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. XXXIV. How to Paint the Dials which you make.

ALthough I never saw any man Make a Dial, nor paint one, but what I made, painted, and guilded my self; as you may see the Piece in the Title, on which I made 26 Dials, and put in the Brass Gnomons or Stiles into the Freestone with Lead, and guilded them with all the Figures, and on the Globe drew the Aequi∣noctial Circle, the Ecliptick, the Tropicks, and Polar Circles, and the 24 Meridians, with such Constellations in the North and South Hemisphere, and Stars, in such Co∣lours as was fit to set out the Dial, with Pole Dials, and Globe Dials, Chap. 32.

To Paint and Finish the Dials, ready to be set up in their Places.

FOr to fasten the Gnomon to the Plane, be it of Wood or Freestone, you must have a small thin Chisel, or Googe, or Gimblet, as is fit for the Stile, be it round as a Rod of Iron, or a piece of Brass, let in with a Foot an inch and half, or more or less, as you will; and in the Wood make such little Mortises as just the breadth and length of the Foot of the Stile; and if it comes thorow to clinch it on the other side, then it is fast.

If it is in Freestone, your Dial drawn first in Paper, lay it upon the Plane ••s it should be; then cut out the Substile-line as neer its breadth as you can, an•• ••••ly leave so much as will just hold it together. The Paper laid as before on the Plane, with a Black-lead Pensil, or such like, draw the Substile Line where it stood in the Paper, and with a small Chisel make such Mortises in that Line as are answerable to the Foot of the Stile; and crook his Foot, and put it into its place, with a small Ladle and some Lead melted, put the Stile perpendicular with the Plane, and pour in the Lead into the Mortise until it is full; and when it is cold, then with a blunt Chisel har∣den the Lead in one Inch side of the Stile or Gnomon: And if the Mortise should be too wide, or broken, and not even enough with the Plane, then wet some Flower of Alabaster, as you may have it fit for that purpose at any Masons, and as soon as 'tis wet make a Plaster, and so smooth it, and spread it even and plain with the Plane; it is presently dry. Now have you the Stile or Gnomon as fast as if it grew there.

To Paint them, you must first Prime them: The Prime is made thus. Take an equal quantity of Bole Armoniack and Red Lead, well ground together with Lin∣seed Oyl, and well rubb'd in with a Brush or Pensil into the Plane; that being dry, for the outside Colour, it is White Lead or Ceruse well ground together with Linseed Oyl. How to know the best. Buy the White Lead, and grind it to a Powder, and put it into Water until it become as thick as Pap, and let it dry; then it is for your use.

For the Hour Lines a Vermillion, and a part Red Lead, well ground together with Linseed Oyl, with a small quantity of Oyl of Spike, or Turpentine that will dure, and make the Lines shine.

For a Gold Border, Rub the Border well with the white Ceruse Paint; be sure it be very thick in the Border: Then with Blew Smalts strew very thick the Border while it is wet; and when it is dry, wing that which is loose off, and save it in a Pa∣per; and for the rest that clings, it is fast enough.

Take Red Lead and White Lead, and as much Red Lead again as White, or Yel∣low Oker, well ground with Oyle of Spike or Turpentine; this is the Sise: Then draw with that the Figure you would have in Gold, and when it is so dry that it will not come off on your Fingers by a slight touch, lay on the Gold; and when it is thorowly dry, wing it off.

How to make a good Black, to shadow or make Figures. Grind well with Linseed Oyl Lam-black, with some Verdigrease, and that is a firm Black. The like you may do with all other Colours, as you fancy for such Work.

A Receipt for Red Ink.

FIrst, Steep one penny-worth of Brazeel Wood all night in Piss or Urin; then boil it well and strain it; then bruise two penny-worth of Cochineel, and boil it, and put in it the bigness of a Hens Egg of Roch Allom, that brings it to a colour, and then it is for your turn.

To Paint Freestone, wash the Stone with Oil, and it will last; and then all the Colours before may be used, as directed.

How to cleanse a Picture.

TAke blew Smalts, temper it in Water, and rub the Picture with it, and after wipe it with a Linnen Cloth, which Cloth should be dipp'd in Beer, or other∣wise with a dry Cloth, and it is clean.

To cleanse a Gold Border.

WAsh it with Beer, and dry it, and then cleanse it with Linseed Oyl.

Masticous is a fine Yellow, ground with some Oyl of Spike or Turpentine.

Bice is a good Blew Colouring, to be ground with Linseed Oyl and Red Lead.

And Spanish Brown will make a lasting Colour for Course Work.

To grind Gold to Write and Paint.

TAke as many Leaves of Gold as you please, Honey three or four drops; mix and grind these, and keep it in some Bone Vessel. If you will write with it, add some Gum-water, and it will be Excellent.

Some Ʋses of the following Tables of Logarithmes, Sines, and Tangents.

