the fame stars be obferved at thefe places. 3. Such stars as are nearest in right afcenfion and declination to the moon, are infinitely preferable. 4. It cannot be too ftrongly urged to get, as near as poffible, an equal number of obfervations of each limb, to take a mean of each fet, and then a mean' of both means. This will in a great measure correct the error of telescopes and fight. 5. The adjustment of the telescopes to the eye of the obferver before the obfervation is alfo very neceffary, as the fight is fubject to vary. 6. A principal error proceeds from the obfervation of the moon's limb, which may be confiderably leffened, if certain little round fpots near each limb were alfo obferved in fettled obfervatories; in which cafe the libration of the moon will perhaps be a confideration. 7. When the difference of meridians, or of the latitudes of places, is very confiderable, the change of the moon's diameter becomes an equation.

"Though fuch are the requifites to ufe this method with advantage, only one or two of them have been employed in the obfervations that I have reduced. Two thirds of thefe obfervations had not even the fame stars obferved at Greenwich and York; and yet none of the refults, except a doubtful one, differ 15" from the mean; therefore I think we may expect á still greater exactness, perhaps within 10", if the above particulars be attended to.

"When the fame ftars are not observed, it is neceffary for the obfervers at both places to compute their right afcenfion from tables, in order to get the apparent right afcenfion of the moon's limb. Though this is not fo fatisfactory as by actual obfervation, ftill the difference will be trifling, provided the ftar's right afcenfions are accurately fettled. I am also of opinion, that the fame method can be put in practice by travellers with little trouble, and a tranfit inftrument conftructed fo as to fix up with facility in any place. It is not neceffary, perhaps, that the inftrument fhould be perfectly in the meridian for a few feconds of time, provided ftars, nearly in the fame parallel of declination with the moon, are obferved; nay, I am inclined to think, that if the inftrument deviates even a quarter or half a degree, or more, fufficient exactnefs can be attained; as a table might be computed, showing the moon's parallax and motion for fuch deviation; which laft may eafily be found by the well known method of obferving ftars whofe difference of declination is confiderable.

"As travellers very feldom meet with fituations to observe ftars near the pole, or find a proper object for determining the error of the line of collimation, I fhall recommend the following method as original.-Having computed the apparent right afcenfion of four, fix, or more ftars, which have nearly the fame parallel of declination, ob. ferve half of them with the inftrument inverted, and the other half when in its right pofition. If the difference of right afcenfions between each fet by obfervation agrees with the computation, there is no error; but if they difagree, half that difagreement is the error of the line of collimation. The fame obfervations may alfo ferve to determine, whether the diftance of the corresponding

wires are equal. In' cafe of neceflity, each limb of the fun might be obferved in the fame magner, though probably with lefs precifion. By a fingle trial I made above two years ago, the refult was much more exact than I expected. Mayor's ca talogue of ftars will prove of great use to those that adopt the above method.—I am rather furprifed that the immerfions of known ftars of the 6th and 7th magnitude, behind the dark limb of the moon, are not conftantly obferved in fixed obfervatories, as they would frequently be of great ufe."

Mr JOHN M'LEAN of the obfervatory, Edinburgh, gives the following tule for finding the fhip's place, with mifcellaneous obfervations on different methods. The rule was examined and approved of by Sir Jofeph Banks, P. K. S.

1. With regard to determining the fhip's place by the help of the course and distance failed, the following rule may be applied. It will be found. as expeditious as any of the common methods by the middle latitude or meridional parts; and is in fome refpects preferable, as the common tables of fines and tangents only are requifite in apply. ing it. Let a and b be the distances of two places from the fame pole in degrees, or their com plete latitudes; the angle which a meridian makes with the rhumb line paffing through the places: and L the angle formed by their meridians, or the difference of longitude in minutes: then A and B being the logarithmic tangents of a and b, S the fine of C, and S the fine of (C+1), we fhall have the following equation: A B (AB fignifies the difference between

L=

S'-S A and B). Also, from a well known property of the rhumb line, we have the following equation:

S+E RD, where S is the logarithmic cofine of C, E the logarithm of the length of the rhumb line or diftance, D the logarithm of the minute's difference of latitude, and R the logarithm of the radius.>

By the help of thefe two equations, we shall have an eafy folution of the feveral cases to which the middle latitude, or meridional parts, are 'commonly applied.

