the sides of the vessel will impel the rudder under the same angle, that is 30 degrees. The part of the rudder under water being 14 feet in length and two in breadth, presents a surface of 28 square feet, impelled at an angle of 30 degrees, by a body of water flowing with the velocity of nine feet per second. But the action of such a current, if it impelled a similar surface in a perpendicular direction, would be 2205 pounds, which must be reduced in the ratio of the square of the sine of incidence to that of radius, or in the ratio to one, since the sine of 30 degrees is, radius being one. The effort therefore of the water will be 551 pounds. Such is the force exer. cised perpendicularly on the rudder; and to find the quantity of this force that acts in a direction perpendicular to the keel, and which makes the vessel turn, nothing is necessary but to multiply the preceding effort by the cosine of the angle of inclination of the rudder to the keel, which in this case is √3 or 0·866, which will give 477 pounds.

The above computation is made on the old supposition, that the force of the water is diminished in proportion as the square of the sine of the incident angle is less than the square of the radius. But, by more accurate experiments it is found (Dr. Hutton's Math, and Philos. Dictionary, Tab. 3, Resistance), that at an angle of 30 degrees, the absolute force is diminished only in the ratio of 840 to 278; hence then, the whole force 2205 pounds, reduced in this ratio, comes out 730 pounds, for the effective or perpendicular force on the rudder, to turn it or indeed the ship about, supposing the rudder held or fixed firm in that position.

But there is one cause which renders this effort more consider. able: the water which flows along the sides of the vessel does not move in a direction parallel to the keel, but nearly parallel to the sides themselves, which terminate in a sort of angle at the sternpost, or piece of timber which supports the hinges of the rudder; so that this water bears more directly on the rudder by an angle of about 30 degrees: hence, in the above case, the angle under which the water impels the rudder will be nearly 60 degrees: we must therefore make this proportion, as the square of radius is to the square of the sine of 60 degrees, or as one is to 2; so is 2205 to 1653. The force therefore which acts in a direction perpendicular to the keel, is 1653 pounds. Or, by the table in the Dictionary

above quoted, as 840 is to 729 (for 60°), so is 2205 to 1913 pounds, the perpendicular force.

This effort will no doubt appear very inconsiderable when com. pared with the effect it produces, which is to turn a mass of 900 tons; but it must be observed that this effort is applied at a very great distance from the point of rotation and from the vessel's centre of gravity; for this centre is a little beyond the middle of the vessel towards the prow, as the anterior part swells out, while the poste rior tapers towards the lower works in order that the action of the rudder may not be interrupted. On the other hand, it can be shewn that what is called the spontaneous centre of rotation, the point round which the vessel turns, is also a little beyond the middle and towards the prow; hence it follows, that the effort applied at the extremity of the keel, towards the stern, acts to move the vessel's centre of gravity, by an arm of a lever 12 or 15 times as long as that by which this centre of gravity, where the weight of the vessel is supposed to be united, exerts its action. And lastly, there is no comparison between the action exercised by this weight when floating in water, and that which it would exert if it were required to raise it only one line. It needs therefore excite no surprise, that the weight of one ton, applied with this advantage, should make the vessel's centre of gravity revolve around its centre of rotation.

If the ship, instead of going at the rate of two leagues per hour sails at the rate of three, the force applied to the rudder will be to that applied in the former case, in the ratio of nine to four; consequently, if the position of the rudder be as above supposed, the actual force will be 3719 pounds, or rather 4304 pounds: if the velocity of the vessel were four leagues per hour, this force, in the same position of the rudder, would be four times as much as at first, or 6612 pounds, or rather 7652 pounds.

Hence it is evident why a vessel, when moving with rapidity, is more sensible to the action of the helm; for when the velocity is double, the action is quadrupled; this action then follows the square or duplicate ratio of the velocity.

If the water moves in a direction parallel to the keel when it impels the rudder, it will be found that this angle ought to be 54 degrees 44 minutes; but, as already observed, the water is carried along in an angular manner towards the direction of the keel con

tinued; which renders the problem more difficult. If we suppose this angle to be 15 degrees, which Bouguer considers as near the truth, it will be found that the angle in question ought to be 46 degrees 40 minutes.

Ships do not receive the whole benefit of this force; for the length of the tiller does not permit the helm to form with the keel an angle of more than 30 degrees.

[Hutton. Montucla's Ozanam.]

SECTION X.

On the Velocity of a Vessel compared with that of the Wind.

A VESSEL can never acquire a velocity greater than, or even equal to, that of the wind, when in a direct course, or when she is sailing before the wind; for besides that in this case a part of the sails injure or intercept the rest, it is evident that if the vessel should by any means acquire a velocity equal to that of the wind, it would no longer receive from it any impulse; its velocity then would begin to slacken in consequence of the resistance of the water, until the wind should make an impression on the sails equal to that resistance, and then the vessel would continue to move in an uniform manner, without any acceleration, with a velocity less than that of the wind.

