Previous to the adoption of this particular instrument, various analogous contrivances had been resorted to in order to produce the same effects. Of these, examples are afforded in the sails of the windmill, the vane of the smoke jack, and of more modern introduction, the _propellers_ designed by Mr. Taylor for the equipment of steam-boats, and which Mr. Green has availed himself of to shew the effect of atmospheric re-action in directing the course of the balloon. Now all these and similar expedients are merely modifications of the same principle, more or less perfect as they more or less resemble the perfect screw, but all falling far short of the efficacy of that instrument in its primitive character and construction. The reason of this deficiency can be readily accounted for. All the modifications alluded to, which have hitherto been applied to the purposes of locomotion, are adaptations of _plane_ surfaces. Now it is the character of _plane_ surfaces to present the same angle, and consequently to impinge upon the air with the same condition of obliquity throughout. But the _rate_ of revolution, and consequently of impact, varies according to the distance from the axis; being greatest at the outer edge, and gradually diminishing as it approaches the centre of rotation, where it may be supposed to be altogether evanescent. Now it is by the re-action of the air against _one_ side of the impinging plane, that the progressive motion is determined in the opposite direction, which re-action is proportioned to the _rate_ of impact, the angle remaining the same. If then we suppose a re-action corresponding to the _greatest rate_ of revolution, which is that due to the _outermost_ portion of the impinging surface (that most removed from the axis of rotation) we shall have a _progressive_ motion in the whole apparatus greater than the rate of impact of the _innermost_ or more central portions of the revolving plane; and accordingly the re-action will be thereabouts transferred from the back to the front of the propulsive apparatus, and tend to retard instead of advancing the progress of the machine to which it is attached. This inconvenience is felt and acknowledged by all those who have employed this principle to obtain a progressive motion, and accordingly a provision has been made against it in the _removal_ or _reduction_ of the central portion of the revolving vanes, with a view to let the air escape or pass through as the instrument advances; a provision which is certainly effectual to that end, but at the cost of the _surface_, which is the ultimate source of the required re-action. All this is avoided in the use of the perfect screw. There, the rate of rotation and the angle of impact mutually corresponding, may be said to play into each other's hands; the spiral becoming more extended as the impact becomes less forcible, that is as it approaches the centre, where both altogether vanish or disappear; thus obviating the possibility of any