EXAMPLE. A fhip from a port, in latitude 56° N. fails SW. by W. till the arrives at the latitude. of 40° N: Required the difference of longitude? Here a 34, 650°, 56° 15′′, A=9°48334, B=9*56107, S=9*9199308, S99198464; there AB 757300 fore, L 897 the minutes dif.. S-S 844 ference of longitude. Also, S=974474, D= 298227; therefore ER+ DS323753, to which the natural number is 1728, the miles in the rhumb line failed over,

2. The common method of finding the differ. ence of longitude made good upon feveral cour fes and diftances, by means of the difference of latitude and departure made good upon the several courfes, is not accurately true.

For example: If a ship fhould fail due S. 600 miles, from a port in 60° N. lat. and then due W. 600 miles, the difference of longitude found by the common methods of solution would be 1053;

whereas

whereas the true difference of longitude is only 933, lefs than the former by 120 miles, which is more than of the whole. Indeed, every confiderable alteration in the course will produce a very fenfible error in the difference of longitude: though, when the feveral rhumb lines failed over are nearly in the same direction, the error in longitude will be but small.

The reason of this will eafily appear from Fig. 2. Plate CCV.; in which the fhip is fuppofed to fail from Z to A, along the rhumb lines ZB, BA; for if the meridians PZ, PkoeBL be drawn; and very near the latter other two meridians PhD, Pmn; and likewife the parallels of latitude Bn, De, mo, hk; then it is plain that De is greater than bk, (for De is to be as the fine of DP to the fine of bP) and ice this is the cafe everywhere, the departure correfponding to the distance PZ and course BZC, will be greater than the departure to the distance oZ, and courfe oZC. And in the fame manner, we prove that nB is greater than mo; and confequently, the departure correfponding to the diftance AB, and course ABL, is greater than the departure to the distance Ao, and courfe AoL: Wherefore the fum of the two departures correfponding to the courses ABL and BZC, and to the diftances AB and BZ, is greater than the departure corresponding to the diftance AZ and course AZC: therefore the course answering to this fum as a departure, and CZ as a difference of latitude, (AC being the parallel of latitudes paffing through A), will be greater than the true courfe AZC made good upon the whole. And hence the difference of longitude found by the common rules will be greater than the true difference of longitudes: and the error will be greater or lefs, according as BA deviates more or less from the direction of BZ.

3. Of determining the ship's longitude by lunar obfervations.

Several rules for this purpose have been lately published, the principal object of which feems to have been to abbreviate the computations requifite for determining the true distance of the fun or a ftar from the moon's centre. This, however, should have certainly been lefs attended to than the investigation of a solution, in which confiderable errors in the data may produce a small error in the required distance. When either of the luminaries has a small elevation, its altitude will be affected by the variableness of the atmosphere; likewife the altitude, as given by the quadrant, will be affected by the inaccuracy of the inftrument, and the uncertainty neceffarily attending all obfervations made at fea. The fum of these errors, when they all tend the same way, may be supposed to amount to at least one minute in altitude; which, in many cafes, according to the common rules for computing the true diftance, will produce an error of about 30 minutes in the longitude. Thus, in the example given by M. CALLET, in the Tables Portatives, if we suppose an error of one minute in the fun's altitude, or call it 6° 26' 34", inftead of 6° 27′ 34"; we fhall find the alteration in diftance, according to his rule, to be 54", producing an error of about 27 minutes in

the longitude; for the angle at the fun will be found in the spherical triangle whose fides are the complement of the fun's altitude, complement of the moon's altitude, and observed distance, to be about 26°; and as radius is to the cofine of 26°, fo is 60" the fuppofed error in altitude, to 54′′ the alteration in diftance. Perhaps the only method of determining the distance, so as not to be affected by the errors of altitude, is that by firft finding the angles at the fun and moon, and by the help of them the correction of distance for parallax and re fraction. The rule is as follows:

