The static principle of the torsion wing is a familiar one in elementary mechanics. It is this: a torque of given magnitude and direction has the same effect on a rigid body whatever its point of application. The longitudinal torque, or moment, may therefore be exerted by the wings, by suitable rudders, by forward planes, by any auxiliary planes, or fins, however placed or moved for the purpose. Accordingly there seems to be an unlimited variety of concrete patentable devices available to the inventor for securing impactual torque about the longitudinal axis, or either of the other two axes. But in planning such devices it is well to remember that the moment of a couple increases with its arm, so that in a wide aëroplane the wing tips may best furnish the torque; while in a high short-winged machine, vertical planes, fins, or rudders may give the desired longitudinal moment. Obviously such vertical guiding or controlling surfaces may be so placed as to tilt the machine toward the center of curvature of its path, at the same time opposing the centrifugal force, and exerting a torque about the vertical axis tending to steer the flyer along its path.[38] The principle of projectile stability is another consideration of some importance in aviation, or more generally in all submerged navigation, whether of air or water. A submerged body has projectile stability if its nose tends always to forerun its centroid, and follow a steady course. A dart is a good example; a fish, a torpedo. Thus if a torpedo-shaped homogeneous solid be hurled in any manner through a fluid, obliquely or even tail foremost, it promptly turns its nose to the front and proceeds steadily along an even course; but if the body has not true dynamical balance, it may oscillate or gyrate, or flit about in the most erratic manner. Projectile stability in a flyer, as in an arrow, may be attained by playing the centroid in or near the line of forward resistance, and well ahead of the side resistance. The reasons for this are manifest. If, however, this arrangement be neglected, a special damping, or controlling, device is required to preserve headlong and steady motion. In particular, the objections to placing the centroid too low were emphasized in the above quoted paper as follows: “I have mentioned the advantage of placing the center of mass below the center of surface; this has also its objections. While the stability against inversion is increased, the stability against rocking is sacrificed. The aëroplane so constructed may not easily overturn; but it will sway to and fro with a pendular motion. This, when lateral, is very objectionable, when fore and aft it is fatal to uniform progress, as we shall see in studying the longitudinal stability of flying machines. We shall then see that the center of mass cannot be lowered with impunity.”