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. XXIX. How to make a Vertical Dial upon the Cieling of a Floor within Doors, where the Direct Beams of the Sun never come.

THe greatest part, and as much as you shall use of the Vertical or Horizontal Dial, described Chap. 8. may by reflection be turned upside down, and placed upon a Cieling; but the Center will be in the Air without doors.

The first thing to do is to fasten a piece of Looking-glass, as brood as a Groat or Sixpence, set level; or a Gally-pot of Fair-water, which will set it self level being placed upon the Sole of the Window, shall supply the use of the Nodus in the Gno∣mon; and the Beams of the Sun being reflected by the Glass or Water, shall shew the Hours upon the Cieling.

Before you can draw a Figure for this Dial well, I would advise you first to find the Meridian of the Room, which may be done thus.

Hang a Plumb line in the Window, directly over the Nodus or place of the Glass; for the shadow which the Plumb-line gives upon the Floor at Noon, is the Meridian-line sought; and by a Ruler, or a Line stretched upon it, you may prolong it as far as you shall need.

Then take the perpendicular Height thereof from the Glass to the Cieling of the Room, which suppose it be 40 Inches, as DB, the Glass being fixed at D: Now from B draw the Meridian-line upon the Cieling, which shall be represenred both ways continued, as ABCK, and from D erect a Perpendicular to DC: Or let a stander by stop one end of a Thred on the Glass at D; extend the same to the Meri∣dian-line, moving the end of the s••ring shorter and longer upon the Meridian, till

another holding the Side of a Quadrant, shall find the Thred and Plummet to fall directly upon the Complement of the Latitude, which in this Example is 38 deg. 30 min. and that is the Intersection of the Aequinoctial. Then raise the Perpendicu∣lar, as DA; take a Chord of 60 deg. and from A sweep the Arch at P, and from Play down the Latitude 51 deg. 30 min. to q, and draw the Line AD.

[illustration] geometrical diagram

Then let fall a Perpendicular from C, as CEFGHI, which is the Aequinoctial Line; and so likewise draw a Parallel Line to the Meridian of 40 Inches at D. Now note, That the Hours must be drawn all one as the Horizontal Dials are.

Then draw a Line Parallel to the Aequinoctial, as KO, at what distance you think convenient, on the Cieling of the Room, which let be here 50 Inches, as CK, as you may measure by the Scale. Now for the placing of the Hours on the Cieling of the Room, you must measure how much by the Scale of Inches each Distance on the Aequinoctial Line is from C to E, and from C to F, and from C to G, H, and I, and likewise on the Parallel from K, collecting them into a Table; so will it be ready to transport on the Cieling.

Here I have made the Table.

	Inches. par.
C E	17 0
C F	38 0
C G	63 3
C H	111 4
C I	222 5
K L	27 7
K M	59 7
K N	101 0
K O	173 0
K P	385 8

So by this Table you shall find the Distance CE, which is from 12 to 1 in the afternoon, or 11 in the morning, to be 17 Inches; which you may prick upon the Cieling. Likewise KL on the Parallel, between 12, 11, and 1, will be found to be 27 Inches 7/10 parts of an Inch in 10 parts; which Hour-line mark out upon the Ciel∣ing. Then draw a straight Line through those two Points L and E; this Line conti∣nued shall be the first Hour from the Meridian, which is 11 in the morning, or 1 in the afternoon: So do for all the rest of the Hours.

Now by this you may know how far the Center is without the Window; measure it, and you will find it 31 82/100 Inches from A to B, and from B to C 52 Inches, and from C to K 50 Inches, as before. I hope now I have given the Practicioner content, in making this so easie to be understood, although I may be condemned by others.

I will give you one Example more, to find the Meridian Line on the Cieling, which is this. Fit a plain smooth Board, about a Foot square, to lie level from the Sole of the Window inwards; then neer the outward edge thereof make a Center in the Board, in the very place of Nodus, or a little under it: Then by Chap. 3. get the Meridian Line from the Glass on the Board; after you have drawn the Line on the Board upon the Center, describe as much of a Circle as you may with the Semidia∣meter of your Quadrant, which Circle shall be Horizon; then from the Meridian you may with your Degrees on the Quadrant graduate your Horizon into Degrees of Azi∣muths both ways as far as you can.

