The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

Geographical Questions. Two Ships being at Sea, their Difference of Longitude was 53 deg. Now upon a day they observed the Sun being between them; the North Ship found the Sun's Meridian Height 33 deg. and the South Ship 77 deg. the middle Latitude between them was 15 deg. North of the Aequi∣noctial Line: I demand the Angle of Position, and Distance from the North Ship to the South?

* 1.1FIrst add the two Meridian Altitudes Complement together, 33 deg. and 77 deg. Complement 57 and 13, the Sum is 70, the half Sum is 35 deg. the middle La∣titude 15; add the middle Latitude and half Sum together, it makes 50 deg. the

[illustration] geometrical diagram

North Ships Latitude; and substract the middle Latitude from the half Sum, and the Remain is 120 deg. the Latitude of the South Ship. The North Ships Latitude is laid from Q to N 50 deg. the Difference of Longitude QF 53 deg. Through F de∣scribe the Great Circle Meridian PFB, on which lay down the South Ships Latitude 20 deg. as FC, and so draw the Great Circle NCD through the Intersection of the prick'd Line IH, with the Meridian at C; for that is the Latitude of the second Ship: So the Angle of Position is NCQ, whose measure is CG on the half Tangents 48 deg. 58 min. from the South Westwards; and the Distance is NH 48 deg. 22 min. that is, 1683 ⅔ Leagues, or 5051 Miles, the nearest Distance of the two Ships, which was required. How to do it by the Tables, you have been shewed in the last Example.

Notes

• * 1.1

  Meridian Altitude.

  33 d. Compl. 57 deg.

  77 d. Compl. 13 deg.

  Sum 70

  ½ Sum 35

  Mid. Lat. 15

  Nor. Ship 50 lat.

  South Ship 20 lat.