The description and uses of the general horological-ring: or universal ring-dyal Being the invention of the late reverend Mr. W. Oughtred, as it is usually made of a portable pocket size. With a large and correct table of the latitudes of the principal places in every shire throughout England and Wales, &c. And several ways to find a meridian-line for the setting a horizontal dyal. By Henry Wynne, maker of mathematical instruments near the Sugar-loaf in Chancery-lane.

THE DESCRIPTION and USES Of the General HOROLOGICAL-RING: OR Universal Ring-Dyal.

BEING The invention of the late Reverend Mr. W. Oughtred, as it is usually made of a portable pocket size. With a large and correct Table of the Latitudes of the principal Places in every Shire throughout England and Wales, &c. And several ways to find a Meridianline for the setting a Horizontal Dyal.

By HENRY WYNNE, Maker of Mathematical Instruments near the Sugar-loaf in Chancery-lane.

London, Printed by A. Godbid and J. Playford,s for the Author, 1682.

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TO THE READER.

I Formerly published half a Sheet on this Subject, and having disposed of all I printed, I found my self necessitated to Print more, to gratify those who bought the Instruments of me, but considering with my self the scantiness of that paper, I took the pains to write a larger which should be more effectual, and as I hope will give better satisfaction. 'Tis confest that there is very little new in this (as in most other Books written now a days) but what may be found among former Authors. My chiefest care herein hath been to collect and alter so that it might serve my present purpose. As for the Instrument it self, being carefully made and graduated as is here described, I know of none for Portableness, Universality, and exactness, that doth exceed it, I mean with respect to its finding the hour, whereby it becomes absolutely useful for any Gentleman to carry in his pocket, or to rectify his Watch or Pendulum by it, &c. I have endeavoured to be as plain as possible for the sake of young beginners, that the reading of this might Create in some a farther Inclination to the Mathematicks, which I heartily wish may flourish not only as they are my Trade, and consequently it is my Interest to promote them, but because they are of so great and general use and advantage to the Kingdom.

H. W.

THE DESCRIPTION and USES Of the General HOROLOGICAL RING: OR Universal Ring-Dyal.

1. Of the Name.

THis Instrument serveth as a Dyal to find the hour of the day, not in one place only (as most sorts of Dyals do) but generally in all Countries whether Northern or Southern; and therefore it is called the General Horological Ring, or Vniversal Ring-Dyal.

2. The Parts.

It consists of these parts, viz. 1. A little Ring and its slider to hang it by. 2. Two circles which fold one within the other. 3. A Diameter a cross in the middle. 4. To this Diameter there is another slider.

3. The Name of each part.

The names given to the parts are: 1. The little Ring and its slider is called the Cursor of the Meridian, and is represented (figl.) by the letter Z. 2. Of the two Circles, the outermost M M M M, is called the Meridian, and the innermost Ae Ae Ae Ae, is called the Aequinoctial. 3. That which crosseth the middle noted with A A is called the Bridge, or more properly the Axis. 4 The slider within it noted C is called the Cursor of the Bridge or Axis.

4. The Divisions on each part.

One side of this Instrument according to fig. I. is thus divided. 1. The Cursor of the Meridian hath but one division or Notch as at O. 2. One half of the Meridian is divided into twice 90 degrees, which are again subdivided into halfs, and these halfs are distinguished from the Degrees, by a shorter line, these Degrees are numbered at every ten, from their middle O both wayes, by 10, 20, 30, &c. to 90, and in these Degrees are the Latitudes of places reckoned when you would find the hour of the day. 3. The Aequinoctial is divided into 24 hours, and each hour is subdivided into eight parts, viz. halfs, quarters, and half quarters, and some of them have the hours divided into 12 parts, and then every division stands for five Minutes of time, whereof 60 make one hour, these hours are numbred with I. II. III. &c. to twice XII. from the two opposite points in the Meridian where this Circle is fastned. 4. On this side the Axis is divided into months and dayes, every division expressing 2 days, except in June and December, at which time the alteration of the Suns course is almost insensible for several days together, these Months are known on one side the slit by these Letters, I. F. M. A. M. I. Signifying, January, February, March, April, May, June, on the other side by these, I. A. S. O. N. D. for July, August, September, October, November, December. 5. The Cursor of the Axis hath a little hole through it and a line a cross the hole, which line when it is used is to be set to the day of the Month.

