in the Jewish antiquities, a measure which held a quarter of a cab, and consequently five-sixths of a pint. There is mention of a log, 2 Kings vi. 25. under the name of a fourth part of a cub. But in Leviticus the word log is often met with, and signifies that measure of oil which lepers were to offer at the temple after they were cured of their disease. Dr Arbuthnot says, that the log was a measure of liquids, the seventy-second part of the bath or ephah, and twelfth part of the hin, according to all the accounts of the Jewish writers.

sea term, signifying a small piece of timber, of a triangular, sectorial, or quadrantial figure, on board a ship, generally about a quarter of an inch thick, and five or six inches from the angular point to the circumference. It is balanced by a thin plate of lead, nailed upon the arch, or circular side, so as to swim perpendicularly in the water, with about two thirds immersed under the surface.

Log-Line, a little cord, or line, about a hundred and fifty fathoms long, fastened to the log by means of two legs (fig. 4), one of which passes through a hole at the corner, and is knotted on the opposite side, while the other leg is attached to the arch by a pin fixed into another hole, so as to draw out occasionally. By these legs the log is hung in equilibrium; and the line thus annexed to it is wound round a reel fixed for that purpose in the gallery of the ship.

This line, from the distance of about ten, twelve, or fifteen fathoms off the log, has certain knots or divisions, which ought to be at least fifty feet from each other; though it was the common practice at sea not to have them above forty-two feet asunder.

The length of each knot ought to be the same part of a sea-mile as half a minute is of an hour; and admitting the measurement of Mr Norwood, who makes a degree on a great circle of the earth to contain 367,200 English feet, or about 69½ English statute miles, and, therefore, 8/10th part of it, or a nautical mile, will be 6120 feet; 1/10th of 6120, or 51 feet, should be the length of each knot. But because it is safer to have the reckoning rather before the ship than after it, therefore fifty feet may be taken as the proper length of each knot. The knots are sometimes made to consist only of forty-two feet each, even in the present practice; and this method of dividing the log-line was founded on the supposition that sixty miles, each of 5000 English feet, made a degree; for 1/10th of 5000 is 41½, or, in round numbers, 42 feet. Mariners, rather than quit the old way, though known to be erroneous, use glasses for half minute ones, that run but 24 or 25 seconds. They have also used a line of 45 feet to 30 seconds, or a glass of 28 seconds to 42 feet. When this is the case, the distance between the knots should be corrected by the following proportion: as 30 is to 50; so is the number of seconds of the glass to the distance between the knots upon the line. The heat or moisture of the weather has often a considerable effect upon the glass, so as to make it run slower or faster; it should, therefore, be frequently tried by the pendulum in the following manner. On a round nail hang a string that has a musket-ball fixed to one end, carefully measuring between the centre of the ball and the string's loop over the peg 39½ inches, being the length of a second pendulum; then swing it, and count one for every time it passes under the peg, beginning at the second time it passes; and the number of swings made during the time the glass is running out shows the seconds it contains. The line also is liable to relax and shrink, and should therefore be occasionally measured.

The use of the log and line is to keep account and make an estimate of the ship's way or distance run; which is done by observing the length of line unwound in half a minute's time, told by a half-minute glass; for so many knots as run out in that time, so many miles the ship sails in an hour. Thus, if there be four knots veered out in half a minute, the ship is computed to run four miles an hour.

The author of this device for measuring the ship's way is not known; and no mention of it occurs till the year 1667, in an East-India voyage published by Purchas; but from that time its name occurs in other voyages among his collections; and henceforward it became famous, being taken notice of both by our own authors and by foreigners; as by Gunter in 1623; Snellius in 1624; Metius in 1631; Oughtred in 1633; Herigone in 1634; Saltonstall in 1636; Norwood in 1637; Pournier in 1643; and almost by all the succeeding writers on navigation of every country.

To Heave the Log, as they call it, they throw it into the water on the lee-side, letting it run till it comes without the eddy of the ship's wake; then one, holding a half-minute glass, turns it up just as the first knot, or the mark from which the knots begin to be reckoned, turns off the reel (fig. 2) or passes over the stern. As soon as the glass is out, the reel is stopped, and the knots run off are told, and their parts estimated.

It is usual to heave the log once every hour in ships of war and East-India men, and in all other vessels once in two hours; and if at any time of the watch the wind has increased or abated in the intervals, so as to affect the ship's velocity, the officer generally makes a suitable allowance for it at the close of the watch.

