~Only proved for slow motions.~ The above refers only to _slow_ motions, and the results given, from experiments with very small velocities; and it is to be expected, that with very rapid motions the form of the fore, as well as the hind part, of the projectile, will influence the amount of resistance in a much higher degree. ~Form of hind part.~ That form for the hind part will be best which has the greatest pressure upon it, when moving with a certain velocity. ~Best shape for fore and hind part.~ The ogivale form seems, from experiment, to fulfil the former condition. The best form for the _hind_ part, for _rapid_ motions, has not been determined; it may, however, be considered to be of much less importance than the shape of the fore part. ~Form determined by extent of range.~ Of course the best form can be determined by extent of range, but deductions from this will depend upon such a variety of circumstances, the effects of some of which must be entirely hypothetical, that the correctness of any formulæ obtained in this manner must be very uncertain. ~Form suggested by Sir I. Newton.~ Sir Isaac Newton, in his “Principia,” has given an indication of that form of body, which, in passing through a fluid, would experience less resistance than a solid body of equal magnitude of any other form. It is elongated. ~Axis of elongated bodies must be fixed.~ It is plain, however, that the minimum of resistance would not be obtained with a shot of an elongated form, unless the axis can be kept in the direction of the trajectory; as not only will the axis perpetually deviate from the true direction, but the projectile will turn over and rotate round its shorter axis, that is, if fired out of a smooth bore. ~Advantages of conical bullets.~ Conical bullets have an advantage, from their pointed end, which enables them to pass through the air with greater facility; and for the same reason they are better calculated to penetrate into any matter than spherical ones. ~Disadvantages of conical bullets.~ A _solid_ bullet cannot be pointed without sending backward the centre of gravity. The sharper the point, the more it is liable to injury, and if the apex of the cone does not lie true, in the axis of the projectile, then such an imperfection of figure is calculated to cause greater deflections in the flight than any injury which a round surface is likely to sustain. In penetrating into solid bodies, it is also important that the centre of gravity should be near its work. RESISTANCE OF THE AIR, AS AFFECTED BY THE WEIGHT OF PROJECTILES. ~Resistance overcome by weight.~ Bodies of similar volume and figure overcome the resistance of the air in proportion to their densities. The amount of the air’s resistance is in proportion to the magnitude of the surface. ~Contents of circles.~