AMongst the many admirable ways that have been from time to time invented for propagating the Arts Mathematical, and especially that of Trigonometry, Logarithmes, invented by the Right Honourable the Lord Napier, Baron of Marcheston, may challenge the priority, and the Tables of Artificial Sines and Tan∣gents, composed by Mr. Edmund Gunter Professor of Astronomy in Gresham-College London; for that they expedite the Arithmetical Work in most Questions; Multipli∣cation being performed by Addition, and Division by Substraction, the Square Root extracted by Bipartition, and the Cubique Root by Tripartition: So that by help of these Numbers, and the aforesaid Sines and Tangents, more may be performed in the space of an Hour, than by Natural Numbers or by Vulgar Arithmetick can be in six. Now of what frequent use the Doctrine of Triangles, both Plain and Spherical, is in Astronomy (for the Resolution of which the Tables following chiefly serve) let the precedent Work testifie. And as Mr. Newton in his Mathematical Institutions, or in the same form as Mr. Vincent Wing in his Harmonicon Coeleste, are these Tables follow∣ing: And therefore I think it not amiss here in this place to insert some few Propositi∣ons, to shew the Use of the Canon and Tables of Sines and Tangents following.

PROBL. I. How to find the Logarithmes of any Number under 1000.

EVery Page in the Table of Logarithmes is divided into 11 Columns; the first of which Columns, having the Letter N at the Head thereof, are all Numbers suc∣cessively continued from 1 to 1000: So that to find the Logarithmes of any Num∣ber,

is no more but to find the Number in the first Column, and in the second Co∣lumn you shall have the Logerithme answering thereunto.

Example. Let the Number given be 415, and if it is required to find the Loga∣rithme thereof, in the Table of Logorithmes, in the first Column thereof, under the Letter N, I find the Number 415, and right against it in the next Column I find 618048, which is the Logarithme of 415. In the same manner you may find the Logarithme under 1000; as the Logarithme of 506 is 704151, and the Logarithme of 900 is 954243, &c.

But here is to be noted, That before every Logarithme must be placed his proper Characteristick; viz. If the Number consist but of one Figure, as all Numbers un∣der 10, then the Characteristick is 0; if the Number consist of two Figures, as all Numbers between 10 and 100, then the Characteristick is 1; if the Number consist of three Figures, as all Numbers betwixt 100 and 1000, then the Characteristick is 2; and if the Number consist of four Figures, as all between 1000 and 10000, the Characteristick must be 3. In brief, the Characteristick of any Logarithme must con∣sist of an Unit less than the given Number consisteth of Di••its or Places: And by ob∣serving this Rule, the Logarithme of 415 will be 2.618048, and the Logarithme of 506 is 2.704151, and the Logarithme of 900 is 2.954243, &c.

PROBL. II. A Logarithme being given, to find the Absolute Number thereunto belonging, by the former Observation; the Characteristick will declare of what Number of Places the Absolute Number consisteth.

Example. Let the Logarithme given be 2.164353; now because the Characteri∣stick is 2, I know by it the Absolute Number consisteth of three places, and therefore may be found in the second Column of the Logarithme Tables, having 0 at the top thereof, against which I find 146, which is the Absolute Number answering to the Logarithme of 2.164353.

PROBL. III. How to find the Logarithme of a Number that consisteth of four Places.

You must find the three first Figures of the given Number in the first Column, as before, and seek the last Figure thereof amongst the great Figures in the head of the Page; and in the common Area or meeting of these two Lines is the Logarithme you desire, if before it you add or prefix its proper Characteristick.

Example. Let it be required to find the Logarithme of 5745; I find 574, the three first Figures, in the first Column, and 5, the last Figure, in the head of the Table; then going down from 5 in the head of the Table, until I come against 574 in the first Column, there I find 759290, before which I place 3 for the Characte∣ristick, which is 3.759290, and that is the Logarithme sought for.

PROBL. IV. Any Number of Degrees and Minutes being given, to find the Artificial Sine and Tangent thereof.

Admit it were required to find the Sine of 21 deg. 24 min. I turn to the Sines in the Table, and in the head thereof I find Degrees 21; then in the first Column (under M) I find 24, and right against it is 9.562146 for the Sine, and 9.593170 for the Tangent of 21 deg. 24 min. But suppose it were required to find the Sine or Tan∣gent of 56 deg. 35 min. look for all else under 45 deg. are found in the head, and the odd min. in the left hand; and all above 45 deg. are found in the foot of the Table, and the min. in the last Column toward the right hand; as in this Example the Sine of 56 deg. 35 min. is 9.921524, and the Tangent is 16.180590.

PROBL. V. If any Sine or Tangent be given, to find what Degrees and Minutes answer thereunto.

Suppose 9.584663 were a Sine given, I look for the Number in the Table of Sines, and I find it stand against 22 d. 36 m. and therefore is the Sine thereof. As admit 9.624330 were a Tangent given, look for the Number in the Column of Tangents, and I find stand against it 22 d. 50 m. The same must be done for Sines and Tangents in the foot of the Tables.

* 1.1Cuncta fluunt omnisque vagans formatur Imago. Ipsa quoque assiduo labuntur tempora motu.

All things pass on: Those Creatures which are made Fail, and by Time's assiduate motion fade. Much like the Running Stream, which cannot stay, No more can the light Hours that poste away. But as one Billow, hast'ning to the Shore, Impels another, and still that before Is by the following driv'n; so we conclude Of Time, it so flies, and is so pursu'd. The Hours are always new; and what hath been Is never more to be perceiv'd or seen: That daily grows, which had before no ground; And Minutes, past once, never more are found.

* 1.2Labitur occulte fallitque volubilis aetas.

The fretting Age deceives, and stealing glides; And the swift Year on loose-rein'd Horses rides.

Quid non longa dies? quid non consumitis Anni?

Notes

• * 1.1

  Ovid. lib. Met.
• * 1.2

  Lib. Eleg. 1.