The log is a very precarious way of computing, and must always be corrected by experience and good sense; there being a great deal of uncertainty in the yawing of the ship going with the wind aft, or upon the quarter in the heaving of it, by its coming home, or being drawn after the ship, on account of the friction of the reel and lightness of the log in the course of the current, and in the strength of the wind, which seldom keeps the same tenor for two hours together; which is the interval between the times of using the log in short voyages, though in longer ones they heave it every hour. Yet this is a much more exact way of computing than any other in use; much preferable certainly to that of the Spaniards and Portuguese, who guessed at the ship's way by the running of the froth or water by the ship's side; or to that of the Dutch, who used to heave a chip over-board, and to number the paces they walk on the deck while the chip swims between any two marks, or bulk-heads on the side.

Compound Log. The above mentioned errors, and particularly the log's being subject to drive with the motion which the water may have at its surface, whereas the experiment requires it to be fixed in the place where it is when the mark commencing the knots goes off the reel, have been considered by writers, and many methods have been proposed to remove, or at least to lessen them. The late Mr. Bouguer proposed a method, which has been thought deserving of particular attention, in the Mem. Acad. Sc. 1747; afterwards in his Treatise on Navigation, published at Paris in 1753, and since reprinted in 1760, by the abbé de la Caille. For this purpose, take for the log a conical piece of wood, which fix to the log-line passed through or along its axis, at about 40, 50, or 60, or more feet, from one end; and to this end fix the diver, which is a body formed of two equal square pieces of tin, or of thin iron plate, fixed at right angles to one another along their diagonals; and its size so fitted to that of the cone, that the whole may float. A cone of three inches diameter in the base, and of six inches in the flant height, is proposed by M. Bouguer to suit a diver made of plates about 9½ inches square; the intersection of the diagonals is joined to the log-line, and the loop and peg fixed as in the common log. However, it has been found, that no kind of wood used in British dock-yards, when formed into a cone of the above dimensions, will float a diver made of stout tin plates, one side of the square being 9½ inches. Such a diver weighing 1 lb avoirdupois required to float it a cone of five inches diameter and twelve inches on the flant side, so as the point of the cone, which was made of light fir, should just appear above the water. Now supposing one side of such a square tin-diver to be about ten inches, and made of plates only two-thirds of the thickness of the former, such a diver would weigh, with its folder, about 20 ounces, and can be floated by a light fir cone of four inches diameter in the base, and ten inches in the flant height or length; and such a compound log might perhaps be found on trial to be affected by about as much again as that proposed by M. Bouguer; and consequently the difference between the numbers given by the common log and compound log, must be augmented by two-thirds of itself for the necessary correction, as below. When the compound log of Bouguer, above described, is thrown overboard, the diver will sink too deep to be much affected by the current or motion of water at the surface, and the log will thereby keep more steadily in the place where it first fell; and consequently the knots run off the reel will show more accurately the ship's rate of sailing. As the common log is affected by the whole motion of the current, so this compound log will feel only a part thereof, viz. such a part nearly as the resistance of the cone is to the resistance of the diver; then the resistances of the above cone and diver are about as 1 to 5; and consequently this log will drive but one-fifth part of what the common log would do; and so the ship's true run will be affected by one-fifth only of the motion of the waters. To obtain the true rate of sailing, it will be proper to heave alternately, hour and hour, the common log and this compound log; then the difference of their knots run off, augmented by its one-fourth part, is the correction; which applied to the knots of the common log, will give the ship's true rate of sailing at the middle time between the hours when these logs were hove. The correction is additive when the compound log's run is the greatest, otherwise it is subtractive. To find the course made good: increase the observed angle between the log-lines by one fourth-part; and this gives the correction to be applied to the apparent course, or the opposite of that shown by the common log; the correction is to be applied to the right of the apparent course, when the bearing of the common log is to the left of the compound log. Or thus: the lengths run off both logs, together with their bearings, being known; in a card or compass apply the knots run off, taken from a scale of equal parts along their respective bearings, from the centre; join the ends; and in this line produced, on the side next the compound log's length, take one-fourth of the interval; then a line drawn from the end, thus produced, to the centre of the card, will show the true course and distance made good. When a current, such as a tide, runs to any depth, the velocity of that current may be much better ascertained by the compound log than by the common one, provided the diver does not descend lower than the run of the current; for as those ships which are deepest immersed, drive fastest with the tide; so the diver, by being acted on below, as well as the log on the surface, their joint motion will give the total effect of the current's motion better than what could be derived from the motion at the surface only. Also, by such a compound log, the depth to which any current runs may be easily tried.