Next you may devise to make your Quadrant stand firm and upright upon one of his straight Sides, which I will call his Foot for this time; and that you may thus do, take a short space of a Ruler or Transom, and saw in one side of it a Notch perpendi∣cularly, in which Notch you may stick fast or wedge the heel of the toe of your Qua∣drant, in such sort as his Foot may come close to the Board, and the other Triangular Side or Leg may stand perpendicular upon it. Let the Foot be round, and with your Compasses strike a Circle round it: when you have fitted the Diameter of the Foot on the Meridian Line on the Board, draw a Circle round the Glass, that so you may set the edge of the Circle according as you may have need, for to lay off the Suns Altitude at every Hour. Now to find the Meridian on the Cieling, you may make a Table for the Suns Altitude every Hour of the Day, in this manner as here is for the Latitude 51 deg. 30 min. and place the Foots Diameter directly on the Meridian of the Board, and elevate the Quadrant to the Tropick of Capricorn, which in this Lati∣tude is 15 deg.

A Table for the Altitude of the Sun in the beginning of each Sine, for all the Hours of the Day, for the Latitude of 51 deg. 30 min.

Hours.	Cancer.	Gemini. Leo.	Taurus. Virgo.	Aries. Libra.	Pisces. Scorpio.	Aquari. Sagitta.	Capric.
12	62 0	58 45	50 0	38 30	27 0	18 18	15 0
11 1	59 43	56 34	48 12	36 58	25 40	17 6	13 52
10 2	53 45	50 55	43 12	32 37	21 51	13 38	10 30
9 3	45 42	43 6	36 0	26 7	15 58	8 12	5 15
8 4	36 41	34 13	27 31	18 8	8 33	1 15
7 5	27 17	24 56	18 18	9 17	0 6
6 6	18 11	15 40	9 0
5 7	9 32	6 50					11 37
4 8	1 32						21 40

Let a stander by stop on the Glass a Thred, and extend the other part straight on to the Cieling, the Thred touching only the Plane of the Quadrant, and making no Angle with it, but held parallel; and where the Thred thus extended touches the Cieling, make a Point; then the Quadrant unmov'd, elevated to 62 deg. of Altitude, and extend the Line, and make another Point as before; and between those two Points draw a straight Line, and that shall be your Meridian, and shall be long

enough for your use. Then elevate the Quadrant to 38 deg. 30 min. and hold the Thred to the Meridian on the Cieling, and where he touches mark; and cross the Meridian at Right Angles with an Infinite Line, which shall be the Aequator: So you may do as you did before. but if the Plane of the Cieling of the Wall is inter∣rupted, and made irregular by Beams, Wall-plates, Cornishes, Wainscot, or Chim∣ney-piece, and such like Bodies, I will shew you the Remedy to carry on your Hour-lines over all.

Extend the Thred from any Hour-line to the Tropick of Cancer in the Cieling, as you were taught before, and fix it there; and extend another Thred in like manner to the Tropick of Capricorn, where-ever it shall happen beyond the middle Beam, or quite beyond the Cieling upon the Wall, and fix the Threds also. Then place your eye so behind these Threds, that one of them may cover another; and at the same instant where the upper Line to your sight or Imagination cuts the Cieling, Beam, Wall, or any irregular Body, about the end of the lower Line, there shall the Hour-line pass from Tropick to Tropick: Direct any By-stander to make Marks, as many as you shall need, and by those Marks draw the Hour-lines according to your desire. This is in Mr. Palmer, pag. 202.

If the Arch of the Horizon, between the Tropicks, be within view of your Win∣dow, you shall draw the same on the Wall to bound the Parallels. The Horizon Altitude is nothing, and therefore it will be a level Line: and the Suns Azimuth when he riseth, commonly called Ortine Latitude, is in Cancer 40 deg. East North∣ward, and in Capricorn as much Southward; and these will be reflected to the contra∣ry Coasts on the Dial.