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rallels of Declination which fhew the Lorgeft and Shortest Day, confifting of whole (or entire) Hours: As with us 16 and 8; and. the Equator. For,
A Line drawn? In the Pa7 rallel of through
8 of Declination
16 of Declination
be the Hour of One from the Sun's rifing. And likewife in the fame order; through 6, 8 and 10, fhall give the Second Hour from Sun-rifing; and in the like Order, all the reft.
In Winter, when the Parallel of 8 Hours fhall fail, the other. two Points will ferve to draw it by, because thofe Hours are Streight Lines. But after the firft Six Hours are infcribed, the Equinoctial alfo failing, fome other Diurnal Arch, (as of 9 or 10 Hours) must be defcribed to fupply that want..
The Italian Hours are accounted by 1, 2, 3, &c. from Sun-fetting: And for the Infcription of these, the fame Parallels of 8 and 16 Hours, with the Equator, will ferve: For a Line drawn through them, in the Hours of 9, 7 and 5, Afternoon (obferving the fame as before) fhall be the hour of One; the like through 7, 5 and 3; fhall be the hour 23: The Night hours of 9, 10, &c. are the Morning hours produced.
The Jewish hours are reckoned like the Babylonish, from Sun-rifing, but unequally; their Sixth hour being (always) Noon; and every hour, one Twelfth part of the Artificial Day, of what length foever that be.
For the Infcription of them: The Vulgar Hours proper for the Plain being firft drawn, and the Diurnal Arches of 15, 12, and 9 hours, divide the degrees in each by 12, and that Quotient by 15; or elfe (which is all one) divide the faid Arches by 180, the three Quotients fhall give the juft Times, in hours, and ufual parts of hours from 12 a Clock, upon the two Parallels and the Aquator: through which, Lines drawn by a Ruler, fhall be the Jewish. bour's required.
Example. In Latitude 51 deg. 32 min. the Diurnal Arch of 15 hours is in Degrees 225, which divided by 180, the Quotient is 1h. and fo much the Jewish hours of 5 and 7 are diftant from Noon; one hour and a quarter being a twelfth part of the Diurnal Arch of 15 hours: And this hour and quarter being doubled, gives the place for 4 and 8: Tripled, the place of 3 and 9, &c. from Noon, upon that Parallel of 15 hours...
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 fhews 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 pur 1 and and 10,; and fo 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 thefe 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 reafon why thefe two Paral.. lels of 15 and 9, are preferred; there being no neceffity of ufing them, more than the Tropicks or other Parallels, only this conveniency of even parts.
Laftly. 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 I in the Equator, and from thence to in the Parallel of 9, is the 7th Jewish hour. And fo are all the reft to be infcribed.
Intend not here to treat of Navigation in the general; it be ing an Art that requires (for the true Understanding, either the Theory, or Practice of it) an infpection into divers other Sciences Mathematical; of which, that of TRIGONOME TRIA, (or the Doctrine of Triangles) is the Principal; for that the folution of all fuch Problems which are of daily Ufe at Sea, are performed thereby; and thofe are fuch as concern Lotgitude, Latitude, Rumb (or courfe) and Distance, &c. And there fore, I fhall Define, Firft, what is meant by Longitude, Latitude, Rumb, Diftance, &c. And Secondly, any two of them being known; how to find the other two; and that by Trigonometrical Calculation with fome other Problems pertinent to that Art. And I fhall perform them, (1) By Plain Sailing. (2) By Mercators Sailing And (3) By the Middle Latitude.
1. Longitude, Is the Diftance of a Place from fome known Meridian to that Place; and is always counted upon the Equi noctial Circle, from that known Meridian towards the Ea or Weft.
II. Latitude, Is the Diffance of any Place from the Equinoctial Circle; counted upon that Meridian Circle which paffeth 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 Courfe) Is that Argle which a Ship in her Sailing. makes with the Meridian of the Place from whence the Ship came, and the Place where the Ship thenis: 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. Diftance, Is the Number of Leagues, Miles, Centefms, &c. that a Shiphath Sailed upon any Rumb or Courfe.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 Eaft or Weft, you alter not your Latitude at all:-If your Courfe be Northward, you continually Raife the North Pole; and you increase your Latitude Northward: Or the South Pole, if you Course be from the Equinoctial Southward.
The Raifing 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 Do&rine of Triangles is fubfervient, it will be neceffary to fay fomething concerning the Situation of Places upon the Earth or. Sea in refpect of Longitude and Latitude: And of their Distances one from another in Leagues, Miles, or Minutes: And then, fhew how to lay down (upon a Blank Chart) any two (or more) Places, according to their refpectve Latitudes and Difference of Longitudes. All which fhall be comprehended under thefe Heads following
I. Of the Situation of Places, in refpect of Longitude and La titude.
this Problem there are variety of Cafes, according as the places may be fituate one from the other, in refpect of the Füft, or General Meridian, as to their Difference of Longitude; and in refpect of the Equinoctial, as to their difference of Latitude: And for the better understanding of thefe Varieties, I fhall exhibit all of them in one Scheme: In which,
Fig. NES is the Firft Meridian, or beginning of Longitude.
Æ E the Eaft part thereof.
. S the South Pole.
DB and T A, two Parallels of North Latitude.
NH CS a Meridian of Eaft Longitude.
CASE I. If the Places lies in the Equinoctial Circle, as the Places L, G, H, and K; and fo have no Latitude---- Or in the fame 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, C and R in the Parallel of 35. 85 deg. of South Latitude: Then, (1.) If the Two Places propofed, do lie both on the Eaft-fide of the Fift Meridian, as H, K---- X, B---C R : Or, both on the Weft-fide, as D, V---- L, G---O, M: Then, The Leffer Longitude fubftracted from the Greater, gives the Difference of the Longitudes of thofe Places. But, (2.) If of the two Places propofed, one do lie on the Eaft-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 thofe two Places. But, Note,
If the Sum of the two Longitudes do exceed 180 deg. fubftra&t the Sum of them from 360 deg. and the Remainder is the Difference of Longitude of thofe two Places,