But, when the course of the vessel is in a direction oblique to that of the wind, this is not the case. Whatever may be its velocity, the sail is then continually receiving an impulse from the wind, which still approaches more to equality, as the course approaches a direction perpendicular to that of the wind: therefore, however fast the vessel advances, it may continually receive from the wind a new impulse to motion, capable of increasing its velocity to a degree superior to that even of the wind itself.

But for this purpose it is necessary that the construction of the vessel should be of such a nature, that, with the same quantity of sail, it can assume a velocity equal to 8-11ths or 3-4ths that of the wind. This is not impossible, if all the canvas which a vessel can spread to the wind, in an oblique course, were exposed in one sail in a direct course. This then being supposed, Bouguer shews, that if the sails be set in such a manner, as to make with the keel an angle of about fifteen degrees, and if they receive the wind in a per.

pendicular direction, the vessel will continually acquire a new acce leration, in the direction of the keel, until her velocity be superior to that of the wind, and that in the ratio of about four to three.

It is indeed true, that, as the masts of vessels are placed at present, it is not possible that the yards can form with the keel an angle less than forty degrees; but some navigators assert, that by means of a small change this angle might be reduced to thirty de grees. In this case, and supposing that the vessel could acquire in the direct line a velocity equal to 3-4ths that of the wind, the velocity which it would acquire by receiving the wind on the sails at right angles, might extend to 1.034 that of the wind, which is a little more than unity, and therefore somewhat more than the velocity of the wind.

If we suppose the same velocity possible in the direct course, and that the sail forms with the keel an angle of 40 degrees, it will be found that the velocity acquired by the vessel, in an oblique course, will be nearly 19-20ths the velocity of the wind.

This at least will be the case, if in this position of the sails, in regard to the wind, they do not hurt or obstruct each other. If all these circumstances therefore be combined, it appears that though it is possible, speaking mathematically, that a vessel can move with the same velocity as the wind, or even with a greater, it will be very difficult to produce this effect in practice.

[Hutton. Montucla's Ozanam.]

SECTION XI.

On sweetening Sea.water.

As a knowledge of the means whereby fresh or sweet water may be procured from salt water is of the utmost importance to seafaring men, we shall here offer a few remarks on this subject.

Sweet water may be obtained from salt water by two methods, by freezing such water, or by distilling it.

When sea-water is exposed to a degree of cold somewhat below the point at which fresh water freezes, its power of holding muriate of soda and other saline substances in solution, is in part destroyed; ice is formed on the upper surface, while the fluid portion underneath becomes a concentrated brine. This ice when melted yields

a water, which contains so little saline matter as scarcely to be distinguished from fresh water by the taste, or indeed by chemical tests. It is evident, however, that this method can only be resorted to in certain latitudes or at certain seasons of the year.

The other method, therefore, viz. that of distillation, is greatly to be preferred, being feasible (with a proper apparatus) at all times and in all situations, and, when properly conducted, yielding a water as pure and as sweet as that procured by congelation. It was for. merly supposed that in order to obtain fresh water from sea-water it was necessary to add to this last, before the distillation, calcareous earth, potash, or certain other substances, for the purpose of absorbing and retaining a bituminous matter, which all sea-water was supposed to contain in greater or less quantity, and to which was ascribed the unpleasant empyreumatic taste of the water distilled from it, especially if too strong a fire is employed, or the distillation is pushed too far. Dr. James Lind, however, has proved that such additions are useless, since pure rain water contracts in like manner a burnt taste by distillation; which shows that it is derived from the action of the elementary water on the heated metallic vessels. This disagreeable flavour, however, goes off, for the most part, on exposing the distilled water to the air. Nothing more is requisite, then, for obtaining fresh water from salt water, than to be provided with a common still; or with still-head covers made to fit the coppers used for boiling provisions on board of ship; and a worm-tub or cooler for condensing the steam. (See Dr. Lind's Essay on preserving the health of Seamen. Also, the Appendix to his Essay on Diseases incidental to Europeans in Hot Climates.) Some years after this discovery was made known by Dr. Lind, [It would appear however that the simple distillation of sea-water, for the purpose of procuring fresh water, was practised by Sir Richard Hawkins, in the reign of Queen Elizabeth. See the Bishop of Llandaff's (Dr. Watson's) Chemical Essays, vol. ii.] an improvement was suggested by Dr. Irving, in the mode of distillation; wherein he substituted for the condensation of the steam, a large open pipe kept constantly wet with mops, in place of the small slender pipe passed through a tub of cold water, in the usual way. This, from being applied to larger coppers than the common method ever had been in the distillation of sea water, yielded in a given time, and with the same quantity of fuel, a larger quantity of fresh water.