OF THE LOG-LINE AND HALF-MINUTE GLASS.

VARIOUS methods have been proposed for measuring the rate at which a ship sails but that most in use is by the Log and Half-Minute Glass.

The Log is a flat piece of thin board, of a sectoral or quadrantal form (see Plate VL fig. 3), loaded, on the circular side, with lead sufficient to make it swim upright in the water. To this is fastened a line, about 150 fathoms long, called the log-line, which is divided into certain spaces called knots, and is wound on a reel (see Plate VI. fig. 4) which turns very easily. The Half-Minute Glass is of the same form as an Hour Glass (see Plate VI. fig. 2), and contains such a quantity of sand as will run through the hole in its neck in half a minute of time.

The making of the experiment to find the velocity of the ship, is called heaving the log, which is thus performed:-One man holds the reel, and another the half-minute g.ass; an officer of the watch throws the log over the ship's stern, on the lee side, and when he observes the stray line is run off (which is about ten fathoms, this distance being usually allowed to carry the log out of the eddy of the ship's wake), and the first mark (which is generally a red rag) is gone off, he cries, Turn; the glass-holder answers, Done; and, watching the glass, the moment it is run out, says, Stop. The reel being immediately stopped, the last mark run off shows the number of knots, and the distance of that mark from the reel is estimated in fathoms. Then the knots and fathoms together show the distance the ship has run the preceding hour, if the wind has been constant. But if the gale has not been the same during the whole hour, or interval of time between heaving the log, or if there has been more sail set or handed, a proper allowance must be made. Sometimes, when the ship is before the wind, and a great sea setting after her, it will bring home the log. In such cases, it is customary to allow one mile in ten, and less in proportion if the sea be not so great. Allowance ought also to be made, if there be a head sea.

This practice of measuring a ship's rate of sailing, is founded upon the following principle-that the length of each knot is the same part of a sea mile, as half a minute is of an hour. Therefore the length of a knot ought to be of a sea mile; but, by various admeasurements, it has been found that the length of a sea mile is about 6086 75. feet; hence the length of a sea knot should be 51 feet. Each of these knots is divided into 10 fathoms, of about 5 feet each. If the glass be only 28 seconds in running out, the length of the knot ought to be 47 feet and 6 tenths. These are the lengths generally recommended in books of navigation; but it may be observed, that, in many trials, it has been found that a ship will generally overrun her reckoning with a log-line thus marked; and, since it is best to err on the safe side, it has been generally recommended to shorten the above measures by 3 or 4 feet, making the length of a knot about 74 fathoms, of 6 feet each, to correspond with a glass that runs 28 seconds.

In heaving the log, you must be careful to veer out the line as fast as the log will take it; for if the log be left to turn the reel itself, the log will come home and deceive you in your reckoning. You must also be careful to measure the log-line pretty often, lest it stretch and deceive you in the distance. Like regard must be had that the halfminute glass be just 30 seconds; otherwise no accurate account of the ship's way can be kept. The glass is much influenced by the weather, running slower in damp weather than in dry. The half-minute glass may be examined by a watch, with a second hand, or by the following method:-Fasten a plummet on a line, and hang it on a nail, observing that the distance between the nail and middle of the plummet be 39 inches; then swing the plummet, and notice how often it swings while the

To correct the distance when the log-line and half-minute glass are faulty

If there be any error in the log-line or glass, the measured distance must be corrected in the following manner, supposing that a 30 glass requires 50 feet to a knot:

(1.) If the glass only is faulty, you must say, As the seconds run by the glass are to 30 seconds, so is the distance given by the log to the true distance. Thus, if a ship sails 8 knots per hour, by a glass of 36 seconds, the true number of knots per hour will be 7.1; for 36: 30 :: 8.5 : 7.1.

(2.) If the log-line only is faulty, you must say, As fifty feet is to the distance of a knot on the line, so is the distance run by the log to the true distance. Thus, if a ship sails 7 knots per hour, by a log-line measuring 53 feet, her true distance will be 7.4 miles per hour; because 50: 53 :: 7 : 7.4.

