hydraulic propeller is very low, and we hope to make the reason why it is low intelligible to readers who are ignorant of mathematics. Those who are not ignorant of them will find no difficulty in applying them to what we have to say, and arriving at similar conclusions in a different way. Professor Greenhill has advanced in our pages a new theory of the screw propeller. As the series of papers in which he puts forward his theory is not complete, we shall not in any way criticise it; but we must point out that the view he takes is not that taken by other writers and reasoners on the subject, and in any case it will not apply to hydraulic propulsion. For these reasons we shall adhere in what we are about to advance to the propositions laid down by Professor Rankine, as the exponent of the hitherto received theory of the whole subject. When a screw or paddle wheel is put in motion, a body of water is driven astern and the ship is driven ahead. Water, from its excessive mobility, is incapable of giving any resistance to the screw or paddle save that due to its inertia. If, for example, we conceive of the existence of a sea without any inertia, then we can readily understand that the water composing such a sea would offer no resistance to being pushed astern by paddle or screw. When a gun is fired, the weapon moves in one direction--this is called its recoil--while the shot moves in another direction. The same principal--_pace_ Professor Greenhill--operates to cause the movement of a ship. The water is driven in one direction, the ship in another. Now, Professor Rankine has laid down the proposition that, other things being equal, that propeller must be most efficient which sends the largest quantity of water astern at the slowest speed. This is a very important proposition, and it should be fully grasped and understood in all its bearings. The reason why of it is very simple. Returning for a moment to our gun, we see that a certain amount of work is done on it in causing it to recoil; but the whole of the work done by the powder is, other things being equal, a constant quantity. The sum of the work done on the shot and on the gun in causing their motions is equal to the energy expended by the powder, consequently the more work we do on the gun, the less is available for the shot. It can be shown that, if the gun weighed no more than the shot, when the charge was ignited the gun and the shot would proceed in opposite directions at similar velocities--very much less than that which the shot would have had had the gun been held fast, and very much greater than the gun would have had if its weight were, as is usually the case, much in excess of that of the shot. In like manner, part of the work of a steam engine is done in driving the ship ahead, and part in pushing the water astern. An increase in the weight of water is equivalent to an augmentation in the weight of our gun and its carriage--of all that, in short, takes part in the recoil.