In like manner, the Diurnal Arch of 9 hours is 135 deg. which divided by 180, the Quotient is, that is 3 quarters of an hour: Which shews the place of the Jewish hours of 7 and 5, to be three quarters after, or before, Noon and that doubled is One bour and a half, which gives the place of 8 and 4; all one with our 1 and and 10.; and so Tripling and Quadrupling and Quintupling 3 quarters, you have the places of the Jewish hours upon this Parallel of 9 hours length of the Day.

And these parts Doubled and Tripled, as is faid, will always (in this Parallel and the former) fall upon even hours, halves and quarters of hours: And that is the only reason why these two Parallels of 15 and 9, are preferred; there being no neceffity of ufing: them, more than the Tropicks or other Parallèls, only this conveniency of even parts.

Lastly. In the Diurnal Arch of 12, that is, the Equator, the Common and the Jewish hours concur; that is, the Jewish hours of 5 and 7, with our hours of 11 and 1: Their 4 and 8, with our 10 and 2, &c. So that a Line drawn from 1 in the Parallel of 15, to 1 in the Æquator, and from thence to in the Parallel of 9, is the 7th Jewish hour. And fo are all the rest to be inscribed.

:

Trigo-

Trigonometria Practica.

SECTION VI.

OF

NAVIGATION.

I

Intend not here to treat of Navigation in the general; it being an Art that requires (for the true Understanding, either

the Theory, or Practice of it) an inspection into divers other Sciences Mathematical; of which, that of TRIGONOME TRIA, (or the Doctrine of Triangles) is the Principal; for that the solution of all fuch Problems which are of daily Use at Sea, are performed thereby, and those are such as concern Longitude, Latitude, Rumb (or course) and Distance, &c. And there fore, I shall Define, First, what is meant by Longitude, Latitude, Rumb, Distance, &c. And Secondly, any two of them being known; how to find the other two; and that by Trigonometrical Calculation: with some other Problems pertinent to that Art. And I shall perform them, (1) By Plain Sailing. (2) By Mercators Sailing; And (3) By the Middle Latitude.

DEFINITION S.

I. Longitude, Is the Distance of a Place from some known Meridian to that Place; and is always counted upon the Equi noctial Circle, from that known Meridian towards the Eaf or Weft.

II. La

II. Latitude, Is the Distance of any Place from the Equinoctial Circle; counted upon that Meridian Circle which passeth over that Place, towards either of the Poles; either North or South: and accordingly the Latitude is. Denominated either North or South Latitude.

III. Rumb, (or Course) Is that Angle which a Ship in her Sailing makes with the Meridian of the Place from whence the Ship came, and the Place where the Ship then is: But the Complement of the Rumb, is that Angle which the Rumb makes with that Parallel of Latitude in which the Ship is; and is the Complement of the Rumb to 90 deg. - The Rumb is made known to the Mariners at all times, by help of his Compass.

IV. Distance, Is the Number of Leagues, Miles, Centesms, &c. that a Shiphath Sailed upon any Rumb or Course. --And this.. is known to the Mariner by the vering (or running out) of the Log-Line in any known quantity of Time..

V. If your Rumb (or Course) be directly East or West, you alter not your Latitude at all: - If your Course be Northward, you continually Raise the North Pole; and you increase your Latitude Northward: Or the South Pole, if you Course be from the Equinoctial Southward.

So that

The Raising of the Pole is, When you Sail from a Leffer La- titude to a Greater: And the Depreffing of the Pole is, when you Sail from a Greater to a Leffer Latitude..

