navigation.

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ccedingly difficult to be .found, and frequent errors must be made,^*hiqh only can be corrected by celestial observations. In manyplates of the .ocean there are currents,, or places yvhere the water,instead of remainingjit rest, runs with .a considerable velocity for3 great way in some parlicuUufedirection, and which will certainlycarry the sbip'greatly out of her comxe. This occasions an. errorof the same nature with tin* lee-way ; and therefore, whenever acurrent ity perceived, its velocity ought to be determined, and theproper allowances made. Another source of error in reckoningthe course of a ship proceeds .from the variation of the compass.There are few parts of the world where the needle points exactlyijortii; and in these where the variation is known, it is subject toyery considerable alterations. By these, means the course of theship is mistaken; for as sailors have no otner standard to directthem than.(lie compass, if the needle, instead,of pointing due N.should point N. E. a prodigious error would be occasioned duringthe voyage, and the ship would not come near the port to whichshe was bound. To avoid errors of this kind lire only method is,to observe the azimuths as frerpiently as possible, by which thedifference of variation will be perceived, and the proper allow-ances can then be made far errors in the .course which this mayhave occasioned. Errors will- arise in the reckoning of a ship,especially when she sails in high latitudes, from the spheroidalfigure of’the earth ; for as llie polar diameter .of our globe is shorterthan the oquatoreal one, if thence follows, that the farther we-re-move from the equator, the longer arc the degrees of latitude. OfConsequence, if a navigator assigns any certain number of milesfor the length of a degree of latitude m ar the equator, he mustyary that measure as he approaches towards the. poles, otherwise hewill imagine that he hath sailed further than lie actually hathdone. It i,s of-consequence to navigators in a long voyage to takeIjie nearest way totlfeir port; but this can seldom be done withoutConsideiable difficulty. The shortest distance between any twopoints of a sphere is measured by an arch of a great circle inter-cepted between them ; and therefore, excepting where both placeshe under the same parallel of latitude, it is adviseable to direct theship along- a great circle of the earth’s surface. But this is a mat-ter of considerable difficulty, because there are no fixed marks bywhich it can he readily known whether the ship sails in the direc-tion of a great circle or not. For this reason the sailors com-monly direct their course by the rhumbs, or the bearing of the placeby the compass. These bearings do not point out the shortest dis-tance between places ; because, on a globe, the rhumbs are spirals,and not arches of greatcirdes. However,when the places lie directlyunder the equator, or exactly under the same meridian, the rhumbthen coincides with the arch of a great circle, and of consequenceshew,s (he nearest way. The main end of all practical navigationis to conduct the ship in safety to her destined port ;. and for thispurpose it is of the utmost consequence to know, in what particularpajt of the surface of tlie globe she is at any particular t-ime. Thiscan only be done by having on accurate map of the sea-coasts ofqll the countries of the world, and, by hawing out the ship’s pro-gress along the map, to know at what time she approaches the de-sired haven, or how she is to. direct her course in order to reach it.It is therefore a matter of great importance for navigators to hefurnished with maps, or charts, as they are called, not only veryaccurate in themselves, but such as are capable of havingtheship’scourse easily traced, upon them, without the trouble of laboriouscalculations, which are ready to create mistakes. The names ofthe two great divisions of navigation are taken merely from theki/nl of charts made use oh Plane sailing is that in which theplane chart is made use of; and Mercator ’s sailing, or globularfailing,-is that in which Mercator ’s chart is used. In both thesemethods, it is easy to find the ship’s place with as great exactnessas. the .chart will allow, either by a. solution of a case in plane tri-gonometry, or by geometrical construction.

Of Plane Sailing.