Add together the complement of the moon's apparent altitude, the complement of the fun's apparent altitude, and the apparent diftance of centres; from half the sum of these, subtract the complement of the fun's altitude, and add toge ther the logarithmic co-fecant of the complement of the moon's altitude, the logarithmic co-fecant of the apparent diftance of centres, the logarithmic fine of the half fum, and the logarithmic fine of the remainder; and half the fum of thefe 4 logarithms, after rejecting 20 from the index, is the logarithmic cofine of half the angle at the moon.

As radius is to the cofine of the angle at the moon; fo is the difference between the moon's parallax and refraction in altitude to a correction of diftance; which is to be added to the apparent diftance of centres when the angle at the moon is obtufe; but to be fubtracted when that angle is acute, in order to have the distance once corrected..

In the above formula, if the word fun be changed for moon, and vice verfa, wherever these terms occur, we fhall find a second correction of distance to be applied to the distance, once corrected by fubtraction when the angle at the fun is obtuse, but by addition when that angle is acute, and the remainder or fum is the true distance nearly.

In applying this rule, it will be fufficient to use the complement, altitudes, and apparent distances of centres, true to the nearest minute only, as a fmall error in the angles at the fun and moon will very little affect the corrections of diftances.

If D be the computed distance in seconds, ✔ the difference between the moon's parallax and refraction in altitude, S the fine of the angle at the ď S2 moon, and R the radius; then will be a 2DR

third correction of distance, to be added to the diftance twice corrected: But it is plain, from the nature of this correction, that it may be always rejected, except when the distance D is very small, and the angle at the moon nearly equal to 90o.

This folution is likewife of ufe in finding the true distance of a star from the moon, by changing the word fun into far, and using the refraction of the ftar, inftead of the difference between the refraction and parallax in altitude of the fun, in finding the fecond correction of distance.

Ex. Given the observed distance of a ftar from the centre of the moon, 50° 8' 41; the moon's altitude, 55° 58'55"; the flar's altitude, 19° 18′ 5"; and the moon's horizontal parallax, 1o 0' 5": Required the true distance?

Cofec.

Here the firft correction of distance is additive, fince the angle at the moon is obtuse; and the se cond correction is also additive, fince the angle at the star is acute: therefore their fum 923"+138" =1061"=17′ 41′′, being added to 50° 8' 41", the apparent distance of the star from the moon's centre, gives 50°26′ 21′′ for the true distance of centres nearly; and 2 × L (d + S)—L (2 LR+L 2 + L D) = L 8", which, being added to the distance twice corrrected, gives 50° 26′ 29′′ for

LON

* LONGITUDINAL. adj. [from longitude; longitudinal, French.] Measured by the length; running in the longeft direction.-Longitudinal is opposed to tranfverfe: thefe veficulæ are diftended, and their longitudinal diameters straitened, and fo the length of the whole muscle shortened. Cheyne. LONGITUDINALLY. adj. placed lengthwife. LONG KANG, a town of Afia, in Corea. LONGLY. adv. [from long.] Longingly; with great liking.

Mafter, you look'd fo longly on the maid, Perhaps, you mark not what's the pith of all.

Shak.

LONGMAY. See LON MAY. LONG-MEN, a town of China, in Canton. LONG-NAN, a city of China, of the firft rank, in Setchuen, on the Mouqua. It has feveral forts, formerly of great use against the Tartars, 710 miles SW. of Pekin.

LONGNY, a town of France, in the dep. of the Orne, 9 miles E. of Mortagne.

