creased or diminished by unit for every ten-fold increase or decrease of the whole number. It will be observed, that where there is but one whole number, the index will be 0; but if the figures be decimals, as .248, the index is one minus, or - - 1; by the prefixing 0 to the decimal figure, the value is diminished in a ten-fold proportion, then the index is - 2, or minus two.

We cannot pursue the subject farther for want of tables, which would be incompatible with this small work.

Logic, the art of thinking and reasoning justly ; or, it may be defined the science or history of the human mind, inasmuch as it traces the progress of our knowledge from our first and most simple ideas through all their different combinations, conceptions, and all those numerous deductions that result from variously comparing them one with another.

LOG-WOOD, in the arts, is derived from a low. prickly tree, which is found in great plenty at Camu peachy, in the bay of Honduras, and is denominated “ hæmatoxylon campechianum." It copies to Europe in large logs, cleared from the bark, and is very hard, compact, heavy, and of a red colour. It is in high request among dyers, especially in dying black. It gives out the colour both to water and alcohol; the liquor at first assumes a fine red colour with a shade of purple. The infusion becomès gradually deeper, and at last almost black. To cloth, previously boiled in alum and tartar, it gives a beautiful violet colour, which, however, will not stand.

Alkalies rènder the colour darker, acids change it to yellow. Froin a variety of ex. periments it is found that the colouriog matter of

log-wood bears, in many respects, a strong analogy to tannin, but in others it differs from it.

LONGITUDE, in geography, the distance of any given point from another, in the direction of east or west; as latitude is that distance, in the direction of north or south. Latitude is reckoned in degrees from the equator; longitude, from a meridian (one of the perpendicular lines, on maps or globes, or a Jine parallel to these), which is fixed upoñ at pleasure: thus the meridian that passes over Greenwich is the meridian of Greenwich ; and it is from this point that the English reckon the distance of places.

As perpendicular lines, drawn from the opposite poles of a globe, are necessarily wider apart at its greatest circumference, than at any other point between that and those poles, it follows that the width of a degree of longitude, which is determined by those lines, increases, either in a southward or northward direction, in the ratio that it approaches the equator. When, therefore, a degree of longi: tude is mentioned, it is impossible to know what number of miles it contains, unless the degree of Jatitude be also ascertained. The following table shows how many miles answer to a degree of longitude, at every degree of latitade. Lat. Miles. Lat. Miles.

bat. Miles. 'Lat. Miles. Lat. Miles. Lat. Miles. 37 47.92 51 37.76 65 25.36 78 12.48 38 47.28 52 36.94 66 24.41 79 11.45 39 46.62 53 36.11 67 23.44 80 10.42 40 45.95 54 35.27 68 22.48 81 9.38 41 45.28 55 34.41 69 21.50 82 8.35 42 44.59 56 33.55 70 20.52 83 7.32 43 43.88 57 32.68 71 19.54 84 6.28 44 43.16 58 31.79 72 18.55 85 5.23 45 42.43 59 30.90 7S 17.54 86 4.18 46 41.68 60 30.00 74 16.5$ 87 3.14 47 40.98 61 29.09 75 15.52 88 2.09 48 40.15 62 28.17 76 14.51 39 1.05 49 39.36 63 27:24 77 13.50 90 0.00 50 38.57 64 26 30

The use of this table will be readily understood. From it, we learn that 10° of longitude in 80° latitude, amount to a hundred and four miles, and two hundredth-parts; while 10° of longitude, in 4o of latitude contain five hundred and ninety-eight miles, and six hundredth-parts.

Longitude, in navigation, is of so much importance to safety and expedition, that the tollowing rewards have been offered by an act of the British parliament as an encouragement to any person who shall discover a proper method for finding it out: the author or authors of any such inethod, shall be entitled to the sum of 10,0001., if it determines the longitude to one degree of a great circle; to 15,000l., if it determines the same to twothirds of that distance; and to 20,000l., if it determines the same to one half of the same distance ; and half of the reward shall be due and paid when the commissioners of the navy, or the major part of them, agree that any such method extends to

the security of ships within eighty geographical miles of the shores, which are places of the greatest danger; and the other half, when a ship by the appointment of the said commissioners, or the major part of them, shall thereby actually sail over the ocean, from Great Britain to any such port in the West Indies, as those commissioners, or the major part of them, shall choose for the experiment, without losing its longitude beyond the limits before-mentioned. The French, Dutch, Spaniards, and other nations, have likewise offered rewards for the same purpose.

In order to find the longitude with the required precision, it is necessary to construct a perfect timepiece ; for, since by the motion of the earth round its axis, every point upon its surface describes the circumference of a circle, or 360°, in twenty-four hours time, it is plain it must describe 15° in one hour, because the twenty-fourth part of three hundred and sixty is fifteen. Hence the difference of longitude may be converted into time, by allowing one hour for every fifteen degrees, and proportionally for minutes: so, also, difference of time may be converted into difference of longitude, by allowing filteen degrees for every hour, and proportionally for a greater or less time. Consequently, the one known, the other is easily found.

Our countryman, Mr. John Harrison, produced a time-keeper of his own construction which did not err more than a second in a month. This was in the year 1726, and he received much encouragement to go on to render his time-piece still more perfect, and in 1761 his son embarked in a voyage, for Jamaica, with a watch of his father's construction, and

he found that it had erred in four months, less than two minutes in time, or about 28{ minutes of longitude, which was within the exactitude required by the act : he therefore claimed the reward of 30,0001. Another trial, to Barbadoes, was demanded, and on his return he received 10,0001., with the promise of the remainder when he should have constructed other watches equally accurate in keeping time. The commissioners likewise agreed with Mr. Kendal, one of the watchmakers appointed by them to receive Mr. Harrison's discoveries, to make another watch on the same construction with this, to determine whether such watches could be made from the account which Mr. Harrison had given, by other persons, as well as bimself. The event proved the affirmative, for the watch produced by Mr. Kendal, in consequence of this agreement, went even better than Mr. Harrison's; it was sent out with captain Cook 'in his second voyage towards the south pole, and round the globe from the year 1772, to the year 1775 : when the only fault found in the watch was that its rate of going was considerably accelerated, though in this trial of 3 years and a half, it never amounted to 14"] a day. The consequence was, that the House of Commons were pleased to order the other half of the reward to be given to Mr. Harrison. This gentleman had also, at different times, received other sums of money, as encouragements to him to continue his endeavours, from the board of longitude ; from the East India company, aud from opulent individuals.

LONGITUDE, of a star, an arch of the ecliptic, intercepted between the first of Aries, and the point