Question. Suppofe two Ships in Lat. 50, diftant 200 Miles, fail both directly North into Lat. 73d. om. I demand their Distance in that Parallel.

Here we fhall ufe but the two firft Figures of the given. Numbers, because the third Figure in each Number is but fmall, viz. 2: And then by the foregoing Rule,

As 64 to 29, fo 2000 to the Distance in Lat. 73.

Their Diftance in Latitude 73, is 90 4, or (if you will avoid Fractions) 91 Miles.

CASE V. Two Ships in one Parallel, with their Diftanee in that Parallel given, and failing both directly North or South, with their Diflance in the Parallel failed, given, to find the Latitude come to.

The RULE.

This is only the former Proportion (in Cafe IV.) inverted, viz. As Distance in one Latitude to the Distance in the other Latitude, fo the given Number for one Latitude to the given Number for the other Latitude.

Question. Two Ships in Lat. 50, diftant 200 Miles, fail both directly North, till they are but 91 Miles diftant; I demand the Latitude come to?

As 200 to 91, fo 64 to the given Number for the Latititude come to.

The Quotient 29 is the two firft Figures of the given Number for the Lat. come to, viz. Lat. 73d. om.

IN

SECT. IV.

Middle Latitude Sailing Arithmetical.

N Working the feveral Cafes and Questions of Middle Latitude Sailing, we shall have Occafion to make Use of both the Tables of given Numbers; for in all Cafes or Varieties, where the Courfe, Diftance, Difference of Latitude, and Departure, are Terms either given or required, the Operation is performed by the firft Table, as in Plane Sailing; but when Difference of Longitude is a Term in the Question, (whether given or required) the fecond Table is of Ufe, as will appear by the following Examples.

CASE I. One Latitude, Courfe, and Distance given, to find the other Latitude, Departure, and Difference of Longitude.

The RULE.

By Course and Diftance find Difference of Latitude and Departure, (and confequently the other Latitude) as in Cafe I. of Plane Sailing Arithmetical; and then for the Difference of Longitude, it is found by the fecond

I 4

Table

Table thus Find the given Number for the Middle Latitude, of which you may use two or three, or four Figures, according to the Rules laid down at the Beginning of Plane Sailing, and alfo at the Beginning of Parallel Sailing Arithmetical; then to the Departure add fo many Cyphers to the Right-hand, as you intend to ufe Figures in the given Number; that Sum divided by the given Number, the Quotient is the Longitude required."

Queftion. A Ship in Lat. 50d. oom. North, fails N.W. by N. 987 Miles: I demand the Latitude come to, with Departure, and Difference of Longitude,

For the Difference of Latitude and Departure by the first Cafe of Plane Sailing Arithmetical.

Although the three firft Figures of the given Number to find your Departure for that Course be 555, yet the laft Figure being 6, I cut it off and add 1 to the third Figure, and call it 556, as in the Operation above, and fo the Difference of Latitude is 819, or rather 820, and the Departure 549, allowing one for the Fraction,

Then for the Difference of Longitude.

The Diff. of Latitude being 820 Min. or 13d 40m. the Latitude come to is 63d. 40m. and confequently the Middle Latitude is 56d. 50m. the given Nunber for that Latitude

Latitude (found by the Rules laid down in the Beginning of Parallel Sailing) is 5470; but the laft Figure being a Cypher, I cut it off, and work with the reft, as in the Rule above, and the Operation ftands thus:

547)549000(1003

⚫. 2000

359

The Difference of Longitude is 1003 Min. or 16d. 43m. Weft.

CASE II. Both Latitudes and Courfe given, to find the Departure, and the Difference of Longitude.

The RUL E.

Find the Distance and Departure, as in Case the second of Plane Sailing Arithmetical, and then find the Difference of Longitude, as in the first Cafe of Middle Latitude Sailing Arithmetical.

Note; In Middle Latitude Sailing Arithmetical, this Way of finding the Longitude answers in all the Cafes thereof, and therefore I fhall not need to mention it in the rest of the Cafes.

Question. A Ship takes her Departure from a Port in Latitude 56d. 25m. North, and fails N.N.E. till fhe finds herself to be by Obfervation in Latitude 68d. 30m. North; I demand the Distance failed, with her Departure, and Difference of Longitude.

The Difference of Latitude is 12d. 05m. or 725 Min.
For the Distance.
For the Departure.

The Middle Latitude 62d. 28m.

The given Number for 62d. 28m. is 4622

Then for the Difference of Longitude.

462)301000(651
2380

**700

238

The Diff. 785; the Departure 301; the Diff. of Longitude 651 Min. or 10d. 51m.

CASE III. Both Latitudes and Difference given, to find the Courfe, Departure and Difference of Longitude.

The RUL E.

Find the Courfe and Departure, as in Cafe IV. of Plane Sailing Arithmetical, and the Difference of Longitude, as in other Cafes hereof.

Question. A Ship in Lat. 55d. oom. fails between the North and Eaft 86 Miles, and then finds herself by Obfervation in Lat. 56d. 10m. her Courfe, Departure, and Difference of Longitude, is required.