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of equal parts, as was used in laying down the fundamental bases, and it will give one primary division for the intended scale of miles.

To measure a straight line on the surface of the sea. First, prepare a measuring line of strong cord, two or three hundred yards in length, with small pieces of cork of equal thickness made fast to it at small distances, all along, like a fishing-net, so that it may float straight on the surface of the water: if the line has been well stretched, or much used before, it is the better; also prepare two ropes somewhat longer than the greatest depth of the water to be measured, with a pig of lead or iron ballast, which we call an anchor, 50 or 60 pounds weight, tied by the middle to one end of each rope, that when it is at the bottom it may be able to anchor a boat, and bear to be stretched straight without shifting the place of the anchor. Let the measuring line be thoroughly wet immediately before you begin to use it, and then stretched on the water close by the shore, and its length measured there with a pole. Then, in the direction intended to be measured, take two remarkable sharp objects on the land in a line, one near the shore, the other as far up in the country as you can; if such are not to be had, place buoys on the water at proper distances in that direction.

2. Take the objects, or buoys, in a line, and holding one end of the measuring line fast on the shore, carry out the other in a boat, in that direction, till it is stretched straight at its full length by one man in the boat, and exactly at the end of the line let another man drop the anchor, which will mark one length of it. There keep the boat, and the end of the measuring line, close to the anchor rope, drawn tight up and down, till another boat takes in the other end which was on the shore, and rows farther on, and lays it straight in the direction of the land marks, or buoys, and there drops another anchor,

which will mark the second length of the measuring line. Go on thus till the whole proposed distance is measured; and immediately after let the measuring line be again measured with a pole on the water near the shore, as at first, and if the lengths differ, take the mean between them for the true length. It is obvious, that to measure with any exactness this way, the sea must not only be smooth, but void of a swell, and of all stream of tide; either of which will hinder the line from lying straight. This method of measuring a straight line may be convenient on some occasions; and if care is taken to keep the anchor rope right up and down when the measuring line is applied to it, will be found sufficiently exact for many purposes, but not for a fundamental base line from which other distances are to be deduced.

There is another way of measuring a straight line, mechanically, on the sea, which is so well known to seamen, that it is needless to describe it particularly here; and that is, by heaving the log over a ship's stern while she is under sail, and observing how many knots of the log line run out in half a minute; for the line is so divided that the ship will run, or is supposed to run, so inany miles in an hour, in a straight course; and twice as much in two hours, and so on. But this conclusion is founded on three suppositions, neither of which is certain, viz. that the log remains in the same place during the whole half minute that the line is running out from the ship's stern; that the ship continues to sail with the same velocity, and also in the same direction, during an hour, or two, that she did during the half minute; the contrary of which is more likely in most cases. For the log line may shrink, or stretch, while it is running out; or may drag after the vessel by the weight of the line, or by not running easily and readily off the reel; the swell of the sea may alter the place of the log; and currents, or streams of tide, stronger or weaker below the surface than

on it, an unsteady helm, lee-way, and varying winds, may change the direction, or celerity of the ship's motion; for neither of which can any certain allowance be made. This way, therefore, of measuring a straight line, or distance, is not to be depended on as exact; but is mentioned here, because rocks, shoals, or islands, sometimes lie so far from the coast, that there is no other way of forming any notion of their distance. If any such distance is to be measured after this manner, let the log-line be thoroughly wet when it is measured; let the length between each knot be 51 feet, which is the 120th part of a geometrical mile, as half a minute isth part of an hour. Choose neap-tide, as much slack water as can be got, and a moderate breeze of following wind; let the line be run off the reel so as never to be stretched quite straight; and if the half minute is measured by a watch that shews seconds, rather than by a glass, it will generally be more exact. Perhaps one second should be allowed for the loss of time in calling out at the beginning, and stopping it at the end of the time; except the person who holds the watch can contrive to observe the going out of the red rag at the beginning, and also to stop the line himself at the end of the time; which does not seem a difficult matter.

To find the distance of two places by the flash and report of a gun. Sound moves 1142 English feet in one second of time, or 6120 feet, which makes a geographical mile, in 5" nearly; therefore, let a gun be fired at one place at an appointed time, and observe the time that elapses between the flash and report, and so many seconds as you observe, so many times 1142 feet are you distant from the place; the operation should be repeated two or three times for greater certainty. The distance to be measured in this way should never be less than two miles, on account of errors that may arise in taking the time.

TO TRANSFER A PLAN FROM ONE PAPER TO ANOTHER.

Method 1. By points. Lay the rough plan upon the clean paper, on which you intend to draw the fair copy, press them close together by weights, and keep them as flat as possible; then with a pointrel, or needle point, prick through all the corners of the plan to be copied; separate the papers, and join by lines the points on the clean paper. This method can only be used in plans, whose figures are small, regular, and bounded by straight lines.

Method 2. By tracing paper. Rub the back of the rough plan with black-lead powder, and having wiped off the superfluous lead, lay the blacked part upon the clean paper, or place a sheet of black tracing paper between the rough plan and the clean paper; weights are to be placed as in the former method, to maintain the papers in the same position.

Then, with a blunt point of brass, steel, or ivory, trace exactly the lines of the plan, pressing the paper so much, that the black lead under the lines may be transferred to the clean paper; when the whole of the plan has been thus delineated, go over the blacklead marks with common, or Indian ink.

Method 3. By squares. See prob. 65, page 87. Method 4. By a copying glass. This is a large square, or rectangular piece of looking glass, fixed in a frame of wood, which can be raised to any angle, like a desk, the lower end resting upon the table; a screen of blue paper fits to the upper edge, and stands at right angles to it.

Place this frame at a convenient angle against a strong light; fix the old plan and clean paper firmly together by pins, the clean paper uppermost, and on the face of the plan to be copied; lay them with the back of the old plan next the glass, namely, that part which you intend to copy first. The light through the glass will enable you to perceive dis

tinctly every line of the plan upon the clean paper, and you can easily trace over them with a pencil; and having finished that part which covers the glass, slide another part over it, and copy this, and thus continue till the whole be copied.

Method 5. By the assistance of proportionable and triangular compasses, fig. A and N, plate 1, and fig. 12, plate 3. These will, in many instances, assist the draughtsman very much, and lessen the labour of copying.

Method 6. By the pantographer. There is no method so easy, so expeditious, nor even so accurate, as the pantographer. It is an instrument as useful to the experienced draughtsman, as to those who have made but little progress in the art. It saves a great deal of time either in reducing, enlarging, or copying of the same size, giving the outlines of any drawing, however crooked or complex, with the utmost exactness; nor is it confined to any particular kind, but may with equal facility be used for copying figures, plans, sea charts, maps, profiles, landscapes, &c. see plate 31, fig. 19.

DESCRIPTION AND USE OF THE PANTOGRAPHER, or PANTAGRAPH.

I have not been able to ascertain who was the inventor of this useful instrument. The earliest account I find, is that of the Jesuit Scheiner, about the year 1031, in a small tract entitled, Pantagraphice, sive Ars nova Delineandi. The principles are self evident to every geometrician; the mechanical construction was first improved by my father, about the year 1750. It is one, among other scientific improvements completed by him, that others have, many years after, assumed to themselves.

The pantographer is usually made of wood, or brass, from 12 inches to two feet in length, and consists of four flat rules, fig. 19, plate 31, two of

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