The other side according to figure II. hath only the Meridian and the Axis divided 1. The Meridian hath a quadrant or 90 Degrees divided on it, whose center is at H. These Degrees are again subdivided into halfs, and this I call the Quadrant of Altitudes, it serving to give the Altitude of the Sun, by the shadow of a pin, or such like wire, which shall be stuck upwright in the Center or hole H. 2. The Axis on that side the slit D is divided into twice 23 ½ and numbered both ways from the middle O by 10, 20, &c and this is called the Line of Declination, its use being to give the Declination of the ⊙, &c. On the other side the slit R, are divided four hours and a half, which are again subdivided, Numbred by IIII / 8 V / 7 VI / 6 VII / 5 VIII / 4 and this line is to shew the Sun's rising and setting at London, but because it is particular this Line is left out in most Dyals. The Cursor on this side as on the other hath the little hole and a line a cross it.

Besides these divisions on each side, on the inside the Aequinoctial, in the middle, is a Line upon which is graduated the 24 hours, and parts agreeable to those on the side described in fig I.

Note that the Instrument thus made is general, and will serve wheresoever you are, and therefore most proper for Seamen and those that Travel far. But for such as shall use them about these his Majesties Dominions, it will be sufficient to have but one Quadrant of Latitudes graduated, and no more than 18 hours or thereabouts, viz. from 3 in the morning to 9 at night, and then the Instrument may be afforded so much the cheaper.

Vses of the Instrument.

THe Principal Uses of this Instrument (although larger may be made to perform many more) are as followeth. 1. Knowing the day of the month to find the Suns Declination. 2. To find the Altitude of the Sun at the Meridian and all Hours. 3. By knowing the Suns Declination and Meridian Altitude, to find the Latitude of any place. 4. To find the hour of the day. 5. To find at what time the Sun rises and sets on any day at London or any other place lying under the same Latitude. 6. To find what days and nights throughout the year are equal.

USE I. To get the Suns Declination by knowing first the day of the month.

Explanation.

THe Sun moves not alwayes in the Aequinoctial, but Declines from it sometimes toward the North, and sometimes towards the South, every day, either moving in it or in Circle parallel to it, this diversity of motion is called the Suns Declination, now about the 10 day of March and 13 of September the Suns course is in the Aequinoctial, and then he is said to have no declination, and from the 10 of March to the 13 of September, the sun moves on the North side the Aequinoctial, and it called his Northern Declination, also from the 13 of September to the 10 of March his motion being on the South side, is called Southern Declination. By this variety of the Suns motion, is caused the diversity of Seasons and inequalities of day and night. Note also, that the greatest declination on either side exceeds not 23 Degrees and ½. Now to find it,

The Rule is:

Slide the Cursor of the Axis to the day the month, and then turn it on the other side, and the division crossing the same hole will shew the Suns Declination in the Line D. Note that the Axis may be turned without turning the whole Dyal.

Example 1.

March the 10, I slide the Cursor to the day of the month, and turning the other side, the division stands at O, which shews the Sun hath no Declination that day, but moves in the Aequinoctial.

Example 2.

April the 8, I slide the Cursor to the day of the month, and turning the otherside, the division shews 11 Degrees to be the Suns declination on that day Northward.

Example 3.

October the 20, the Cursor being set to the day, on the other side it will shew 14 Deg. for the Suns declination on that day to the Southward.

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USE II. To find the Suns Altitude on the Meridian and all Hours.

Explanation.

