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A Sea-chart may be made either generall or par∣ticular; I call that a generall Sea-chart, whose
line AE, in the following figure, represents the E∣quinoctiall, as the line AE there doth the parallel of 50 gr. and so containeth all the parallels successive∣ly from the Equinoctiall towards either Pole: but they can never be extended very neere the Pole because the distances of the parallels increase so much, as the Secants doe. But notwithstanding this, it may be termed generall, because that a more generall Chart cannot be contrived in plano, except a true Projection of the Sphere it selfe. And I call that a particular Chart which is made properly for one particular Navigation, as if a man were to sail between the Latitude of 50 and 55 gr. and his difference of Longitude were not to exceed 6 gr. then a Chart made (as the figure following is) for such a Voyage, may be called particular.
Now the making of such a Chart, is Master Gunters first proposition page 104 of the Sector, and this the line of Secants will sufficiently perform.
For it were required to project such a Chart: Having drawn the line AB, and having crossed it at right angles with another line AE, representing the parallel of 50 gr. you must then take the Se∣cant of 51 from your Scale, and set it from 50 to 51 on both sides the Chart, and draw the parallel 51 51.
Again, take the Secant of 52 from your Scale, and set it upon your Chart from 51 to 52, and so draw the parallel 52 52. And so you are to draw the rest of the parallels.
Then for the Meridians, or divisions of the line BC, they are all equall to the Radius.
If therefore you take the Radius, and run it above and below, you shall make the spaces or distances of the Meridians such as in the bottome of the Chart are figured with 1, 2, 3, 4, 5, 6.
These degrees thus set on the Chart, may be sub-divided into equall parts, which in the gradua∣tions above and below ought so to be. But in the graduations upon the sides of the Chart, they ought as they goe higher, still to grow greater. Yet the difference is so small that it cannot produce any considerable errour, though the sub-divisions be all equall. Divide them therefore either into 60 mi∣nutes, or English miles, or into 20 leagues, or into 100 parts of degrees, as shall best be liked of.
It a little more curiosity should be stood upon for the graduations of the Meridian, instead of the Se∣cants of 51, 52, 53, &c. you may take 50½, 51½, 52½, &c. alwayes halfe a degree lesse than is the Latitude that should be put in.
Now if each of those divisions at the bottome of the Chart, as A 1, &c. be made equall to the common Radius of the Sines, Secants, and Tan∣gents, and if a Chart be made to that extent upon a skin of smooth Velame; well pasted on a board; you may work upon it many conclusions very exactly.
Are set down in 12 Propositions by Master Gunter, beginning page 121. In each of which Propositions is shewed how to resolve the Question upon the Chart it selfe, which will be direction enough how
the work must be performed, without any more words here used.
The working of these propositions also may be applyed to the Scales of Sines and Tangents, on the Ruler, and wrought by protraction, according to the rules given in the first Chapter, if the pro∣portions, as he layes them down in the forecited pages, be so applyed.
If a Scale of Rumbs be thought more expedi∣ent for these operations then is a Scale of Chords, it may be put into some spare place of the Ruler.
His two Propositions, page 114. 116, may be done upon the Chart as is there shewed, but his second Proposition, which is,
THis (I say) may be done upon the Scales of Sines and equall parts: And for this purpose, the two last inches of the same Scale of equall parts, being equall in length to the Radius or Sine of 90, are di∣vided into 20 at one end, and into 60 at the other end.
Take therefore upon the line of Sines, the com∣plement of the parallels distance from the Equator, (or the complement of the given Latitude) and mea∣suring it upon the Scale of 20 parts, it will shew
you what number of Leagues make one degree of Longitude in that parallel of Latitude. And be∣ing measured upon the Scale of 60 parts, it gives so many of our miles, or so many minutes of the Equinoctiall, or any other great circle, as are answe∣rable to one degree of Longitude in that Latitude.
Let it be required to finde how many Leagues doe answer to one degree of Longitude, in the La∣titude of 18 gr. 12'.
Take out of the line of Sines, the complement of the given Latitude, namely. 71 gr. 48'. Then ap∣plying this distance to the Scale of 20 equall parts, you shall finde it to reach 19, and so many Leagues doe answer to one degree of Longitude, in the La∣titude of 18 gr. 12'.
And the same distance being measured upon the Scale of 60 equall parts, will give you 57 parts, and so many minutes of the Equator are answerable to one degree of Longitude, in that parallel of La∣titude.
So likewise, in the Latitude of 25 gr. 15', if you take the complement thereof 64 gr. 45', out of the Scale of Sines, and apply it to the former line of 20, you shall finde it to reach 18 parts, and so many Leagues doe answer to one degree of Longitude, in the Latitude of 25 gr. 15'.
¶In the Appendix to Master Norwoods Do∣ctrine of Triangles, there is by him laid
down 15 Questions of sailing by the plain Sea-chart, and others by Mercators Chart, all which the line of Chords and equall parts will sufficiently perform, if the work of the third Chapter of this Booke be rightly un∣derstood.
IF the two places lie under one parallel, and so dif∣fer only in Longitude, then the course leading from one to the other is East or West: As A and E being two places under the parallel of 50 gr. and differing 5½ gr. in Longitude.
But if the two places differ only in Latitude, and lie under one Meridian, as A and B, then the course is North or South.
But if the places differ both in Longitude and Latitude as AC, then the course is upon some other point so much distant from the Meridian, as is the quantity of the angle BAC.