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. XVI. How to make an East or West Reclining or Inclining Dial.

AS it hath been shewn Chap. 15. That the Base or Horizontal-line of a South Recliner lieth always in the East Azimuth; so the Base of an East Recliner lieth always in the Meridian of the Place: And as all Declining Planes lie in some Azimuth, and cross one another in the Zenith and Nadir, by Chap. 13. So these Reclining Planes lie in some Circle of Position, and cross one another in the North and South Points of the Horizon; which being considered; these East Recli∣ners, West Incliners, and West Recliners, and East Incliners, shall be made as easily as the former.

For these East Recliners be in very deed South Decliners to those that live 90 deg. from us Northward or Southward, and have one of those Poles elevated as much as the Complement of our Latitude; for the Perpendicular or Plumb-line of those Peo∣ple is parallel to the Horizontal Diameter of our Meridian.

EXAMPLE.

I Have an East Plane reclining 45 deg. which I would make a Dial.

In the former Diagram I number 45 deg. from E to F, and then lay a Ruler from N to F, and it will cut the Semidiameter ZW in 45 deg. in V. And then draw the Arch SVN, which Circle shall represent the Plane proposed.

Then the Arch of the Plane between the Horizon and the Substiler Distance is re∣presented in the Diagram by NQ, and may be found by resolving the Triangle QN P, wherein the Angle at Q is known to be Radius, and the Angle at N to be Recli∣nation, and the Angle at P the Latitude. Then work thus.

As the Radius or Sine of 90 deg. Q	1000000
Is to the Sine of Reclination 45 deg. N	984948
So is the Tangent of the Latitude 51 deg. 30 min. PN	1009939
To the Tangent of the Substile QN 41 deg. 38 min.	994887

Or upon Gunter's Ruler, Extend the Compasses from the Sine of 90 deg. to the Sine of 45 deg. the same will reach from the Tangent of the Latitude 51 deg. 30 min. to neer 41 deg. 38 min. as before, in the Line of Sines; and such is the Substiler distance.

Secondly, The Height of the Pole above the Plane may be represented by the Arch PQ, and may be found, by which we have given in the Triangle QNP: For,

As the Sine of 90 Q	1000000
To the Sine of 51 deg. 30 min. PN	989354
So is the Sine of Reclination 45 deg. N	984948
To the Sine of the Stiles Height 33 deg. 36 min. or Pole above the Plane PQ	974302

Extend the Compasses from the Sine of 90 deg. to the Sine of 51 deg. 30 min. the same Extent will reach from the Sine of Reclination 45 deg. to 33 deg. 36 min. as be∣fore, which is the Height of the Stile.

Thirdly, The Inclination of Meridians (or indeed you may call it Longitude) is here represented by the Angle PQN; for having drawn the Arch of the Meridian of the Plane SQN, or let fall a Perpendicular PQ, and that from the Pole unto the Plane, this Perpendicular shall be the Meridian of the Plane; so that from Q to N is the Distance of Inclination of both Meridians, which will be found as before: For,

As the Sine of 51 deg. 30 min. PN	989354
To the Sine of 90 deg. Q	1000000
So is the Sine of the Substiler Distance 41 deg. 38 min.
To the Sine of Inclination of both Meridians	971594

which will be found to be 58 deg. 40 min. NPQ.

Extend the Compasses from the Sine 51 deg. 30 min. to the Sine of 90; the same Extent will reach from 41 deg. 38 min. the Substiler Distance, to 58 deg. 40 min. and such is the Angle PQN of the Inclination, between the Meridian of the Place and the proper Meridian of the Plane: which resolved into time, doth make about 3 ho. 54 min. and so the Substiler must be placed neer the Hour of 8 in the morning.

[illustration] geometrical diagram

For to draw the Hour-lines on the Plane, first draw the Horizontal-line SN: Then take off your Line of Chords with your Compasses the Chord of 60 deg. from your Scale, and sweep the Semicircle: Then take off your Line of Chords with your Com∣passes the Substiler Distance, and lay it from N on the Arch to A; Then draw through the Center and A in the Arch, the Substiler Line, crossing it in the Center at Right Angles with the Line KF: Then take off with your Compasses the Height of the Pole above the Plane, or the Stiles Height 33 deg. 36 min. from the Gnomon Line of the Scale, and lay it from the Center of the Dial both ways from K to F. Then take the whole Line of 6 Hours, and sweep the two small Arches from K towards G, and the like from F toward G: Then draw the Lines KG and FG: Then extend the Compasses from G to N, and apply it to the Hour-line, and you shall find the Incli∣nation of Meridians to be as before 3 ho. 54 min. Then take 4 ho. 54 min. and lay it to O, and the same Distance from K unto O toward G; and the like do with 2 ho. 54 min. and make such marks on the Line GF and KG as you see in the Figure to

[illustration] geometrical diagram

draw the Hour-lines by; and then take off the Line of Chords 33 deg. 36 min. the Stiles Height, and lay from A to B, so drawing the Hour-lines, and you have done. And then you may see as in a Glass the West Recliner, the opposite Face, as you were shew'd before Chap. 13. that is, strike the Substiler Line, and all the Hour Lines through the Center, and the same Figures to every Hour beyond the Center, which you had on the first side, and set the Gnomon upon the Substile downwards, to behold the South Pole, and you have done both: So have you on the back side, looking through the Paper, the West Recliner and East Incliner, if you draw in the like manner, or prick on the back side, for 11 in the East 1 in the West Recliner, and so contrarily of the rest.