LONGOBARDI. See LANGOBARDI. LONGOBARDS. See LOMBARDS, § I. LONGOBUCO, a town of Naples. LONGOMONTANUS, Chriftian, a learned aftronomer, born in a village of Denmark in 1562. He was the fon of a ploughman, and was obliged to fuffer during his ftudies many hardships, dividing his time, like the philofopher Cleanthes, between the cultivation of the earth and the leffons he received from the minifter of the place. At laft, when he was 15, he stole away from his

the true distance. By comparing this distance with the computed distances in the ephemeris, the time at Greenwich corresponding to that of obferving the diftance will be known; and the difference of thofe times being converted into degrees and minutes, at the rate of 15 degrees to the hour, will give the longitude of the place of observation: which will be E. if the time at the place be greater than at Greenwich, but W. if it be less.

LON

family, and went to Wiburg, where there was a college, in which he spent 11 years; and though he was obliged to earn a livelihood, he ftudied with fuch ardour, that among other sciences he learned the mathematics in great perfection. He afterwards went to Copenhagen; where the profeffors of that univerfity in a fhort time conceived fo high an opinion of him, that they recommend. ed him to the celebrated Tycho Brahe. He lived 8 years with that famous aftronomer, and was of great service to him in his obfervations and calculations. At length, being extremely desirous of obtaining a profeffor's chair in Denmark, Tycho Brahe confented, though with fome difficulty, to deprive himself of his fervice; gave him a discharge, filled with the highest teftimonies of his esteem; and furnished him with money for the expense of his journey. He obtained a profefforship of mathematics in the univerfity of Copenhagen in 1605; and discharged the duty of it worthily till his death, in 1647. He wrote many learned works, the chief of which is his Aftronomia Danica: 1640, fol. He also endeavoured to fquare the circle, and thought he had made that discovery; but Dr John Pell, an English mathematician, attacked him, and proved that he was mistaken.

(1.) LONGSIDE, a parish of Aberdeenshire, in the diftrict of Buchan, about 5 miles fquare, but irregular in its form. The furface is so level, that it

is often overflowed by the Ugie, which runs through it from W. to E. This has fuggefted the idea of making a canal along its banks, from its

mouth

the branches; appearing in May, and fucceeded by blue berries joined together at their base.

3. LONICERA CAPRIFOLIUM, the Italian honey fuckle, rifes with fhrubby declinated ftalks, fending out long flender trailing branches, terminated by verticillate or whorled bunches of clofefitting flowers, very fragrant, and white, red, and yellow colours.

4. LONICERA DIERVILLA, the yellow-flowered Arcadian honeysuckle, rifes with fhrubby upright ftalks, branching erect to the height of three or four feet; the branches terminated by clusters of pale yellow flowers, appearing in May and June, and fometimes continuing till autumn; but rarely ripening feeds here.

5. LONICERA NIGRA, the black-berried upright honeysuckle, rifes with a shrubby ftem, branching 3 or 4 feet high, with white flowers fucceeded by fingle and diftin&t black-berries.

6. LONICERA PERICLYMENUM, the common climbing honeysuckle, hath two principal varieties, viz. The English wild honeyfuckle, or woodbine of our woods and hedges, and the Dutch or German honeyfuckle. The former rifes with fhrubby, weak, very long, flender stalks, and branches trailing on the ground, or climbing round a fupport; all terminated by oval imbricated heads, furnishing smallish flowers of white or red colours, and appearing from June or July till autumn. The latter rifes with a fhrubby declinated stalk, and long trailing purplish branches, terminated by oval imbricated beads, furnifhing large beautiful red flowers of a fragrant odour, appearing in June and July.

7. LONICERA SEMPERVIRENS, the evergreen trumpet-flowered honeyfuckle, rifes with a fhrubby declinated ftalk, fending out long flender trailing branches, terminated by naked verticillate fpikes, of long, unreflexed, deep fcarlet flowers, very beautiful, but of little fragrance.

8. LONICERA SYMPHORICARPOS, the fhrubby St Peter's-wort, rifes with a fhrubby rough ftem, branching erect 4 or 5 feet high, with fmall greenith flowers appearing round the stalk in Auguft.

9. LONICERA TARTARICA, the Tartarian bomey fuckle, rifes with a fhrubby upright ftem, branching erectly 3 or 4 feet high; heart-shaped, oppofite leaves, and whitifh erect flowers, fucceeded by red berries, fometimes diftinct, and sometimes double.

