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that being done, you see where, and in what Proportion the Rumb cuts every Meridian and Parallel it meets with ; then in fuch Parts or Proportion you must make Points, the Meridians and Parallels of the Globular Chart ; and a Curve Line drawn through those Points (with a steady Hand, or a Bow) will be the Rumb required.
Thus suppose I would draw the N. E. by N. Rumb on the Globular Chart, in the Latitude of 20 Degrees. First I draw the Meridians and Parallels of Mercator's Projection, and from the Parallel of 20° I draw the straight' Rumb Line A B, and obferve it to cut the Parallels and Meridians it passeth over in the Points a, b, c, d, e, f, g, h, i, k, l; then I take similar or like Points in the Meridians and Parallels of the Globular Chart, and thro' them draw the Rumb required.
And after this Manner I have drawn all the Rumbs of the above mentioned Cafe on the Globular Chart ; having allo ( for the sake of the young Learner) subjoin'd a Scheme of their Projection on Mercator's ; so that by comparing both in one View, the Facility and Truth of the Matter will the more evidently appear.
Nate. It will be sufficient to project only one Quadrant of the Rumbs ; the rest falling in the fame Manner, only in different and contrary Parts of the Chart.
The Use of the Globular Chart take briefly thus in the following Problems.
To find the Latitude of any Place lying between two Parallels on the Chart.
PraEtice. If the Place lye on any Parallel defcribed, the Latitude is known by Inspection.
But if the Place lye between two Parallels described on the Chart, as suppose the Pointe, between the Parallel of ten and twenty Degrees latitude ; then with the Compasses take the Distance be, and fet from E on the graduated Meridian upwards, and the other Foot will fall on 170 oo' the Latitude required.
To measure the Degrees of Longitude on any Pa. rallel.
Practice. This is best done by the Sector, thus ; take the Distance between two Meridians on that Parallel, and set it parallel-wise from 10 to 10 on the Line of Numbers, then meafure the intermediate Distance required, and it will be the Answer.
Thus suppose I take b c on the Parallel of 10°, and apply it on the Line of Numbers, then by applying b o in the fame Manner, I find it to be 40 17'; consequently the Point O hath 24° 17' Longitude from the first Meridian A C. And though the Parallels between two Meridians might be graduated from the Equator to the Poles, yet is it not necessary
V, I demand the Difference of Longitude ?."
where and when a Sector may be had.
PROBLEM III. To describe a Rumb required from any given Point.
Practice. Suppose from the Point S, I would draw the NNE Rumb"; First, I must consider where the same Rumb (or its opposite S'S W) doth cross the same Parallel, which I find to be at O. Secondly, I measure the Distance So, by Prob. 2, and find it 20°. Then thirdly, I set of 200 on every Parallel from the Intersection of the said Rumb there with And lastly, thro’ the Points in each "Parallel by this Means found, I describe the Curve SP, which will be every where 20o Distance from the given Rumb O R ; and it will be the NNE Rumb from the Point S as required.
PROBLEM IV. To measure the Difference of Longitude made by a Ship’s Way
Practice. Suppose a Ship at T in Latitude 25° 30' fail N E by E 'till it arrive in the Parallel of 600 Latitude in
See where the Meridian passing through T cuts the Parallel of 600, which is at U; then meafure U V as directed in Prob: 2, and you will find it 719 30', the Difference of Longitude required:
To measure the Distance failed on the Rumb, and also on the Arch of a great Circle. VOL. II.
PraEtice. This is to be done by a Scale of equal Parts or Leagues on the Chart, thus ; fuppofe I would know the Distance failed from T to V, I take an 100 Leagues in my Compasses, and run it along on the Rumb TV, and by so doing find the said Distance to be very near 1580 English Leagues ; each of which contains 237. English Statute Miles.
The dotted Line from T to V is the Arch of a great Circle passing through both Places ( as being the nearest Distance between them ) which measured by the fame Scale of equal Parts will be found 1515 Leagues ; which is less than in the Rumb by 65 Leagues, or above 1505 English Miles.
To measure the Meridian Distance, or Departure.
Practice. Take an 100 Leagues in your Scale, and run it along in the Parallel of 60 from U to V, and you'll find this Parallel Distance from the Meridian or Departure to be about 920 Leagues.
Again measure the dotted Line from U to V, by the fame Scale, and you will find it to be about 850, which is 70 Leagues nearer than in the Parallel.
And these Distances being measured by a Scale of equal Parts is the greatest Excellency of this Chart. But when every thing is considered, the Preference will always be due to Mercator's Projection.
CH A P.