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.

PROBL. V. Both Latitudes and the Meridian Distance of two Places being given, To find the Difference of Longitude, and Course and Distance on the True Sea-Chart.

THis is a most useful Problem, when the Mariner hath cast up his Traverse: Sup∣pose a Ship sail upon the S. W. Quarter of the Compass, from Latitude 51 deg. 22 min. unto Latitude 13 deg. 10 min. and the Departure from the first Meridian to the Westward 865 Leagues.

You must find first the Difference of Latitude inlarged, as is before-directed in the first Problem 934 5/10.

As the true Difference of Latitude AB 764 Leagues	288309
Is to the Meridian-distance or Departure BE 865 Leagues	293701
So is the Difference of Latitude inlarged AC 934 5/10 Leagues	297057
To the Difference of Longitude in Leagues 1058 CD	590758
	302449

By the Line of Numbers.

EXtend the Compasses from AB the true Difference of Latitude 764 Leagues, to BE 865 Leagues Meridian-distance; the same Extent will reach from AC. 934 5/10 Leagues the Difference of Latitude inlarged, to the Difference of Longitude 1058 Leagues; which laid off upon the Parallel-Line from C to D, is the Point and Place of the Ship in Mr. Wright's or Mercator's Chart.

As the true Difference of Latitude 764 Leagues AB	288309
Is to the Meridian-distance 865 Leagues BE	1293701
So is the Radius 90 deg.	10,
To the Tangent of the Course 48 deg. 33 min. at A	1005392

By the Artificial Lines on the Scale.

EXtend the Compasses from AB 764 Leagues, to BE 865; the same Distance will reach from 90 deg. to the Tangent of 48 deg. 33 min. that is, 4 Points and above a Quarter from the South Westward, that is, S. W. ¼ Westerly, the Course the Ship hath kept.

As the Sine of the Course at A, 48 deg. 33 min.	987479
Is to the Radius 90 deg.	10
So is the Departure from the Meridian 865 Leagues	1293701
To the Distance sailed AE 1154 2/10 Leagues	306222

By the Scale.

EXtend the Compasses from the Sine of 48 deg. 33 min. at A, to the Sine of 90 deg. the same Extent will reach from 865 Leagues BE, to 1154 Leagues AE, the Distance sailed.