(3.) If the log-line and glass are both faulty, you must say, As 50,* multiplied by the length of the glass, is to 30, multiplied by the length of the line, so is the measured to the true distance. Thus, if a ship sails 6 knots per hour, with a glass of 24 seconds, and a log-lime of 60 feet per knot, her true velocity will be 9 miles per hour, because 50 X 24: 30 × 60 :: 6 : 9.

The following description of Massey's Patent Log, used in surveying operations, is from Capt. Edward Belcher's treatise on Nautical Surveying :

"It is composed of a brass wedge-shaped box, having within, three cogged wheels, acting on each other in such proportion that a total revolution of one completes a division of the next, (or one-twentieth,) a revolution of the next one-eighth, registering thus from one hundred and sixty miles to tenths, and decimal parts; the action is by the rotation of a spindle with four spirally fixed wings, (termed the rotator, or fly,) which turns an endless screw in the box, acting directly on the decimal wheel. It is towed astern by a stout lead line of sixty fathoms, and is registered every time the course is changed, angles taken, &c., but should not be reset until the twenty-four hours have elapsed, the ship anchors, or goes less than three knots-(when it becomes uncertain from not towing horizontally.)"

A new instrument for measuring the vessel's velocity, and also to find the depth of water by sounding, has been invented by Professor W. P. Trowbridge of the United States Coast Survey. It is more accurate than any other instrument used for such purposes, and has been adopted by the United States Navy Department.

Instead of multiplying the length of the glass by 59, and the line by 20, you may multiply the former by 5, and the latter by 3. If any one chooses to mark the log-line at less than 50 feet for a glass of 30 seconds, hə must put his estimated length of the knot, instead of 50, in all the above rules.

TABLE,

Showing the length of a mile of Longitude, in fect, for different Latitudes

[A Geographical or Nautical Mile at the Equator is 6086.4.]

MR. JOHN HADLEY was the first who published a description of the Quadrant of Reflection, for measuring angular distances; and the instrument still bears his name, although it has been ascertained that Sir Isaac Newton invented a similar one some years before, but never made it public. One of our countrymen, Mr. Thomas Godfrey, of Philadelphia, had also contrived an instrument, on the same principles, some time before Mr. Hadley made known his discovery,

Plate IX., figure 1, represents a quadrant of reflection, the principal parts of which are, the frame ABC, the graduated arc BC, the index D, the nonius er vernier scale E, the index glass F, the horizon glasses G and H, the dark glasses or screens I, and the sight vanes K and L.

The graduated are BC is an octant, or eighth part of a circle, but, on account of the double reflection, is divided into 90°, numbered from 0° towards the left, and each degree is commonly divided into three equal parts, of 20 minutes each. The graduation on the limb is continued a few degrees to the right of 0°. This portion is called the arc of excess, and is found very convenient for several purposes.

The inder D is a flat bar, commonly made of brass, movable round the centre of the instrument, and broader towards the axis of motion, where is fixed the index glass Fat the other end is fixed the nonius or vernier scale, used in estimating the subdivisions of the arc; at the bottom or end of the index, there is a piece of brass which leads under the arc, having a spring to make the vernier lie close to the limb, and a screw to fasten it in any position. Some quadrants have a tangent screw affixed to the lower part of the index to adjust its motion. The vernier is a small, narrow slip of brass or ivory, fixed to that part of the index which slides over the graduated arc, and usually contains a space equal to 21 or 19 divisions of the limb, and is divided into 20 equal parts. Hence the difference between a division on the limb, and a division on the dividing scale, is one twentieth of a division of the limb, or one minute. Therefore, if any division on the vernier is in the same straight line with a division of the limb, then no other division on the vernier can coincide with a division of the limb, the extreme divisions excepted. Some time ago, it was usual to reckon the divisions on the vernier from its middle towards the right, and from the left towards the middle; but, this being found inconvenient, a more commodious method has been introduced of numbering from right to left. Hence the degree and minute pointed out oy the vernier, may be found thus:-Observe what minute on the vernier coincides with a division on the limb; then this minute, being added to the degree and parts of a degree on the limb immediately preceding the first division on the vernier, will be the degree and minute required. Thus, suppose 10' on the vernier coincides with a division on the limb, and that the division on the limb preceding the first division of the vernier is 8° 20′; the division pointed out by the vernier will be 8° 30′.