THe Altitude or height of the Sun is the the number of deg. contained between the middle or Center of the Sun, and the Horizon or Circle which bounds our sight, and the Meridian Altitude is its height every day just at 12 a Clock, the Sun at that time coming to touch the Meridian. To find it,

The Rule is:

When the Sun shines slide the division on the Cursor of the Meridian to the beginning of the Degrees in fig. I. marked with O, then turn the Dyal and stick a wire or pin upright in the hole H, fig. II. and holding it by the little Ring turn it gently towards the Sun, so that the shadow of the Pin may fall among the Degrees in the Quadrant of the Altitudes, now the Deg. whereon the shadow falleth is the Suns Altitude at that time, but to know the Meridian Altitude you must observe the Suns height just it 12, now that you may be sure to have it right make several observations just about 12, and the greatest is the truest, for as the Sun all the morning from its rising grows higher and higher untill it comes to the Meridian where it is highest, so having past the Meridian, all the Afternoon it grows lower and lower until it sets: Wherefore the Suns greatest Altitude on any day is the Meridian Altitude for that day.

Examples.

deg. m. March the 10th. the Suns MeridianAltitude, at Londonwill be found by the foregoing Rule to be 38 28 April the 8th. 49 28 October the 20th. 24 28 June the 11th. 61 58

Now before I proceed further to shew the uses, it will be necessary to explain some terms in Astronomy, such as I shall here make use of, that the young Practitioner may with more ease understand what follows.

1. Degrees and Minutes.

And first what is meant by Degrees and Minutes. All Circles according to Astronomy are conceived to be divided into 360 parts, which are called Degrees, every Degree is subdivided into 60 Minutes, every Minute into 60 Seconds, &c. So that one Degree is the three hundred and sixtieth part of a Circle, and one Minute the 60th part of a Degree, &c. Now the whole Circle containing 360 Degrees, the half must contain 180 deg. the Quadrant, or quarter part of a Circle, contains 90 deg. so likewise one deg. containing 60 Minutes, 45 Min. are 3 quarters, 30 Min. are one half, 20 Min. one third part, 15 Min. are one quarter, 12 Min. are one 5 part, 10 Min. are one 6 part, 5 Min. are one 12 part, &c. On the Meridian of the Dyal Fig. I. there are two Quadrants, or twice 90 Deg. graduated, one of which next N P is called the Northern Quadrant of Latitudes, and serves for those places whose Latitudes are on the North side the Aequinoctial, the other is the Southern Quadrant, and serves in South Latitudes.

2. Meridian.

It is a great Circle imagined in the Heavens, lying directly North and South, dividing them into two equal parts, the Eastern and Western, passing through both Poles, and the Zenith and Nadir; to this Circle when the Sun cometh at all times it is noon or midnight, and note that every place hath a several Meridian, except such as ly directly North and South one from the other.

3. Poles.

The Poles are two imagined points in the Heavens opposite to each other, one North the other South.

4. Axis.

A Right Line imagined to run from one Pole to the other, is called the Axis.

5. Zenith.

The Zenith or Vertex is the Point in the Heavens directly over our heads.

6. Nadir.

The Nadir is the opposite Point to the Zenith, it being directly under our feet.

7. Equinoctial.

The Equinoctial is a great Circle imagined to run directly East and West, it exactly crosseth the Meridian, and lyeth in the middle between the Poles, and divideth the Heavens into two equal parts, the Northern and Southern, when the Sun moves in this Circle, which is twice a year, the days and nights are of an equal length throughout the world.

8. Tropicks.

The Tropicks are two lesser Circles dividing the Heavens into two unequal parts, they are Parallel to the Equinoctial, and distant from it 23 deg. 30 min. one on the North side of it the other on the South, these Circles are the utmost bounds of the Suns Declination.

