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. VII. By the Course and Distance, and one Latitude, To find the other La∣titude, and Difference of Longitude.

SUppose I sail S. W. 3 deg. 33 min. Westerly, 1157 Leagues, and by observation find my self in the Latitude of 13 deg. 10 min. I require the Latitude of the Place from whence I came, and the Difference of Longitude between the two Places.

For the Difference of Latitude,

As the Radius B 90 deg.	1000000
To the Distance sailed 1154 Leagues AE	306222
So is the Sine-Complement of the Course E, 41 deg. 27 min.	982083
To the D fference of Latitude 764 Leagues	288315

Extend the Compasses from the Sine of 90 deg. to 1154 Leagues; the same will reach from the Sine of 41 deg. 27 min. to 764 Leagues, which converted into Degrees, is 38 deg. 12 min. the Difference of Latitude; which added to 13 deg. 12 min. the Latitude of the last Place, the Total is 51 deg. 22 min. the Latitude of the first Place required.

The Difference of Longitude is found as before in the third Problem, saying,

As the Radius, To the Difference of Latitude inlarged 934 5/10:

So is the Tangent of 48 d. 33 m. To the Difference of Longitude in Leagues 1058, which is 52 deg. 55 min.

Now to convert the Difference of Longitude found in any Latitude into Leagues, do it after this Example.

Suppose two Places in one Parallel of Latitude, as in the Parallel of 51 deg. 22 min. whose Difference of Longitude is 52 deg. 55 min. I require the Distance of those two Places.

As the Radius	10
Is in proportion to the Compl. Sine of the Latitude 51 d. 22 m.	979573
So is the Difference of Longitude 1058 Leagues	302448
To the Distance in that Latitude 661 Leagues	282092

You must understand, That the Leagues of Longitude in any Parallel of Latitude, are in proportion to the Distance in Leagues, as the Aequinoctial is to that Parallel; or, as the Semidiameter of the one, is to the Semidiameter of the other, as was said in the Seventh Chapter.