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. XI. How to make a Declining Horizontal Dial, or South erect declining from the South Eastwards 32 deg. 30 min. in the Latitude of 51 deg. 30 min.

HEre three things are required; for besides the Distance of the several hours from 12, and the Elevation of the Gnomon, which are requisite to the ma∣king of all direct and regular Dials, we must here also know the Declinati∣on of the Gnomon, which some call the Distance of the Substile from the Meridian, or the distance of the Meridian of the Plane from the Meridian of the Place. For in all Dials the Noon-line in the Meridian of the Place, projected on the Dial, and in all Horizontal or Mural Dials, not reclining or inclining, the Noon-line is a Perpen∣dicular cutting the Center of the Dial, how much soever they decline.

But declining Dials which look awry from our Meridian, have a Meridian of their own, which is called the Meridian of the Plane and the Substile (because the Stile or Gnomon stands upon it) and is indeed the Meridian of that Place where this Decli∣ning Dial would be a Vertical Dial, and where the Substile would be Noon-line; and to this Substile, the Hours of the Plane are always so conformed, that the neerer they be to the Substile, the narrower are the Hour-spaces; and contrarily, because the Meridians do cut every Oblique Horizon, that is thickest neer the Meridian of the place; and this Declining Dial being a Stranger with us, followeth the fashion of his own Country, and so hath his narrowest Hour-spaces neer his own Meridian, rather than ours: And now, as that is the Meridian of our place, which cutteth our Horizon at Right Angles, passing through his Poles, Zenith, and Nadir; so the Meridian of any Plane is that which cutteth the Plane at Right Angles, and passeth through his Poles.

Before we draw the Hour-lines in these sort of Dials, it will be very convenient to shew a general way for all Latitudes in a Diagram by it self, and how to find the Substiler Distance from the Meridian or 12 a clock Line, and the height of the Gno∣mon or Stile above the Plane. First, Draw the Horizontal-line AB, and upon the Center at C, take off your Scale with your Compasses a Chord of 60 Degrees, de∣scribe the Semicircle ADB, and with a Chord of 90 you may lay from A to D, and from B to D, so shall you draw CD from the Meridian-line of 12 a Clock; Then take the Complement of the Latitude 38 deg. 30 min. and lay from D to E, and so draw EF parallel to the Horizon AC; next take the Declination of the Dial 32 d. 30 m. and lay from D to G, drawing the Radius OG thereon, you must lay the Di∣stance EF from the Center at C, as CH. Now with the neerest distance from H to the Meridian CD, as HI, make FL; and drawing a Line from C through L, it will cut the Limb in the Point M; so measuring DM on the Line of Chords, you shall have the Substiler Distance 23 deg. 8 min. all which you may see in this Scheme following.

By Calculation,

As the Radius 90 deg.	10
Is to the Sine of the Declination SE 32 deg. 30 m.	973021
So is the Co-tangent of the Latitude 51 d. 30 m.	990060
To the Tang. of the Substiler Dist. from the Meridian 23 d. 8 m.	963081

For the height of the Stile, take the neerest Distance from H to the Horizon K, and lay the same from L to cut the Arch in N: So measure MN, you shall have on the Line of Chords the Height of the Stile neerest 31 deg. 40 min.

By Calculation, viz.

As the Radius 90 deg.	10
Is to the Co-sine of the Latitude 51 deg. 30 min.	979414
So is the Co-sine of the Declination 32 deg. 30 min.	992602
To the Height of the Stile 31 deg. 40 min.	972016

To find what Hour or how much Time the Substiler is distant from the Meridian or Inclination of Meridian.

[illustration] geometrical diagram

TAke the neerest Distance from M to FE, and lay it on the Meridian from F to O: Then take the Distance from O unto G, and lay it from O unto P on the Meridian; so the Distance from P to M, measured on a Line of Chords, will be found to be 39 deg. 9 min. or thereabouts; which in time, allowing 15 deg. for an hour, and four Minutes to a Degree, you shall have 2 ho. 36 min. 36 sec. which is the di∣stance of the Substile Line from the 12 a Clock Line, which in this Dial is between 9 and 10 of the Clock in the morning. And by Calculation,

As the Radius 90 deg.	10
Is to the Sine of the Latitude 51 deg. 30 min.	989354
So is the Co-tangent of the Declination 32 deg. 30 min.	1019581
To the Co-tangent of the Inclination 39 deg. 9 min.	1008935

Thus is shadowed a Geometrical way, and by Calculation, for any Latitude: But for one particular Latitude, Mr. Philip Staynred, which first composed the Scale and Gnomon Line, and Inclination of Meridians, and the greater and lesser Pole on the Dialling Scale, for 37 years since, as I have seen by him calculated, and the Projecti∣on Geometrical in his Study: he hath for the more ease set two Lines upon the Dial∣ling Scale, as he usually makes, to find the Substile for the Latitude of 51 deg. 30 m. against the Lines stands the Letters Sub or Stile joyned with it; so if you take from off the Substile-line the Declination of the Dial, and lay it from D unto M, which in the last Example was 32 deg. 30 min. you shall find it to reach in the Diagram from D unto M, as in the Line of Chords 23 deg for the Substile, as before. Also, the other Line noted with the word Stile, you shall likewise take from thence the Declination 32 deg. 30 min. which you shall find to reach in the Diagram from M unto N, or in the Line of Chords 31 deg. 40 min.