9. Latitude and Eleva •••• of the Pole.

The Latitude of any 〈◊〉 is the Number of Degrees contained between the Zenith of that place and the Aequinoctial, which Degrees are counted in the Meridian, either on the North or South side of the Aequinoctial, according as the place is situated. This Latitude is always equal to the elevation of the Pole, which is the number of Degrees in the Meridian contained between the Pole and the Horizon; thus those that live under the Aequinoctial are said to have no Latitude, and those that live under the Pole, if any such there be, are in 90 Deg. of Latitude; hence also it is manifest, that those places which are situate directly East and West one from the other, have one and the same Latitude.

10. Colatitude.

The Compliment of the Latitude is the number of degrees contained between the Zenith and the Pole, which is also the same with the distance between the Aequinoctial and the Horizon, or it is so much as the Latitude wants of 90 Deg. for subtract the Latitude from 90, the remainder is the Colatitude.

USE. III. By knowing the Suns Declination and Meridian Altitude to find the Latitude.

The Rule.

If the Suns declination be North, subtract it from the Meridian Altitude, and the remainder is the Colatitude, but if the Suns Declination be South add it to the Meridian Altitude, and the Sum shall be the Colatitude, which subtracted again from 90 Deg. the remainder is the Latitude.

Example 1.

March the 10. the Sun hath no Declination, and I find the Meridian Altitude at London, to be 38 deg. 28 min. therefore 38 deg. 28 min. subtracted from 90 deg. the remainder is 51 d. 32 m. the Latitude of London, and by this we see when the Sun is in the Aequinoctial, its Meridian Altitude is equal to the Compliment of the Latitude.

Example 2.

April the 8. the Suns declination is 11 deg. North and its Meridian Altitude 49 deg. 28 m. now subtract 11 deg. from 49. 28. there rests 38 deg. 28 min. which subtracted again from 90 there rests 51 deg. 32. min. the Latitude required.

Example 3.

October the 20. the Suns Declination is 14 d. South, and the Meridian Altitude is 24 d. 28 m. then add 14 d. to 24 d. 28 m. the sum is 38 d. 28 m. which subtracted from 90 d. there rests 51 d. 32 m. as before.

Example 4.

Thus if the declination were 23 d. 30. m. North and the Meridian Altitude 65 d. 10 m. the Latitude would be found to be 48 d. 20. m.

Example 5.

Let the Declination be 12 d. 15 m. South, and the Meridian Altitude 39 d. 40 m. the Lat. would be 38d. 5 m. Note that these Rules hold good only for finding the Latitudes of such places as ly to the North of the Aequinoctial, for South Lat. the contrary are true, for there if the declination be North, you must add it as you do now when it is South, and if the Suns Declination be South, you must subtract it as you do here when it is North.

And least it be thought troublesome to find the Lat. there is added at the end of this Book a Table of the Latitudes of the principal Places in England, Scotland, and Ireland. So that being near any of those places you may make use of the Lat. of that place, for 10 or 20 miles in this case will make a very insensible or no Alteration.

USE IV. To find the Hour of the day.

NOte that although the Equinoctial fold up within the Meridian to render the instrument the more portable, yet when you would find the hour, the Aequinoctial must be drawn forth according to fig. III. and 'tis a little Ray or speck of light that coming through the hole of the Cursor of the Axis falleth upon the line in the middle of the Aequinoctial and sheweth the hour.

The Rule.

First the Latitude being got by the foregoing Rules, or by the Table at the end of this book, slide the division on the Cursor of the Meridian to it, either in the North or South Quadrants, according as the place is situated. Secondly slide the Cursor of the Axis to the day of the month. Thirdly open the Equinox as far as 'twill go, which is just to cross the Meridian, then guess as near as you can at the hour, and turn the Axis towards the hour you guess, that the Sun may the better shine through the hole, and holding the Instrument by the little ring so that it may hang freely, move it gently this way and that, till the Sun shining through the hole you can discern a little Ray or speck of light to fall upon the Aequinoctial within side among the hours and parts, now the point in the middle line whereon the Ray falleth is the true hour. A little practice will make it very easie. Fi. III. representeth the Dyal as it is when you would find the hour, where the Cursor Z is set to the Lat. of London, 51 32. the Cursor of the Axis is set to the day being April the 8, and the Aequinox is drawn open to cross the Meridian. Now when the Dyal is thus set, and shews the true hour, the Meridian of it hangeth directly North and South, according to that imagined in the Hea ens, the point N P represents the North Pole, S P Represents the South, the Cursor Z Represents the Zenith, and its oposite point N represents the Nadir; the Axis lyeth according to that of the World passing from Pole to Pole, the points of VI and VI in the Aequinoctially directly East and West, and the middle line within lyeth according to the true Aequinoctial in the Heavens.

