theory, that it may be picked to pieces, and I may be set right on the subject. My theory is as follows: [Illustration]