The index glass F is a plane speculum or mirror of glass, quicksilvered and set in a brass frame. It is so placed that the face of it is perpendicular to the plane of the instrument, and is fixed to the index by the screw M; the other screw N serves to replace it in a perpendicular position, if, by any accident, it has been put out of order. The use of this mirror is to receive the rays from the sun, or other object observed, and reflect them towards the horizon glasses.

The horizon glasses G and H are two small speculums. G is called the fore horizon glass, from its being used in the common or fore observation, where the observer's face is turned towards the object; and H the back horizon glass, being used in the back observation, where the observer's back is turned towards the object. These mirrors receive the reflected rays from the index glass, and reflect them to the eye of the observer. The horizon glasses are not entirely quicksilvered. The fore horizon glass G is only silvered on the lower half, the other half being transparent, and the

through it. The back horizon glass H is silvered at both ends; in the middle as a transparent slit, through which the horizon may be seen. These two glasses are set in brass frames, similar to that of the index glass, and fixed on movable bases, which are adjusted by screws so as to set the glasses in their true positions. In general there are three dark glasses or screens, I; two red ones, of different shades, and one green. Each is set in a brass frame, which turns on a centre, that they may be used separately or together They serve to defend the eye from the rays of the sun ring an obser-. vation. The green glass is peculiarly adapted to take off the glare of the noon, but may be used for the sun when much obscured by clouds. When these glasses are used for a fore observation, they are to be fixed as in figure 1; but when used for a back observation, they are to be placed at O.

The sight vanes, K and L, are pieces of brass, standing perpendicular to the plane of the instrument. The vane K is called the fore sight vane, and L the back sight vane There are two holes in the fore sight vane, the lower of which and the upper edge of the silvered part of the fore horizon glass are equidistant from the plane of the instrument, and the other hole is opposite to the middle of the transparent part of that glass. The back sight vane has one perforation, which is exactly opposite to the middle of the transparent slit in the back horizon glass.

The adjusting lever (fig. 2), which is fixed on the back of the quadrant, serves to adjust the horizon glass, by placing it parallel to the index glass. When this lever is to be made use of, the screw B must be first loosened; and when, by the adjuster A, the horizon glass is sufficiently moved, the screw B must be fastened again; by this means the horizon glass will be kept from changing its position.

To adjust a quadrant.

As the quadrant, from various accidents, is liable to be out of order, it is necessary that the mariner should be able to ascertain the errors, and re-adjust the several parts, before he proceeds to make his observations. For this purpose, he must examine whether the index glass and the horizon glasses be perpendicular to the plane of the instrument, and whether the plane of the fore horizon glass be parallel, and that of the back horizon glass perpendicular to the plane of the index glass, when 0 on the vernier stands against O on the limb.

1st. To ascertain whether the index glass be perpendicular to the plane of the quadrant.

Place the index on the middle of the arc, and hold the index glass near the eye. Look into it, in a direction parallel to the plane of the instrument, and see if the reflected arc appear exactly in a line with the arc seen direct, or if the image of any point of the are near B appear of the same height as the corresponding part of the are near C seen direct; if so, the index glass is perpendicular to the plane of the quadrant; if not, the error must be rectified by the screws on the base, behind the frame, by loosening the screw M, and tightening the screw N, or by loosening the screw N, and tightening the screw M.

2d. To ascertain whether the fore horizon glass be perpendicular to the plane of the quadrant.

Having adjusted the index glass, hold the instrument in a vertical position Lock through the fore sight vane, and move the index till the reflected and direct images of the horizon, seen in the horizon glass, coincide. Then incline the instrument till its plane is nearly parallel to the horizon; if the images still coincide, the horizon glass stands perpendicular; otherwise it does not, and must be adjusted by the screws placed before and behind it, loosening one of them, and tightening the other.

