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. III. The Latitude of two Places, and their Distance given; To find the true Course and Point, or Place you are in, by Mercator's Chart.

ADmit I sail from the Island of Lundy, in the Latitude 51 deg. 22 min. in the Southwest Quarter of the Compass, 1154 2/10 Leagues; and then find my self in the Latitude of 13 deg. 10 min. I would know what Point of the Compass I have sailed upon, and my Difference of Longitude to the Westward.

The Difference of Latitude AB is 38 deg. 12 min. which reduced into Leagues is 764 Leagues.

As the Distance sailed 1154 2/10 Leagues AE	306226
Is in proportion to the Radius 90 deg.	10
So is the true Difference of Latitude 764 Leagues AB	288309
To the Sine-Complement of the Rhomb 41 deg. 27 min. at D	982083

that is, S. W. ¼ W. or Southwest 3 deg. 33 min. Westerly, the Course that the Ship hath sailed upon.

Extend the Compasses from 1154 Leagues the Distance, to the Sine of 90; the same Distance will reach from the Difference of Latitude 764 Leagues, to 41 deg. 27 min. the Co-sine of the Rhomb: The Sine is 48 deg. 33 min. that is, 4 Points and above a Quarter from the South Westward from the Meridian.

Secondly, For the Difference of Longitude.

Find by the First Problem the Difference of Latitude inlarged, as is there dire∣cted, 934 5/10 Leagues: Then it is,

As the Radius 90 deg.	10
To the Difference of Latitude in Parts 934 5/10 AC	297057 Inlarged.
So is the Tangent of the Rhomb 48 deg. 33 min. A	1005395
To the Difference of Longitude in Parts 1058 Leagues	302452

Extend the Compasses from the Sine of 90 deg. to the Difference of Latitude inlar∣ged 934 5/10 Leagues; the same Extent will reach from the Tangent of the Course 48 deg. 33 min. to 1058 Leagues: which laid off from C to D, shall be the Point or Place in Mercator's Chart where the Ship is.

Or, 1058 Leagues ⅓ converted into Degrees, by dividing by 20, the Quotient is 52 deg. 55 min. the Difference of Longitude required.