Other Logs. We have an account in the voyage to the North Pole, p. 97, of two other logs, which were tried by captain Phipps: one invented by Mr Ruffel, the other by Foxon; both constructed upon this principle, that a spiral, in proceeding its own length in the direction of its axis through a resisting medium, makes one revolution round the axis; if, therefore, the revolutions of the spiral are registered, the number of times it has gone its own length through the water will be known. In both these the motion of the spiral in the water is communicated to the clock-work within-board, by means of a small line fastened at one end to the spiral, which tows it after the ship, and at the other to a spindle, which sets the clock-work in motion. That invented by Mr Ruffel has a half-spiral of two threads, made of copper, and a small dial with clock-work, to register the number of turns of the spiral. The other log has a whole spiral of wood with one thread, and a larger piece of clock-work with three dials, two of them to mark the distance, and the other divided into knots and fathoms, to show the rate by the half-minute glass, for the convenience of comparing it with the log. This kind of log will have the advantage of every other in smooth water and moderate weather; and it will be useful in finding the trim of a ship when alone, in surveying a coast in a single ship, or in measuring distances in a boat between head-lands and shoals; but it is subject to other inconveniences, which will not render it a proper substitute for the common log.

Perpetual Log, a machine so called by its inventor, Mr Gottlieb of Houndsditch, London. It is intended by it to keep a constant and regular account of the rate of the ship's velocity through the water; whereas the common log hitherto used does not indicate the variation in her velocity in the interval of heaving the log, and consequently does not ascertain the true distance that the ship has run in any given length of time. LOG

Fig. 1. is a representation of the whole machine; the lower part of which, EFG, is fixed to the side of the keel; H representing only the boundary line of the ship's figure. EF are the section of a wooden external cage, left open at the ends KL, to admit the passage of the water during the motion of the ship. At M is a copper grating, placed to obstruct the entrance of any dirt, &c., into the machine. I, is a section of a water-wheel, made from 6 to 12 inches in diameter, as may be necessary, with float-boards upon its circumference, like a common water-wheel, that turn by the resistance of the water passing through the channel LK. It turns upon a shouldered axis, represented by the vertical section at K. When the ship is in motion, the resistance of the water through the channel LK turns round the wheel I. This wheel, by means of a pinion, is connected with and turns the rod contained in the long copper tube N. This rod, by a pinion fixed at its upper extremity, is connected with and turns upon the whole system of wheels contained in the dial of the cage ABCD. This dial, by means of the copper tube N, may be fixed to any convenient place aboard the ship. In the front of the dial are several useful circular graduations, as follows: The reference by the dotted line A has a hand which is moved by the wheels within, which points out the motion of the ship in fathoms of 6 feet each. The circle at B has an hand showing the knots, at the rate of 48 feet for each knot; and is to be observed with the half-minute glass at any time. The circle at C has a short and a long hand; the former of which points out the miles in land-measure, and the latter or longer the number of knots contained in each mile, viz. 128, which is in the same proportion to a mile as 60 minutes to the hour in the reckoning. At e, a small portion of a circle is seen through the front-plate called the register; which shows, in the course of 24 hours (if the ship is upon one tack), the distance in miles that she has run; and in the 24 hours the mariner need take but one observation, as this register serves as an useful check upon the fathoms, knots, and miles, shown upon the two other circles.

f3 Is a plate showing 100 degrees or 6000 miles, and also acts as another register or check; and is useful in case of any mistake being made in observing the distance run by the other circles. The reckoning by these circles, without fear of mistake, may therefore be continued to nearly 12,000 miles.

A communication from this machine may easily be made to the captain's bed-side, where by touching a spring only, a bell in the head ABCD will sound as many times in an half minute as the ship sails miles in an hour.

Mr Gottlieb has applied this machine to the Carteret and Westmoreland packets. He is very sanguine in the hopes of its success and utility; and conceives that the mariner will, by this contrivance, be better enabled than heretofore to keep the vessel and his reckoning together; it being well known that the most experienced navigator is too frequently erroneous in this respect, the ship being sometimes ahead, or sometimes astern, off the reckoning.

He also observes, that the construction of the log is such, that if the vessel was to be aground, strike a rock, or strip off her false keel, the parts would not be disarranged; and further, should she be laid up for repairs, &c., fix months, in half an hour after coming again into the water, the lower immersed part of the log would clear itself, and be in proper action.

Log-Board, a sort of table, divided into several columns, containing the hours of the day and night, the direction of the winds, the course of the ship, and all the material occurrences that happen during the 24 hours, or from noon to noon; together with the latitude by observation. From this table the different officers of the ship are furnished with materials to compile their journals, wherein they likewise insert whatever may have been omitted, or reject what may appear superfluous in the log-board.

Log-Book, a book into which the contents of the log-board is daily copied at noon, together with every circumstance deserving notice that may happen to the ship, or within her cognizance, either at sea or in a harbour, &c. The intermediate divisions or watches of the log-book, containing four hours each, are usually signed by the commanding officer in ships of war or East-Indiamen. See Navigation.

LOGARITHMS.