As a necessary preliminary to this method of navigation, weshall giv.e the construction of the plane chart. This chart supposesthe earth to be a plane, and the meridians parallel to one another ;and likewise the parallels, of latitude at equal distance from oneanother, as they really are upon the globe. Though thismethod be in itself evidently false ; yet, in a short run, and espe-cially near the equator, an account of the ship’s way may be keptby.it tolerably well. Having determined the limits of the chart,

that is, how many degrees of latitude and longitude, or meridionaldistance (they being in this chart the same), it is to contain : sup-pose from tlie lat of 20° N. to the lat. of 71° N. ; and from thelongitude of London in 0. deg. to the ion. of 50 W. ; then choosea scale of equal pans, by which the chart may be contained withinthe size of a sheet of paper on which it is intended to he drawn.In the chart annexed, llie scale is such, that each degree of lati-tude and longitude is one-eighth part of an inch. Make a parallelo-gram ABCD, fig. 2, the length of which AB from N. to S. shallcontain 51°, tiie difference of latitude between the limits of 20° and71°; and the breadth AI) from E. to W. shall contain the pro-posed 50 degrees of longilude, the degrees being then from thesaid scale of 8 degrees to an inch ; and this parallelogram wilL bethe boundaries of the chart. About the boundaries of the chartmake scales containing tlie degrees, halves and quarters .of degrees(if the scale be large enough) ; drawing lines across the chartthrough every. 5 or 10 degrees; let the degrees of latitude andlongitude have their respective numbers annexed, and tlie sheet isfitted .to receive the places intended to be delineated thereon.On a strait slip of pasteboard, or stiff paper, let tlie scale of tliedegrees and parts of degrees of longitude, in the line AD, belaid close to tlie edge ; and the divisions numbered from the righthand towards tlie left, being all west longitude. Seek in a geo-graphical tuble for the latitudes and longitudes of tlie places con-tained within the proposed limits; and let them be written out intlie order in which they increase in latitude. Then, to lay downany place, lay tiie edge of the pasteboard-scale to tlie divisionson each side of the chart, shewing the latitude of the place ; sothat the beginning of its divisions tall on the right hand borderAB ; and against the divisions shewing.the longitude of the givenplace make a point, and this gives the position of the place pro*posed ; and in like manner are all the other places to be laid down.Draw waving lines from one point to the other, where thecoast is contiguous, and thus the representation of tiie landswithin the proposed limits will be delineated. Write the namesto tlie respective parts, and insert a compass, and the chartwill be completed. The angle, formed by the meridian andrhumb that a ship sails upon, is called the sbip"s- course.'Thus if a ship sails oil (he N. N. E. rhumb, then her coursewill be 22° 30'; and so of others. 'The distance betweentwo places lying on the same parallel counted in miles of tlieequator, or the distance of one place from the meridian of anothercounted as above on tlie parallel passing over that place, is calledmeridional distance ; which, in plain sailing, goes.under the nameof departure. I.et A, fig. 3, denote a certain point on the earth’ssurface, AO its meridian, and AD the parallel of latitude passingthrough it; and suppose a ship to sail from A on the N. N. E.rhumb till she arrive at B; and through B draw the meridianBD, (which, according to the principles of plane sailing, must beparallel to CA,) and the parallel of latitude BC : then the lengthol AB, viz. how far the ship lias sailed upon tlie N. N. E. rhumb,is called her distance: AC or BD will lie-her difference of lati-tude, or northing ; CB will be her departure, or easting; and tlieangle CAB w ill lie tlie course. Hence il is plain, that the distancesailed will always be gruater than either tlie difference of latitudeor departure ; it being the hypollienuse of a right-angled triangle,whereof the other two are tiie legs ; except the ship sails either ona meridian ora paiallel of latitude: for if tlie ship sails on a me-ridian, then it is plain, that her distance will be just equal to herdiflerence of latitude, and she will have no departure ; but if shesail on a parallel, then her distance will be the same with her de-parture, and she will have no difference of latitude. It is evi-dent also from llie figure, that if the course be less than 4 points,or 45 degrees, its complement, viz. tlie other oblique angle, willbe greater than 45 degrees, and so the difference of latitude willhe greater than the departure; hut if the course be greater than4 points, then the diflerence of latitude will be less that, the de-parture ; ajid lastly, if tlie course lie just 4 points, tlie differenceof latitude will be equal to tlie departure. Since the distance,diflerence of latitude, and departure, form a right-angled triangle,in which the oblique angle opposite to the departure is the course,and the other its complement; therefore, having any two of thesegiven, we can (by plain trigonometry) find the rest; and lieneearise tiie caites^of plane sailing, v. Inch are as follow :

Case 1. Course and distance given, to fin cl difference of lati-tude and departure ?

ExamP‘