USE V. To find the Suns Rising and Setting.

NOte this line of Rising and setting is particularly for the Latitude of London, or any other place, situated directly East or West from it, but it may indifferently serve the whole Kingdom. Note also that the great figures stand for the Rising and the other for the setting.

The Rule.

Slide the Cursor of the Axis to the day of the Month, then turn the other side, and the division crossing the hole, shews the Suns Rising, and Setting in the line R.

Example 1.

I slide the Cursor to March the 10, and on the other side it shews VI. and 6, for then the Sun rises at 6 and sets at 6.

Example 2.

April the 8, I set the Cursor to the day, and on the other side it shews V. and 7, which is 5 for the Suns Rising and 7 for its Setting.

Example 3.

October the 20, the Cursor being set to the day, on the other side it will shew the Rising to be at a quarter after VII, and the Setting three quarters after 4.

Now having found the Suns Rising and Setting, you may likewife from thence find the length of the day and night, for double the time of the Suns Rising, and you have the length of the Night, and double the time of its setting, gives you the length of the Day, as will appear by the three following Examples.

Example 1.

March the 10, the Sun rises at 6 and sets at 6, now twice 6 is twelve for the length both of day and night.

Example 2.

April the 8, the Sun rises at 5 and sets at 7, now twice 5 is 10 the length of the Night, and twice 7 is 14 the length of the day.

Example 3.

October the 20, The Sun rises at a quarter after 7 and sets at 3 quarters after 4, now twice 7 and a quarter is 14 and a half for the length of the Night, and twice 4 and 3 quarters is 9 and an half for the lenghth of the day; in all which Examples it appears that both the sums of the length of the day and night being added together will make 24, the hours contained in a natural day.

USE VI. To find what days and Nights throughout the year are Equal.

The Rule.

THe Days on one side the slit are equal to the days on the other.

Example.

Slide the Cursor to March the 10, and the day equal to it will be found on the other side Sept. the 13, So equal to April the 8 is August the 14. And the day equal to the 20 of October is February the Second.

Now these days are said to be equal each to the other, in these respects; 1. in respect of the Suns Declination, it being on both the same. 2. Of the Suns Altitude, for what Altitude the Sun has on any hour on one, the same will be its Altitude on the same hour on the other. 3. The Time of the Suns Rising and Setting is on both the same. 4. They are equal in length both of Day and Night.

