UPON THE RESISTANCE OF THE AIR TO BODIES OF DIFFERENT FORMS.
Difficulties of the question.
The influence of the form of a body upon the resistance offered to it by a fluid, is a problem of the greatest difficulty; and although the most celebrated mathematicians have turned their attention to the subject, still, even for slow motions, they have only been able to frame strictly empirical formula, founded upon the data derived from practice; while with regard to the resistance at very high velocities, such as we have to deal with, very little light has hitherto been thrown upon the subject.
Compressed fluid.
When a body moves in the atmosphere, the particles which are set in motion by the projectile, act upon those in proximity to them, and these again upon others; and also from the elasticity of the fluid, it would be compressed before the body in a degree dependant upon the motion and form of the body. Moreover, the atmosphere itself partakes so much of the nature of an infinitely compressed fluid, as to constantly follow the body without loss of density when the motion is slow, but not when the velocity is great, so that the same law will not hold good for both. In an infinitely compressed fluid (that is, one which would fill up the space left behind the body instantaneously) the parts of the fluid which the body presses against in its motion would instantaneously communicate the pressure received by them throughout the whole mass, so that the density of the fluid would not undergo any change, either in front of the body or behind it, consequently the resistance to the body would be much less than in a fluid partially compressed like the atmosphere; and the form of the body would not have the same effect in diminishing or increasing the amount of resistance.
When a vacuum is formed behind the ball.
When the velocity of a body moving in the atmosphere is so great that a vacuum is formed behind it, the action of the fluid approaches to that of the discontinued fluid.