10. LONICERA XYLOSTEUM, the FLY HONEYSUCKLE, rifes with a strong fhrubby ftem, branching erect to the height of 7 or 8 feet; with erect white flowers proceeding from the fides of the branches; each fucceeded by large double red berries, joined together at their base. The flowers appear in June, and the berries ripen in September. The eafieft method of propagating all these plants is by layers and cuttings. In both cafes they readily emit roots, and form plants in one year fit for tranfplantation. Some forts are alío propagated by fuckers and feed.

(1.) LONICERUS, John, a learned German lexicographer, born at Örthern. He was a Proteftant, and published a Greek and Latin lexicon, with fome other works. He died in 1569.

(2.) LONICERUS, Adam, the fon of the preVOL. XIII. PART II.

ceding, was bred a phyfician, and published feve ral books on natural history and botany; parti cularly a Hiftory of Plants, Animals, and Metals. He died in 1586.

LONIGO, or LEONICO, a trading town and diftrict in the Vicentino.

LONINGEN, a town of Germany, in Weft phalia; 8 miles SSW. of Cloppenbourg.

LONJUMEAU, a town of France, in the dep. of the Seine and Oife; 9 miles SE. of Verfailles, and 10 S. of Paris.

LONKA, a town of Poland, in Podolia. LONLAY, a town of France, in the dep. of the Lower Charente, 6 m. N. of St Jean d'Angely.

LONMAY, a parish of Scotland, on the coaft of Aberdeenshire, 10 miles long, but hardly 4 broad; 12 miles from Peterhead. The foil is va rious; the air moift, but healthy. Husbandry is not yet much improved. The population, in 1795$ was 1650; the decrease 24, fince 1755. There are feveral extenfive moffes.

LONS, or LONS LE SAUNIER, a city of France, capital of the dep. of Jura, formerly famous for its falt works, whence its name, le faunier, i. e. falter. It is feated on the Solvan, 30 miles from Dole. Lon. 5. 30. E. Lat. 46. 41. N.

(1.) LONSDALE. See KIRKEY, N° 1. (2.) LONSDALE, a vale of Weftmoreland. LONTHAL, a river of Germany, in Suabia. (1.) LOO, a town of Holland, in the dep. of the Rhine, and late province of Guelderland, 8 miles W. of Deventer. Lon. 6. o. E. Lat. 52. 18. N.

(2.) Loo, a town of France, in the dep. of Lys, and late province of Auftrian Flanders; 6 miles SSE. of Dixmude.

(3.) Loo, or Low, a river of Cornwall, running into the British Channel, between E. and W. LOOE, where it is navigable for vessels of 100 tons. (4.) *Loo. n. f. A game at cards.-A fecret indignation, that all thofe affections of the mind, fhould be thus vilely thrown away upon a hand at loo. Addifon,

In the fights of loo.

Pope.

* LOOBILY, adj. [looby and like.] Awkward; clumfy. The plot of the farce was a grammar school, the mafter fetting his boys their leffons, and a loobily country fellow putting in for a part among the scholars. L'Etrange.

LOOBY. n. f. [Of this word the derivation is unfettled. Skinner mentions lapp, German, foolish; and Junius, llabe, a clown, Welsh, which feems to be the true original, unless it come from lob.] A lubber; a clumfy clown.

Who could give the looby fuch airs! Sawift. (1.) LOOE, an island in the British Channel, on the coaft of Cornwall, 2 miles SE. of E. LOOE.

(2.) LOOE, EAST, or EAST Low, an ancient borough of Cornwall, incorporated by charter from Q. Elizabeth, feated on the E. fide of the Loo, 16 miles W. of Plymouth, and 232 WSW. of London. It has 2 fairs; and a battery of 4 guns; and is connected with W. Looe, by a large ftone bridge of 15 arches. It is governed by a mayor, recorder, aldermen, and burgeffes. Fff (3.) Loos,