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. IV. How to make the South Aequinoctial Dial, or Polar Plane.

THe Aequinoctial Dial we call that which hath his Poles in the Aequinoctial Circle, of which there be three kinds.

1. The Direct or South Aequinoctial Dial, which faceth the Meridian directly, not looking from him to the one side more than to the other, having his Poles in the Intersections of the Aequinoctial and Meridian.

2. The East or West Aequin••••tial Dials, which may also be called Aequinoctial Horizontal Dials, for an Horizontal Di••l declaring just 90 Degrees from the South or North, becomes an Aequ••noc••ial Dial, as well as Horizontal, because there is his Polar height, upon the Intersection o•• the Horizon with the Aequinoctial: and though this Dial be of kin to both, yet his Gnomon shews that he should be sorted rather with the Aequinoctial Dials, than with the Horizontal. These two sorts are regular, having the Poles in the four notablest Points of the Aequator. The third is somewhat irregular, but may be brought to Rule.

How to make the first of these, draw the Horizontal Line AB, and about the midst at C let fall the Perpendicular CD, which is the Meridian or 12 a clock Line. Let CD be equal to a Chord of 60 Degrees, or the Tangent of three hours, and through D draw the Line FE, parallel to AB; make also DE and CB equal to D, so have you a true Square CDEB. Now take one hour with your Compasses off your Scale, and lay the same both ways from E towards B and D, as E 1. Do the like with two hours, and draw the pricked Tangent-lines from C to these Marks.

Next, Let the length or height of the Gnomon or Stile be GH, equal to C••, or 3 hours; so drawing a Line through GH, parallel to the Horizon, you shall find it cut the former Lines drawn to the Center C, in the Points l, m, n, o, p: through which Points, if you draw Parallel-lines to the 12 a clock Line CD, you shall have all the afternoon hours as far as V: and the morning hours must be drawn in like manner and distance, to the left hand or West side, beginning from 7 in the morn∣ing unto 12, as in the Figure following.

Note, that the height or length of the Stile is always 3 hours from the Meridian, as you see HG, which you may make with Copper or Brass Plate, or Iron, in form as you see shadowed, whose breadth on the top is here HR, which may be made more or less as you please.

This Dial will serve in any Latitude, if the Plane be placed parallel to the hour of 6, so that the Plane be even with the Pole of the World.

[illustration] geometrical diagram

How to calculate the Height of the Stile, and the Points of Hour-distance from the Meridian.

SUppose the length of the Horizontal Line AB or FE be 12 Inches, and that it were required to put on all the Hours from 7 in the morning to 5 in the even∣ing; here we have 5 hours and 6 inches on either side of the Meridian, ••herefore I allow 15 Degrees for an hour. The Rule to find the height of the Stile is,

As the Tangent-compl. of the given Hour 15 deg.	1057194
Is to half the Horizon or Distance from the Meridian 6 inches	277815
So is the Tangent of 45 Degrees	1000000
To the ••eight of the 〈…〉〈…〉 inches and parts	220621

And likewise the distance of the Hour points of 9 and 3 from the Meridian will be 1 61/100, or 1 inch and 61 parts of 100.

How to find the length of the Tangent between the Substile and the Hour-Points.

HAving found the length of the Stile in our Example to be 1 inch 61 parts of 100, then in this Example, as we find the first Hour, so find the rest.

As the Tangent of 45 deg.	1000000
Is to the Tangent of the Hour from the Meridian 15 deg.	942805
So is the height of the Stile 1 61/100 inches	220621
To the length of the Tangent-line between the Meridian or Sub∣stiler 43/100 inch	163426

Hours	An. Po.	Tang.
deg.	mi.	In.	par.
12		0	0	0	0
11	1	15	0	0	43
10	2	30	0	0	93
9	3	45	0	1	61
8	4	60	0	2	79
7	5	75	0	6	0
6	6	90	0	Infinit.

and the Hour-point of 1 and of 11 a clock. And so of the rest, take them off a Scale of an Inch divided into 100 parts, and prick them from C and D both ways to BA and EF, and draw the Hour-lines parallel to the Meridian; and so do with the rest, until it be finished, as you may see by the Table.