Professor G. H. Bryan’s mathematical researches are indeed epoch-making, and their study by the aëronautical engineer should be prolific of practical result. He does much to elucidate points of the problem of stability that before had been imperfectly grasped. For instance, take the case of his remarks as to distinction between equilibrium and stability. We say that the motion of a flying machine is steady when the resultant velocity is constant in direction and magnitude, and when the angle of the machine to the horizontal is constant. If this motion is slightly disturbed the machine may either return after a time to the original motion, or it may take up a new and altogether different mode of motion. In the first case, the steady motion is said to be stable, and in the second unstable. It is evidently necessary for steady motion of any kind that there should be equilibrium--_i.e._, that there should be no forces acting on the machine (apart from accidental disturbances) which tend to vary the motion, and hence it follows that the number of modes of steady motion of which a machine is capable is, in general, limited, and that when an unstable, steady motion is disturbed, the new mode of motion taken up is entirely different from the old. It is necessary to distinguish carefully between equilibrium and stability, as the two are very often confused together. Equilibrium is necessary to secure the existence of a mode of steady motion, but is not sufficient to ensure the stability of the motion. The question of the stability of a rigid body moving under the action of any forces has been solved by Routh. In order to apply his results to the stability of flying machines, it is necessary to know the moment of inertia of the machine about its centre of gravity, the resistance of the air on the supporting surfaces as a function of the velocity and angle of incidence, and also the point of application of this force--_i.e._, the centre of pressure for different angles of incidence. If these are known for the surfaces constituting any machine, then the problem of its stability for small oscillations can be completely solved. Unfortunately, our knowledge of these points is very unsatisfactory. Several valuable series of experiments have been made to determine the resistance on planes, but there is still some doubt as to the position of the centre of pressure at small angles of incidence, especially for oblong planes, and very little indeed is known as to the movement of the centre of pressure on concave surfaces. Until experiments are made on this point it will be impossible to solve the problem of stability for machines supported on concave surfaces. The subject of the stability of aëroplanes falls under two heads:-- 1. Automatic stability. 2. Inherent stability.