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. XV. To find the Altitude of the Sun by the Shadow of a Gnomon set Perpendicular to the Horizon by Scale and Compasses; as also by Calculation.

VVIth your Compasses on a piece of Board, describe the Circle ABCD, place it Horizontal with a Gnomon in the Centre O, cross it with 2 Diameters; then turn the Board, until the shadow be upon one of the Diameters, at the end of the shadow make a Mark, as here at E; lay down also the length of the Gnomon-Pin or Wire from the Centre on the other Diameter from O to F, draw a right-Line from E to F, as EFH; then with the Chord of 60 deg. sweep the Arch GH upon E as a Centre; apply the distonce GH the Arch to your Line of Chords, and that will give you the Altitude of the Sun required, as in this Example will be 52 deg. 53 min.

[illustration] geometrical diagram

As the parts of the shadow 28	144715
are to the parts of the Gnomon 37	156820
So is the Radius 90 deg.	1000000
to the Tangent of 52 deg. 53 min.	1012105

So the Pin or Gnomon OF being 37 parts, and th•• shadow OE 28, such equal parts, the Altitude will be found to be 52 degr. 53; or ••••e Gnomon being 28, and the shadow 37 parts, the Altitude will be IK 37 d. 07 m. or the shadow being 83, the Gnomon or Staff 100, the Tangent of the Angle will be 50 deg. 18 min. 20 the Alti∣tude of the upper edge of the Sun or Angle HEG; from which, taking the Semi-dia∣meter of the Sun 16 m. 27″, there remains 50 d, 1′ 59″ the true Altitude of the Centre of the Sun.

After this manner, if you observe the greatest Meridian-Altitude of the Sun the 11 of June, and 10 of December, you shall by the difference of them find the distance of the Tropicks; the greatest Declination of the Sun, and Elevation of the Equator, and La∣titude of the Place.

As for Example.

At London the greatest Meridian-Altitude of the Sun is 61 deg. 59″ 30″, and the least 14 deg. 56′ 30″.

The Suns greatest Meridian-Altitude taken June 11, is	61 d. 59:30″
The Suns least Meridian-Altitude taken December 10	14:56:30
The distance of the Tropicks, take the half of	47:03:00
And it is the Suns greatest Declination, Substracted from the Alt.	23:31:30
Leaves the Elevation of the Equator,	38:28:0
Whose Complement is the Latitude of the Place,	51:32:0