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.

CHAP. III. How to make the Polar Dial, and how to place it.

THe Plane of the Polar Dial lieth in the Aequinoctial, where the 12 chief Meridians or Hour-circles divide both the Aequinoctial and this Plane into 24 Hours or equal parts; the Gnomon stands upon the Center at Right An∣gles with the Plane.

First draw the Horizontal Line AB, and cross the same at Right Angles with the Line CD; now on the Center at G, with the Chord of 60 Degrees, or with the Tangent of three hours, you may describe the Circle ACBD, and about it make the Square EFHI; then take out of the Hour-line one Hour, and lay it from each corner, as EFHI both ways: also do the like with two hours as you see done, and from the Center at G draw Lines to those Hour-points: so shall you have the Hour-lines in the Aequinoctial Dial; CD being the Meridian or 12 a clock Line, and AB the East and West Line, serving for 6 in the morning at B, and 6 in the afternoon at A, and so number the rest of the Hours in order: You need draw no more hours than from 4 in the morning unto 8 at night, for this Latitude of Bristol, being neer 51 d. 30 min.

For the Gnomon or Stile, you must have a straight Pin or Wyre set upright in the Center, of such length as you see convenient; but if you will have it of such a length as may neither be too short nor too long, then take this Rule.

How by Calculation to find the length of the Stile, and Semidiameters of the Parallels of Declination.

IF it were required to proportion the Stile to the Plane, suppose the Semidiameter of the greatest Parallel upon the Plane were but 6 Inches, and the Parallels should be the 5 d. of Declination, the Rule is general.

As the Tangent of 45 deg.	1000000
Is to the Tangent-parallel of Declination 5 deg.	894195
So is the Semidiameter of the Plane 6 inches OA	277813
To the length of the Stile 53 parts	172010

which shews that the length of the Stile must be 53/100 parts of an Inch divided into 100 parts.

How to find by the length of the Stile, the Semidiameter of the Pa∣rallel Circles of Declination.

SUppose the length of the Stile above the Plane to be 10 inches, and you were to find the Semidiameter of the Tropick, whose Declination is known to be 23 deg. 30 min. the Rule is for this and any other Declination,

As the Tangent of 45 deg.	1000000
Is to the length of the Stile 10 inches	100000
So is the Co-tangent of Declination 23 deg. 30 min.	1036169
To the Semidiameter of his Circle 23 inches	136169

which shews the Semidiameter of the Tropick to be 23 inches: So if the Declination be 20 d. the Semidiameter will be 27 inches 47/100; if 15 d. then 3732/100; if 10 d. then 56 71/100; if 5 d. then 114 305/1000; and so of any other height of the Stile: as admit it were 53/100 parts of an inch high, then the Semidiameter of 23 deg. 30 min. would be 1 21/100, and for 20 deg. it will be 1 57/100, and for 15 deg. 1 96/100; if 10, then 2 98/100; if 5 deg. then 6 inches; if Stile be 13/100 and 75/100, the Semidiameter 23 deg. 30 min. is 37/100 parts, as you may see the Figure makes all plain; and so of any other.

[illustration] geometrical diagram

Of all Dials this is the plainest; for it is no more but divide a whole Circle into 24 equal parts: and this is the very ground to all the rest.

With this Dial, the Hour-lines being equally divided into 24 equal parts, on the inner circle you may make a Mariners Compass, with the 32 Points drawn upon it, to know in all Latitudes whether the Moon being upon such a Point maketh High-wa∣ter; or upon what Point the Moon must be, when at those Places set together it ma∣keth High-water or Full-Sea.

For to know upon what Point the Moon is, may be done two manner of ways; by setting it by the Compass, or by reckoning according to the age of the Moon, and the Hour of the day. The setting according to any Point, may not be done with a common flat Compass as the Mariners steer by (as many, wanting better reason, think they may, to their great mistake) by reason it doth only divide the Horizon into equal Points, and sheweth in what Vertical Circle or Azimuth the Sun or Moon stands: But this must be done with a Compass, which being elevated according to the Superficies of the Aequinoctial, divideth the Aequinoctial so likewise into equal parts, as the common flat Mariners Compass doth divide the Horizon. Such an Aequinoctial Compass, with a Dial in, as abovesaid, is of fashion as hereafter fol∣loweth pourtrayed. Whereof the Wheel ABC sheweth the Superficies of the Aequinoctial, the Wyre ED the Axle-tree of the World. The foresaid Wheel must be all alike marked on both sides, as well under as above, with the 32 Points of the Compass, and with twice 12 Hours: and right against the East and West at Land M, must so hang upon two Pins, as upon an Axletree, that it may be turned

[illustration] geometrical diagram

up and down, and the Wyre at the under end at D, by the Quadrant FDG, may be set unto any height of the Pole. If then you set such a Compass with the under bottom level, the Line HK North and South, viz. H to the North, and K to the South, and the under end of the Wyre right against such a Degree of the Quadrant FG, as the height of the Pole that you find your self in, then shall the Wheel ABC stand equal with the Superficies of the true Aequinoctial, and the Wyre ED with the Axle∣tree of the World; and the setting by such a one, and a common Compass, giveth great Difference. And the neerer the Aequinoctial, the greater; as may be understood by the Examples following.

EXAMPLE I.

IN the height of 50 deg. or thereabouts, the Sun being in the beginning of Cancer, at his greatest Declination to the North, by a common Compass cometh not before half an hour after seven of the Clock to the East, and at half an hour after four to the West; that is, he goeth from the East to the South and round to the West in nine hours; but from the West through the North, until again in the East, in 15 hours.

EXAMPLE II.

IN the height of 30 deg. he cometh a little before half an hour past nine of the clock to the East, and a little after half an hour past two of the Clock in the West, and so goeth in less than five hours and a half from the East through the South to the West; but from the West through the North, until again in the East, he go∣eth more than 18 hours. Thirdly, Being under the Line, and the Sun having no Declination, he ariseth in the morning right in the East, and so rising higher and higher, continueth East until that he goeth over our heads through the Zenith into the West; and so continueth West, still going down West, until he cometh again to the Horizon: and so according to a flat Compass he is the one half of the day East, and the other West, without coming upon any other Point. It is not so with this Aequi∣noctial Compass. The Sun and Moon go always a like time on every one Point of the Compass, to wit, from the East to the South 6 hours, from the South to the West 6 hours, from the West through the North to the East in twice 6 hours.

This Dial will serve for all Latitudes, if you put the end of the Wyre at D, to the height of the Pole or Latitude of the place as beforesaid; so the shadow of the other end at E will fall upon the Hours and true Points of the Compass, all the time the Sun is to the North of the Aequinoctial; but when the Sun is to South of the Aequi∣noctial, you must look for the Hours and Points of the Compass upon the under side of the Dial.