These things known, before I proceed to the Solution of the feveral Questions or Problems in Navigation, unto which the DoArine of Triangles is subservient, it will be neceffary to say something concerning the Situation of Places upon the Earth or Sea in respect of Lorgitude and Latitude: And of their Distances one from another in Leagues, Miles, or Minutes: And then, shew how to lay down (upon a Blank Chart) any two (or more) Places, according to their respectve Latitudes and Difference of Longitudes. All which shall be comprehended under these Heads following

4

I. Of the Situation of Places, in respect of Longitude and La titude.

TN N this Problem there are variety of Cafes, according as the places
may be situate one from the other, in refpect of the Firft, or
General Meridian, as to their Difference of Longitude; and in re-
spect of the Equinoctial, as to their difference of Latitude : And
for the better understanding of these Varieties, I shall exhibit all
of them in one Scheme: In which,

Fig. NÆS is the First Meridian, or beginning of Longitude.
LXI. WEE the Equinoctial Circle.

Æ E the East part thereof.

EW the West part thereof.

N the North Pole.

S the South Pole.

DB and T A, two Parallels of North Latitude.
OR and Z X, two Parallels of South Latitude.
NILMSa Meridian of West Longitude.

NHCSa Meridian of East Longitude.

:

CASE I. If the Places lies in the Equinoctial Circle, as the Places L, G, H, and K; and so have no Latitude---- Or in the same Parallel of Latitude, as the Places D, V, X, and B, in the Parallel of 40 de. of North Latitude; and the Places O, M, Cand R in the Parallel of 35. 85 deg. of South Latitude: Then, (1.) If the Two Places proposed, do lie both on the East-fide of the First Meridian, as H, K---- X, B----CR: Or, both on the Weft-fide, as D, V---- L, G----O, M: Then, The Leffer Longitude substracted from the Greater, gives the Difference of the Longitudes of those Places. But, (2.) If of the two Places proposed, one do lie on the East-fide, and the other on the Weft fide of the First Meridian: As V and X---- L and H, M and C: Then, the two Longitudes added together, gives the Difference of Longitude between those two Places. But, Note,

If the Sum of the two Longitudes do exceed 180 deg. fubstrat the Sum of them from 360 deg. and the Remainder is the Difference of Longitude of those two Places,

CASE

CASE II. If One Place lie in the Equinoctial Circle, as L, and Fig.

the other under the fame Meridian NLS, as the Places V, LXI. in the Parallel of 40 deg of North, and M, in the Parallel of 35. 85 deg. t of South Latitude: Then, the Latitudes them-† In all this selves are esteemed (or are to be taken) for the Difference of Section,

Latitude.

the Der grees are not divided

Centesms,

CASE III. If Two Places proposed differ both in Latitude and into60min. Longitude, do lie both of them on the North, as V in the Pa- but into rallel of 40 deg. and I in the Parallel of 18. 25 deg. the leffer La-or huntitude taken from the greater, leaves 21. 75. deg. for the Diffe-dred Parts. rence of Latitude of those Two Places: The like, if both the Plates had lain on the South-fide of the Equinoctial, as at C and Y-But if the Two Places proposed had been V, in 40 deg. of North Latitude, and C, in 35.85 deg. of South Latitude; then, the Sum of them two Latitudes 75.85 deg. would be the Difference of Latitudes; which can never exceed 90 deg.

How to Reduce Degrees and Minutes, (or Degrees and Centesins, or hundred parts of Degrees) into Miles, or Minutes.

T

HIS is

done by multiplying the Degrees by 60. and adding the odd Minutes, if any be, and the Product will be Miles. Also Degrees, and Centesms of Degrees, multiplied by 60, the Product will be Degrees, and Centesms. So,

26 de. 33 m. multiplied by 60: The Product of 26 by 60, is 1560, to which add the 33 Minutes, and it makes 1593 Miles.

Or, 72. 75 deg. multiplied by 60, will produce 4365 Miles: And 26. 47 deg. by 60, will produce 1588. 20 Miles; that is 1588 Miles, and or of a Mile; and so of any other.

III. How to lay down (upon a Blank Chart) any two Places, which differ both in Longitude and Latitude.

L

ET the two Places proposed bethe Harbour of Famaica, which lies in 18. 25 deg. of North Latitude, and 78.35 deg. of West Longitude And the Cape of Good Hope; which lies in 35. 85 deg. of South Latitude, and 27. 50 deg. of East Longitude..