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. The Elevation of the Pole, and Declination of the Sun being given; to find his Amplitude.

MEasure the extent CL with the Compasses in the Line of Signs, and it will reach to 34 degr. 40 min. and so much doth the Sun Rise and Set to the Northward of the East and West in the Latitude of Bristol, when his Declination is 20 deg. 30 min. North; but he Riseth and Setteth so much to the Southward of the East and West, When his Declination is so much South.

Now on the Concave-Sphere, the extent CL on the Horizon, applyed to the Line of half-Tangents, is 34 deg. 40 min. the Amplitude, as before.

If the Suns Parallel of Declination doth not meet with the Horizontal-Line HO, as in Regions far North, the Sun doth not Rise nor Set.

In the Right. Angled Spherical-Traingle LOC of the 4 Problem, having the Angle LCO, the Complement of the Latitude 38 degr. 32 min. and LO the Suns Decli∣nation 20 degr. 30 min. in 1 d. 18 m. ♊ his Amplitude by Calculation may be found thus.

The Artificial Lines by this Rule answers the same.	As the Co-Sign of the Latitude 51 deg. 28 min. LCO	979446
is to the Radius 90 degr.	10
So is the Sign of the Declination 20 degr. 30′ LO	954432
to the Sign of the Amplitude CL 34 deg. 40 min.	974986

This Rule is the common Rule Mariners make use of for the finding of the Variation of the Compass at Sea, by comparing the Coast, or bearing of the Sun, observed by an Amplitude or Azimuth-Compass at the Suns Rising or Setting, and by his bearing, found by these Rules beforegoing, the difference sheweth the Variation.

As for Example.

Admit you observed the Suns Amplitude of Rising or Setting by your Compass in the first Chap. and fifth Book of the Art of Surveying described.

And by the Compass found, the Magnetical Amplitude	45 d. 55′ compl. 44 d. 05′ N.
By the Rules beforegoing find the true Amplitude,	34 d. 40 compl. 55 d. 20′ N.
Substract the less out of the greater, the difference	11 d. 15 m. Variation.

And by reason the Magnetical Amplitude is more than the true Amplitude; there∣fore the Variation is 11 degr. 15 min. which is one Point Westerly; and if you are bound to a place that bear North of you, you must Sail upon the North by West Point; or if you bare West, you must Sail W and by S; and if South, the Course must be South and by East; or if you bear East, then the Course must be East and by North, to make good a North, or West, or South, or East Course; and so of all the rest of the Points you must allow in like manner.

2. But admit the Magnetical Amplitude observed by the Compass, were but 23 deg. 25 min. and the true Amplitude by the former Rules found to be 34 degr. 40 min. the upper Substract from the lower, the difference is 11 degr. 15 min. and by reason the Magnetical Amplitude is less than the true Amplitude, and the difference 11 degr. 15 m. which is one Point Variation Easterly; and so the North Point is the N by E Point, and NE is the NE by E, and E is E by S, and South is S by W, and W is W by N Point of your Sailing Compass, when you have such a Variation, and the Complement of the Amplitude is the Suns Azimuth from the North or South part of the Meridian, according as your Declination is. And this is sufficient for an Example to find the Vari∣ation of the Compass in any place or time.

As likewise by his Oblique-Ascension, and Ascensional difference; or by the Suns being East and West by the following Rules, or by the Suns Azimuth at the hour of Six; as likewise his Azimuth at any other time or place observed, as shall be shewn for the help and benefit of young Mariners.