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.

I. Sailing 57 Leagues upon the first Rhomb, How much shall I alter my Parallel of Latitude?

THe Angle that any Point makes with the Meridian, we call the Rhomb; but the Angle that it makes with any Parallel, is called the Complement of the Rhomb. Unto every Point of the Compass there answers 11 deg. 15 min. therefore the fifth Rhomb from the Meridian makes Angles therewith of 56 deg. 15 min. namely, S. W. b. W. S. E. b. E. N. W. b. W. N. E. b. E. whose Complement 33 deg. 45 min. is the Angle of the same Rhomb with every Parallel.

Now admit I sail from A to D, S. W. b. W. 57 Leagues, I demand the difference of Latitude EA.

[illustration] geometrical diagram

First, by the following Traverse-Table, at the Head of the Table, over every Co∣lumn, is put the Figure of Halfs, Quarters, and whole Rhombs; and in one of the Columns over head is N. S. and at the foot E. W. and so is numbred at the Head, from the left hand to the right. N. S. stands for Northing. Then the Rhombs are reckon∣ed at the bottom, from the right hand back again; The Margent of the Tables shews the Leagues sailed; and over E. W. or under E. W. shews how much you have sailed East or West from the Meridi∣an. N. S. shews North or South from the Latitude. As in this Example, The di∣stance sailed is 57 Leagues on the fifth Rhomb; therefore under

3 Rhomb.
N S	W E
47 39	31 67
E W	N S
5 Rhomb.

Distance Sailed, in the Side, I enter with 57 Leagues, and in the Common Angle or Line of Meeting, I find 31. 67/100 over N. S. in the Foot; and in the next Column, over E. W. is 47. 39, as you see in the Table in the Side: So that the Difference of Lati∣tude is 31 Leagues and 67/100 Parts of a League. And if it were required to find the Departure, you see it to be 47 Leagues and 39/100 Parts. This is very plain and easie, you need no farther Precept.

By the Traverse-Scale.

EXtend the Compasses in the Line of Numbers from 100 to 57, the same Distance will reach from 5 Points to 31, and about 7/10 in the Line of Numbers.

By the Artificial Sines and Numbers on the Ruler.

EXtend the Compasses from 100 in the Line of Numbers, to 57, as before; the same Distance will reach from the Sine-Complement of the Rhomb, to the Diffe∣rence of Latitude, which is the same way as by the Traverse-Scale.

By the Tables of Artificial Sines and Numbers, by the Fourth Case of Plain Triangles.

As the Radius, which is the Sine of 90 deg. or Angle at E	1000000
Is to the Distance run 57 Leagues AD	175587
So is the Sine Complement of the Rhomb at D 33 deg. 45 min.	974473
To the Difference of Latitude required AE 31 Leag. 7/••••	150060

In like manner you may find the Difference of Latitude for any Distance run upon any Point of the Compass: But remember to add the second and third Numbers together, and from it to substract the first or uppermost.