Eaft and Weft-South-Weft, if reckoned to the fouthward, is South by Weft, or if to the northward, it is North by Eaft, which proves that the South by West point of the Compafs, is the true South, and the North by Eaft Point, is the true North, and as the Flower-de-Luce, or North point of the Compass, lies one point to the weftward of the North by East point of the Compafs, which points to the true North, it proves that the Variation is one Point wefterly, or that the Flower-de-Luce lies one point to the weftward of the true North, &c.

THEY fometimes ufe a fourth Method. They that are skilled in spherical Trigonometry, or can use an universal Planifphere, by taking only one Obfervation of the Sun's Altitude, by which, with the Latitude of the Place, and the Sun's Declination, those that understand spherical Trigonometry may find the Sun's true Azimuth, or point of the Compafs that he bears upon, in the Heavens, which compared with the point that the Sun bears upon by the Compafs, their difference is the Variation; as for Inftance, if the Sun's Azimuth found by Calculation be 45 Degrees, or 4 Points, from the North wefterly, which to fpeak. in the Terms of Navigation is North-Weft, but if by the Compass, the Sun bears at the fame time North-Weft by North, that Point difference is the Variation of the Compafs, and fhews that the North Point of the Compafs declines one Point to the weftward, or that the Variation is one Point weiterly; and then will every Point of the Compass be removed, one Point towards the left Hand, as the West Point of the Compafs will stand West by South, the South Point will direct to the true South by East, &c.

THIS being a thing fo ufeful at Sea, and a great many having Tables of Logarithms, Sines,

and

and Tangents that do not throughly understand spherical Trigonometry; it may not be amifs, for the fake of fuch, to infert the following Operation to find the Sun's Azimuth, for which the moft convenient Data, as being both the most easily found, and the leaft trouble in the Operation, is,

THE Sun's Altitude, his Declination, and the Hour of the Day given to find his Azimuth. Note. The Sun's Altitude is found by a Quadrant, his Declination by the Tables for that purpose, in moft Books of Navigation, and the Hour of the Day by a good Watch; and then,

AS Sine Complement of Sun's Altitude, to Sine of the Hour from Noon, So Sine Complement of Declination to Sine of the Sun's Azimuth, from the South or North.

EXAMPLE.

LET the Sun's Altitude be 47 48 (it's Complement is 42 12) the Hour from 12, is 2 Hours 9 Minutes which is either 9 Minutes after 2, or 9 before 10, which, at 15 Degrees to an Hour, is 32 15, the Declination 20 12 North, it's Complement 69 48 then Co. Ar.

As Sine Comp. of Altitude

42.12.0.17281

To Sine of the Hour from Noon 32.15.9.72723

So Sine Comp. Declination

To Sine of the Azimuth

69.48.9.97243

48.12.9.87247

WHICH 48 12 is the Sun's Azimuth from the South, or taken from 180 Degrees, leaves 131.48 the Azimuth from the North.

ANOTHER way to find the Azimuth, is by having the Latitude of the Place, the DecliVOL. II.

Y

nation

SECT. VI. nation of the Sun, and the Sun's Altitude given, and then the Method of finding it is,

ADD the Complement of Altitude (or Zenith Distance), the Complement of Latitude of the Place, and the Complement of the Sun's Declination together, and from their half Sum fubftract the Complement of Declination.

THEN to the Complement Arithmetical of the Sines of the Complement of Latitude, and of the Complement of Altitude, add the Logarithm Sines of the half Sum, and remainder half, the Total of these four Logarithms, is the Sine Complement of half the Azimuth.

Note. If the Sun's Declination be South, and the Latitude North, or the Declination North and Latitude South, you must, instead of the Complement of Declination, ufe the Declination added to 90, for what is there meant by the Complement of the Sun's Declination, is always it's Distance from the elevated Pole.

THAT half Sum is the Sine Complement of 68 57, which doubled is 137 54, the Azimuth from the North required.

T

CHA P. XXXIX.

Of the Line of a Ship's way.

HIS is the most difficult Part in all Geography, of which Authors have written fo obfcurely, and a great many fo falfely, that the Readers can only have from them an obfcure Idea without understanding them. We shall endeavour to give an Explication as clear and diftinct as poffible and the Reader must give close Attention to it, and to make this Explanation the more compleat, and render those Directions intelligible and applicable, which have been left so obscure and impracticable, we fhall, in this Edition, exhibit thofe Methods, by which not only a general Idea of Navigation may be formed, but by which alfo all the useful practical parts thereof are actually performed, and that with respect to Course, Distance, Latitude, Longitude, and all the Data and Quefita that can occur in the Pra&tice of Navigation, in order to which (omitting plain Sailing, which is but the ABC of Navigation, and falfely fuppofes the Surface of the terraqueous Globe to be a regular Plain) we fhall act from another Foundation, and deduce all our subfequent Rules and Tables from that Suppofition, or rather reality of the Earth's being a Globe; and not only adapt our Tables to that Principle, but give the Reafons and Conftructions of them,

in