The form of the air-propeller has passed through a long and varied development, starting with that of the marine propeller, which was found to be very inefficient in so loose a medium as air. On account of this lack of density in the air, it was found necessary to act on large masses of it at practically the same time to gain the thrust needed to propel the aeroplane swiftly, and this led to increasing the diameter of the propeller to secure action on a proportionally larger area of air. The principle involved is simply the geometric rule that the areas of circles are to each other as the squares of their radii. Thus the surface of air acted on by two propellers, one of 6 feet diameter and the other of 8 feet diameter, would be in the proportion of 9 to 16; and as the central part of a propeller has practically no thrust effect, the efficiency of the 8-foot propeller is nearly twice that of the 6-foot propeller--other factors being equal. But these other factors may be made to vary widely. For instance, the number of revolutions may be increased for the smaller propeller, thus engaging more air than the larger one at a lower speed; and, in practice, it is possible to run a small propeller at a speed that would not be safe for a large one. Another factor is the pitch of the propeller, which may be described as the distance the hub of the propeller would advance in one complete revolution if the blades moved in an unyielding medium, as a section of the thread of an ordinary bolt moves in its nut. In the yielding mass of the air the propeller advances only a part of its pitch, in some cases not more than half. The difference between the theoretical advance and the actual advance is called the “slip.” [Illustration: The Call Aviation Engine, of the opposed type; water-cooled. The cylinders are large and few in number. The 100 horse-power engine has but 4 cylinders, and weighs only 250 pounds. (The Gnome 100 horse-power engine has 14 cylinders.) This is an American engine, built at Girard, Kansas.] In practical work the number of blades which have been found to be most effective is two. More blades than two seem to so disturb the air that there is no hold for the propeller. In the case of slowly revolving propellers, as in most airship mechanisms, four-bladed propellers are used with good effect. But where the diameter of the propeller is about 8 feet, and the number of revolutions about 1,200 per minute, the two-bladed type is used almost exclusively.