light by lines drawn to the ship at both stations: in the same way the angle formed at the second light by lines drawn to each station comes out 44° 12'.

Employing now these angles and the given side or ship's course, 12 miles, we find the distances of the ship at both stations from each light-house to be the following:

We are next to calculate the distance and bearing between the two light-houses themselves, which may be done from either station; thus having discovered the distance from the ship at the first station to each light, and the angle formed at that station by their bearings being given, we discover the remaining side opposite to the given angle to be 17.6 miles (see Case 3d of oblique-angled Trigon. vol. I. p. 420.)

Then in the triangle formed by lines from the first station to both lights, and by that from the one light to the other, knowing all the sides the angles are readily discovered: by this means the angle formed at the second light by lines to the first light, and the first station is found to be 38° 24', which added the bearing of the second station from the second light, S. 9° 28′ E, (N 9° 28′ W. reversed) will give the bearing of the first light-house from the second S. 47° 52′ E. The two light-houses, therefore, bear the one from the other, N 47° 52' W, and S. 47° 52' E, distance 17.6 miles, the things required to be known.

This problem is the foundation of the practice in making a survey of a bay or other tract of coast, where it is inconvenient

venient or impracticable to perform the operations on shore; for by carefully observing the true bearings of objects on the land, and measuring the courses and distances run by the ship from one place of observation to another a series of triangles may be formed, of which all the angles are either given or may readily be calculated, and one side is given, that is the ship's course from station to station.

WINDWARD SAILING.

Were a ship or other inert body to be placed in and acted upon by one substance or medium only it would remain at rest or move precisely in the direction and with the velocity of the surrounding medium: but if, as is the case with a ship, one part of the body, the hull, is immersed in one medium, the water, while another part, the rigging, is surrounded by a different medium, the air or wind, the motion impressed on the ship will be compounded of the effects of the resistance of the different fluids in which she is inclosed; her motion through the water will, therefore, be much slower than that of the wind, in proportion to the greater density and resistance of the water above those of the air; and the pressure of the wind on the ship must amount to a certain quantity exceeding the opposite pressure or resistance of the water before the ship can move at all.

From the structure of the hull of a ship, narrowing gra dually to a sharp edge, and also from the arrangement of the sails, by which the pressure of the wind is made to act in a direction oblique to its own, a ship under the impulse of the air, instead of moving forward in the course of the wind, is pressed on with the sharp end forwards, in a course inclined to the direction of the wind, varying according to the circumstances of her construction and management. Suppose the wind to blow from the N off a shore stretch

ing

ing E and W, and that a ship out at sea could make good her way only E or W; in such a case she would sail for ever parallel to the land, neither approaching to nor receding from it. When the water, however, is sufficiently smooth, and the wind is only so strong as to admit the ship to carry a due proportion of sail, it is found by experience, that she will make her course good at an angle, considerably less than a right angle, with the direction of the wind. Suppose the wind as above stated, to blow due S, that is to be a north wind, and that the ship can according to the sea phrase, ly within 6 points of the wind; that is, in standing along the land to the westward, instead of running due W, she can make her way good 6 points W from N, or WNW, her course being no longer parallel, but inclined to the direction of the shore, she must at last fall in with it. If a ship is bound to a port situated due N from her, while the wind blows due S, and that she can make her way good within 6 points of the wind, she may run either WNW, or ENE at pleasure; let her run WNW for a certain time, by which she will gradually approach the land, and then turning about, or tacking so as to bring the other side to the wind, she will from that point run within 6 points of the wind in the NE quarter, or ENE in the same way, still gaining upon the land. By continuing these courses, or boards as they are called for the requisite distance, she will at last arrive at the desired port: and this part of navigation is termed windward sailing, or turning to windward.

A ship on the western side of an island, lying N and S, is bound to a port due N 36 miles, but the wind being also due N, she can only turn up against it to the westward, making her way good within 6 points of the wind: it is required to ascertain how far she must run to the westward, in order, on putting about and standing to the eastward, to reach the port.

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From this statement, it is evident that the ship must run

an

an equal distance in both directions, thus forming two sides of an isosceles triangle, of which the base is given 36 miles, and the angles at the base each containing 6 points of the compass, or 67° 30', consequently the angle at the vertex, or that formed by the two courses, will be 45°; for as she can sail within 6 points of the wind, her first course will be WNW, and the second also within 6 points of N must be ENE, the angle formed hy which with the first course reversed ESE, is 4 points or 45°.

We have now obtained a simple case of oblique-angled trigonometry, having all the angles and one side of a triangle to find the other sides :-saying therefore

Consequently the ship must run first out to sea WNW 47 miles, and then to the land ENE 47 miles, to arrive at the port in view.

Had it been preferred to perform the same voyage on 4 boards, 2 WNW, and 2 ENE, the distance run upon each would have been one-half of the above, or 23 miles ; so that the whole number of miles run down would still have been the same or 94, to gain a port situated $6 miles off.

CURRENT SAILING.

Although the ocean be confined within certain bounds which, unless in the case of the rise and fall of the tides, it never transgresses, yet in many parts of this vast body of water, portions are observed to move in various directions; in one place constantly advancing, in others at one time advancing and then returning to their original place. To these partial motions of the ocean we give the name of currents,

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rents, or setting of the waters; and they are not only partial with respect to the surface of the sea, but also with respect to its depth; for counter currents are often met with, where the water on the surface is found to set in one direction, while that nearer the bottom is proceeding in a contrary direction. Similar effects are observable in the atmosphere, where the upper range of clouds may often be abserved in progress towards one point of the heavens, at the same time that those floating in a lower region of the air are following a course directly contrary, or in some way inclined to that of the upper clouds.

A ship in the midst of a current, or in a river, and not acted upon by any wind, will follow the course of the stream, proceeding conformably to the rate and the direction of the waters, so that if the stream travel 2 miles in an hour, the ship's progress will likewise be 2 miles in an hour; should, however, the wind blow in the direction of the current, with such force as would impel the ship, if in perfectly still water, at the rate of 2 miles in the hour, this effect will be produced in the current, and the ship pushed forward by the wind 2 miles in 1 hour, at the same time that the current in which she is placed carries her forward 2 miles in the same time, it is evident that the ship will have made a progress equal to the sum of the 2 moving forces, or at the rate of 4 miles in the hour.

On the other hand, should a vessel have to advance against a current or stream, setting 2 miles in the hour, with a wind in her favour just sufficient to carry her forward 2 miles per hour in still water, the two opposing forces being equal, the one would precisely counterpoise the other, no effect in any direction would be produced, and the vessel would preserve her position unchanged, as if in dead water, where neither current nor wind were perceptible. Were the current, however, to set down the river at the rate of 3 miles per hour, while the wind continued to blow against