Spheres receiving this motion are not likely to retain it, because the periphery of the spherical bullet is, in all cases, subjected to much more friction than the rest of the sphere; a change would therefore certainly be induced, the axis of the spinning motion being changed from one coincident to the line of flight to that of one vertical to the same. The two grooved rifle was an illustration of this; for in all cases the projections on the bullet induced a change, the ring of the bullet revolving parallel to the horizontal line, as I predicted in 1841. Enough has been said to point out the prejudicial action of any projections on projectiles, both as regards their accuracy and length of flight; perfect smoothness of surface being, in fact, absolutely necessary. Lengthened study and a series of experiments with bullets of a sphero-cylindrical shape having grooves and projections on their exterior identical with the grooving of the interior of the barrel, led me to consider the production of a bullet with a considerable cavity (equal, in fact, to two-thirds of its length) at the same time adopting as a standard one and a half diameters in the length of the bore of the gun; thus the thickness of the metal between the apex of the bullet and apex of the cavity was nearly one half of the diameter, as the following diagram will show. [Illustration] This enabled me to insure two important principles, on which depended the success of the whole invention. 1st. The centre of gravity was in the head of the projectile. 2nd. “_The force was communicated directly to the centre of gravity during the explosion._” This is a most important principle, which all writers presuming to give their version to the theory of the expansive system, have entirely overlooked. If the arrow could receive the propelling force in the head, its motion would be even, and free from “hobbling,” as Roger Ascham wishes it to be; but if, on the contrary, it is received at the opposite extremity, then there is a struggle between the head and the tail, as to which shall be first, and a “wobbling” motion is induced, enduring until an equilibrium of velocity is established. It is essential to all future progress in the science of projectiles, that this point should be remembered, and its importance duly estimated; and it is possible to apply this principle to projectiles of any weight. If this point be attended to, where is the difficulty in extending the length of our projectiles to that of arrows? thus increasing their range indefinitely. There is, in fact, no law to limit the length of expansive bullets: the only limit to their length now is the tendency of lead to squash; but alloys of lead and other metals may yet be beneficially used for projectiles, and that to an extent of which at present we can form no conception.