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. VIII. Having the Latitude of the Place, and the Suns Declination, to find the time when the Sun cometh to be due East and West.

IN the Parallel of Declination, the hour from Six is represented by SM; with that extent upon the Point X draw the Arch b the Ruler laid from C to the outward edge of the said Arch, cuts the Circle at (e,) the distance O e applyed to the Line of Chords sheweth 17 deg. 20 min. it converted into Time is 1 h. 9 m. 20 sec. and so much after Six in the Morning, and before Six in the Afternoon, will the Sun be due East and West; by the Concave-Sphere, if you lay a Ruler from A over M, it cuts the Limb in (e,) measure N e on the Line of Chords, and it is the same 17 deg. 20 min. the Rule by Artificial Signs and Tangents holds as by Calculation. viz.

Suppose the Latitude 51 degrees 28 min. and Declination North 20 degrees 30 min. therefore in the Right-Angled Spherical Triangle ZNM are given (1) Z N the Com∣plement of the Latitude 38 degr. 30 min. (2) N M the Complement of the Sum Decli∣nation 69 degr. 30 min. Then I say.

As the Radius 90 is in proportion	10
To the Co-Tangent of the Declination 69 degr. 30 min. NM	957273
so is the Tangent of ZN compl. of Latitude 38 degr. 32 min.	990112
is to the Co-Sign of ZNM 17 deg. 20 min. which Reduced is 1 h. 9 m. of time, as before.	947385

Which 1 h. 9 m. added to 6 h. is 7 h. 9 m. the moment in the Morning, the Sun will be due East; and if you Substract 1 h. 9 m. 20 sec. from 6 h. 00 m. and the Remain will be 4 h. 50 m. 40 sec. the moment in the Afternoon the Sun will be due West.