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reaction would be effective in propelling the ship; but this is not the case—the water pressed by the paddle or blade recedes aftward, and therefore the reaction of the water is that only which is due to the difference between the velocity of rotation in the paddle or screw and that of the water's recession.

It should be observed that the action of the water on the anterior surface of a paddle, or on the anterior surface of a screw-blade, is also a cause of retardation in a ship’s motion.

If the pitch of a screw were 10 feet, one revolution of the screw would, if it were not for these impediments, cause the ship to be moved forward 10 feet; whereas, in ordinary circumstances, it is moved only about 8 feet.

27. In the early days of screw-propulsion the propelling surface consisted of a single and continuous blade or feather, making at least one entire revolution about the spindle or axis of the screw; but this formation was soon found to be defective in practice, on account, first, of the great cross-strain it gave to one side of the axis, and the disturbance it occasioned in the different parts of the system ; secondly, the severe vibratory motion it caused in the stern, which is the weakest part of the vessel. It was at first supposed that all parts of the

& TABLE I.—Showing the elements of several vessels.

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It therefore appears that the average loss by slip is about one-third of the whole effective speed : the ratio of the loss to the whole speed varies very sensibly for the several vessels considered individually ; but, in general, we believe that one-third will be very near the truth.

surface of a screw are equally effective in producing propulsion, and this opinion led to the formation of a screw having an entire, or more than one, convolution about the axis; but the supposition is erroneous, and so much the more as the screw revolves on its axis with greater velocity.

28. The most effective part of a screw-blade is that which is near the periphery of the spiral, and the action of any part on the water becomes less as the part is nearer the axis or spindle. Science has, however, as yet done little in investigating the propelling properties of a screw in water; and the intricacy of the subject is such that the formulæ expressing those properties are too complex to admit of being practically applicable except under very limited conditions.

29. If the screw were supposed to consist of a feather or blade forming two or three convolutions in the length of the axis, the reaction of the water on it would be precisely the same as on a screw with one convolution only in its length, since corresponding parts in each of the two or three portions are in corresponding positions in the water, and all are in action at the same time, The water between the posterior part of one turn of the blade and the anterior part of the next, towards the stern of the ship, is nearly quiescent, the water at the posterior surface of the last turn of the blade alone receding; and there appears to be no foundation for the opinion that the water between every two turns of the blade is made to revolve with the screw, or even to be in any state of commotion.

30. Experiment soon showed that, when the length of the screw was diminished so that the feather had successively three-quarters, one-half, and even less than one-third of a turn in the length, there did not appear, with equal engine-power, to be any diminution in the speed of the ship. This apparently anomalous circumstance caused at first much surprise, and the cause of it is not, even now, free from uncertainty ; but the explanation, for which the author is indebted to Mr. Lloyd, Director-General of the Steam Department

turn in wer, to be contiy anong the at the Admiralty, is the most satisfactory that has yet been offered. This gentleman supposes a screw, whose blade makes one complete turn only in the length, to be divided by planes all perpendicular to the axis of the screw, and at small intervals from one another, so that the surface of the screw is divided into a great number of sectoral or fan-like areas oblique to the axis, and following one another in succession from one end of the screw to the other. Now, the water in which the screw turns being supposed at rest, a vertical lamina of water, which is acted upon by the first of these sectors, is, by the pressure of the posterior surface in the revolution of the screw, pressed with a certain force towards the after-part of the screw; the water thus receding is acted upon by the second sectoral portion of the screw in its revolution, and impelled aftward, but with less force than before, on account of the retiring movement of the water: a part of this water is acted upon by the third sectoral portion of the screw in its revolution, and still impelled aft, but with a force further diminished by the greater retiring movement of the water, and so on, to the end of the screw.

31. Thus, the pressive force of the screw on the water, and, consequently, the reaction of the water, by which the ship is propelled forward, go on diminishing; and the slip, or recession of the water, goes on increasing with the length of the screw. The diminution of the power of motion on this account is probably very small when the velocity of the screw's rotation is small; and, in that case, an entire screw with one turn in its length may have some advantages; but, when the velocity of rotation is great, it is probable that the propelling power of the after-part of the screw becomes so small as to permit its removal without diminishing in a sensible degree the speed of the ship ; in fact, experience has shown that, with high velocities of rotation, one-third or one-fourth of an entire convolution of the blade is sufficient to produce the full effect of the moving power,

32. In what has been said it is supposed that the water

to 51. Thus, the prethe reaction of the diminishing ; an

has immediate access to the screw, and that the particles pressed by it are free to move aftward; but neither of these suppositions is correct. From the position of the screw, in an aperture close under the ship's counter, the water, which is divided by the body of the ship, subsequently flows obliquely towards the screw; and, again, the water, after being pressed by the screw, is broken by the stern-post and rudder, where, being arrested, part of it is forced forward in the direction of the ship's motion : on both these accounts the power of the screw must be in some degree modified ; in some cases, indeed, the slip has been found to be negative, that is, the actual speed of the ship has been greater than the theoretical speed, or that which is due to the power of the engine.

33. From such considerations, and from repeated experiments, it has been determined that the best form which can be given to a screw is that of two halves of a spiral feather, placed on opposite sides of the axle of the screw in reverse positions : these, while they occupy only half the space in length which they would otherwise require, are found, with equal surface, more efficient than the continuous spiral formerly in use.

The two sectors, or fan-shaped blades, composing the present screw, have generally what is called a uniform pitch; that is, they constitute two equal and similar figures, one on each side of a plane perpendicular to the axle and bisecting the length or pitch of the original screw, supposed to be of one complete turn : each blade occupying exactly half that length. But some screws have been made which occupy much less of the length, and with what is called an increasing pitch : thus, imagining a vertical plane perpendicular to the axle to divide the whole pitch in the ratio of 11 to 12, the forward fan occupies half the shorter portion and the aftward fan half the longer portion; consequently, the extent of the interval between the extremities of the two blades, if measured on a line parallel to the axle, is half the entire pitch of the complete screw. This is Mr. Wood

and with Wical plane perptio of 11 to via the aftward the

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croft's construction : in that of Mr. Atherton the two fans are equal and similar to one another, but each is formed so that the parts about the axle are portions of spirals, of smaller pitch than those of the parts about the extremities, the pitch increasing gradually from the axle towards the periphery.

34. In a manner similar to that which has been used in finding the propulsive effect of water on a common paddle-wheel, may be found the effect of water on the blades of a screw in giving motion to a vessel. Thus,

let C D be a horizontal Fig. 3.

line parallel to the keel of the ship or to the screw-axle, and let ZC be at right angles to it in a plane passing through CD, perpendicular to the radius or arm of a screw. blade; also let A B in the same plane be the intersection of the plane with the anterior surface of the blade. Imagine A B at present to be a straight

line; and let it be observed that the vertical plane in which any point, as C, in A B revolves about the screw-axle is perpendicular to that axle, and to the horizontal line CD.

Now, let the velocity of the point C, by the revolution of the screw-blades about the screw-axle, be represented by V, and be supposed to act in the direction ZC; and let the horizontal velocity of C, by the forward movement of the vessel, be represented by V', in the direction CD; also let the angle ZCB=0: then ZCD being a right angle, V' cos. O is the velocity of the ship resolved perpendicularly to A B, and V sin. 0 is the velocity of the blade also resolved perpendicularly to AB; consequently V sin. 0-V' cos. O represents the relative velocity of the paddle and ship in the

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