This adjustment may be made by the sun, moon, or a star, by holding the quadrant in a vertical position, and observing if the object seen by reflection appears to the right or left of the object seen direct, and moving the screws, as above, till both images coincide.

After having made the horizon and index glasses parallel, according to the directions in the following article, it will be best to re-examine this adjustment.

3d. To make the horizon glass parallel to the index glass, when 0 on the vernier stands on on the arc.

Having fixed the index, so that 0 on the vernier stands on 0 on the arc, look at any distant object, and see if the image of it coincides with, the object itself; if it does, the

adjustment is complete; if not, they must be made to coincide by means of the adjusting lever. The horizon may be used for this purpose in the following manner:— Hold the plane of the instrument vertical; look through the lower hole in the vane K, and direct the sight through the transparent part of the glass G to the horizon; then if the horizon line, seen in the silvered and transparent part, coincides, or makes one straight line, the horizon glass is said to be adjusted; but if the horizon lines do not coincide, slacken the screw B (fig. 2) in the middle of the adjusting lever, and turn the horizon glass on its axis until the horizon lines coincide; then fix the lever firmly by tightening the screw B. If this adjustment be again examined, it will perhaps be found unperfect. In this case, therefore, it remains either to repeat the adjustment, or find the error of it (usually called the index error), which may be done thus:-Let the horizon glass remain fixed, and move the index till the image and object coincide; then the difference between 0 on the vernier and 0 on the arc is the index error, which is to be added to the angle or altitude observed, if the 0 on the vernier be to the right hand of 0 on the arc, otherwise to be subtracted. Thus, if the horizon is used, the instrument being held in a vertical position, you must look through the lower hole of the vane K, towards the horizon; then move the index till the reflected and direct images of the horizon coincide; the difference between 0 on the vernier and 0 on the arc will be the index error.

4th.

To adjust the back horizon glass, that it may be perpendicular to the plane of the index glass, when 0 on the vernier stands on 0 on the arc.

Set the index as far to the right of 0 on the arc, as twice the dip of the horizon (taken from Table XIII.); hold the quadrant in a vertical position; look towards the horizon through the hole in the back horizon vane L, and the transparent slit of the back horizon glass II; then, if the reflected horizon, which will appear inverted, coincide with that seen direct, the glass is truly adjusted; otherwise the screw, in the centre of the lever on the under side of the quadrant, must be slackened, and the glass turned on its axis till both horizons coincide, when the lever should be fixed by tightening the screw.

5th. To adjust the back horizon glass, that it may be perpendicular to the plane of the quadrant.

Put the index on 0; hold the quadrant nearly parallel to the horizon; look through the hole on the back sight vane, and if the true and reflected horizons appear in the same straight line, the glass is perpendicular to the plane of the instrument; but if they do not coincide, the sunk screws, before and behind the glass, must be turned till both appear to form one straight line.

To take an altitude of the sun by a fore observation.

If the sun is bright, turn down one or more of the dark glasses; hold the instrument in a vertical position; apply the eye to the upper hole in the fore sight vane, when the image is so bright as to be seen in the transparent part of the fore horizon glass. otherwise to the lower hole; direct the sight to that part of the horizon beneath the sun, and move the index till you bring the image of his lower limb to touch the horizon directly under it; but as this point cannot be exactly ascertained, the observer should move the instrument round to the right and left a little, keeping, as nearly as possible, the sun always in that part of the horizon glass which is at the same distance as the eye from the plane of the quadrant;* by this motion the sun will appear to sweep the horizon, and must be made to touch it at the lowest part of the arc; the degrees and minutes pointed out by the index, will be the observed altitude of the sun's lower limb at that instant.

To take an altitude of the moon by a fore observation.

In the night, when the moon is bright, her image may be seen in the transparent part of the fore horizon glass, and the observation may be taken exactly in the same

* In common quad. ants, if the upper hole be looked through, the sun's image must be made to appear in the middle of the transparent part of the horizon glass; but if the lower hole he looked through, the image must be made to appear on the line joining the silvered and transparent parts of the horizon glass, as these parts of the horizon glass are at the same distances from the plane of the instrument, as