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.

The Ʋse of the Back-Staff or Quadrant.

SEt the Vane G to a certain number of Degrees, as the Altitude of the Sun re∣quireth; and looking through the Vane F, to the upper Edge of the Slit of the Sight of the Horizon, if you see all Skie and no Water, then draw your Sight-Vane a little lower towards E: but if you see all Water and no Skie, then put your Eye-Vane up higher towards F; and when you have done so, observe again; and then if you see the Shade lie upon the upper part of the Slit, on the Horizon-Vane, and you at the same time do see the Horizon through the Sight-Vane, then that is all you can do untill the Sun be risen higher; and tending the Sun until he be upon the Meridi∣an, you will perceive he is descending, or as we commonly say he is fallen, you will see nothing but Water; your Vanes fast in this posture, you have done observing the Sun upon the Meridian that day: Therefore reckon the Degrees from B to the up∣per side of the Vane G; to it add the number of Degrees from E to the Eye-Sight, and their Sum is the Distance of the Sun from the Zenith to the upper Edge of the Sun; to which Sum if you add 16 minutes, which is the Sun's Semidiameter, you will have the true distance of the Sun's Center from the Zenith or Complement of the Meridian Altitude. Note this, If you observe the upper Limb of the Sun by the up∣per

part of the Shade, then it is the upper Limb that gives the Shade; but if you observe the lower part of your Shade, then it is the lower side of the Sun that gives the Shade: Therefore you must substract 16 min. from what your Back-Staff gives you, and the Sum or Difference gives you the right Distance of the Sun from the Zenith. You may have the Altitude of the Sun from your Quadrant, if you work thus; from C to G is 40 deg. for the Vane stands at 20 deg. from D to F is 16 deg. being added together makes 56, the Altitude or Height of the Sun above the Hori∣zon, which you may use as you were shewn by the Fore-Staff: But in regard the English Navigators work their Observation by the Complement of the Sun's Altitude, when he is upon the Meridian, being so ready to be counted by their Quadrant; Therefore we will direct you in general, and after in particular Rules.

[illustration] geometrical diagram

The Figure of the Quadrant

First, If the Sun hath North Declination, and you in North Latitude, and the Sun upon the Meridian, South of you; then if you add the Sun's Declination to his Ze∣nith-Distance, that is the Complement of the Sun's Meridian Altitude, the Sum will be the Latitude you are in.

But if the Sun hath South Declination, you must substract the Complement of the Meridian Altitude, and the Remainder will be the Latitude the Ship is in.

If you be to the Southward of the Aequinoctial, and the Sun to the Northwards of the Aequinoctial, in such case you must add the Sum of the Declination to the Zenith-distance, and the Sum will be your Latitude South.

But if the Sun be to the Northwards of the Aequinoctial (that is, have North De∣clination)

you must substract the Declination from the Zenith-distance, and the Re∣mainder will be the Latitude South.

If you understand the fore-going Rules given of the Use of the Fore-Staff, you cannot mistake the Use of the Quadrant or Back Staff.

We will now come to Examples what are needful.