A Table shewing the Latitudes of most of the Principal Places in every Shire throughout England and Wales. Shires. Places Names. d. m. Anglesey, Beaumaris, 53 27 Holy-head, 53 33 Berkshire, Abington, 51 42 Newbery, 51 25 Reading. 51 28 Bedfordshire, Bedford, 52 09 Dunstable. 51 53 Brecknockshire, Bealt, 52 12 Brecknock. 52 04 Buckinghamshire, Alesbury, 51 45 Buckingham. 52 00 Cambridg • hire, Cambridge, 52 06 Ely. 52 30 Cardiganshire, Aberistwith. 52 35 Cardigan. 52 20 Carmarthenshire, Carmarthen, 51 58 Kidwelley. 51 50 Carnarvonshire, Arberconway, 53 30 Bangor, 53 21 Carnarvon, 53 18 Cheshire, Chester, 53 15 Nantwich. 53 03 Clamorganshire, Cardiff, 51 30 Landaff. 51 34 Cornwall, Fallmouth, 50 20 The Lizard, 50 10 Truro. 50 25 Cumberland, Carlisle, 55 00 Cockermouth. 54 45 Derbyshire, Chesterfield, 53 20 Derby. 53 00 Denbighshire, Denbigh, 53 18 Ruthyn. 53 12 Devonshire, Dartmouth, 50 20 Exeter, 50 41 Plymouth. 50 30 Dorset shire, Dorchester, 50 40 Shaftsbury, 50 58 Weymouth, 50 32 Durham, Aukland, 54 45 Durham. 54 50 Essex, Colchester, 52 00 Harwich. 52 05 Flintshire, St. Asaph, 53 25 Flint. 53 20 Gloucestershire, Gloucester, 51 56 Tewxbury. 52 15 Hampshire, Portsmouth, 50 45 Southampton, 50 54 Winchester. 51 03 Hertfordshire, Hertford, 51 50 Ware. 51 48 Herefordshire, Hereford, 52 12 Lemster. 52 24 Huntingtonshire, Huntington, 52 15 St. Ives. 52 20 Isles of Gernsey, 49 38 Jersey, 49 28 Man, Douglas, 54 25 Wight, Newport. 50 45 Kent, Canterbury, 51 15 Dover, 51 25 Rochester. 51 30 Lancashire, Lancaster. 54 15 Manchester, 53 39 Preston. 53 55 Leicestershire, Harborough, 52 33 Leicester, 52 40 Lincolnshire, Boston, 53 16 Lincoln, 53 16 Stamford. 52 48 Merionethshire, Bala, 52 57 Harlech. 53 00 Middlesex, LONDON, 51 32 Stanes, 51 30 Uxbridge 51 35 Monmouthshire. Chepstow, 51 42 Monmouth. 51 54 Montgomery, 52 40 Montgomeryshire. Montgomery, 52 40 Welchpool. 52 50 Norfolk, Linn, 52 52 Norwich, 52 44 Yarmouth. 52 40 Northamptonshire. Northampton, 52 15 Peterborough. 52 38 Northumberland, Barwick, 55 50 Newcastle. 55 03 Nottinghamshire, Nottingham, 53 00 Workensope. 53 25 Oxfordshire, Banbury, 51 57 Oxford. 51 45 Pembrookshire, St. Davids, 52 00 Pembrook. 51 48 Radnorshire. Prestein, 52 30 Radnor. 52 25 Rutland, Okeham, 52 43 Uppingham. 52 38 Shropshire, Ludlow, 52 28 Shrewsbury. 52 48 Somersetshire, Bath, 51 20 Bristoll. 51 30 Staffordshire. Lichfield, 52 48 Stafford. 52 52 Suffolk, St. Edm. Bury, 52 22 Ipswich. 52 20 Surrey, Guilford. 51 14 Suffex, Chichester, 50 49 Lewis. 50 46 Warwickshire, Coventry, 52 32 Warwick. 52 28 Westmoreland, Apleby, 54 40 Kendal. 54 24 Wiltshire, Marlborough, 51 25 Malmsbury, 51 35 Salisbury, 51 04 Worcestershire, Kidderminster 52 28 Worcester. 52 15 Yorkshire, Bridlington, 54 50 Doncaster, 53 38 Hull, 53 48 Leeds, 53 50 York. 54 00

The Latitudes of the most Eminent places in Scotland. Places names. d. m. Aberdeen. 57 06 St. Andrews. 56 24 Barwick. 55 50 Dunblain. 56 20 Dunbriton. 56 10 Dunbar. 56 03 Dundee. 56 31 Dunfrees. 55 03 Edenburgh. 56 04 Fair-head. 58 43 Glascow. 56 05 Irwin. 55 50 Isles of Orkney. 58 50 Kaithness. 57 48 Larnack. 55 51 Montross. 56 44 Nairn. 57 30 Perth or St. Johns Town, 56 32 Sterlin. 56 15 Withern. 54 57

The Latitudes of the most Eminent places in Ireland. Places names. d. m. Armagh. 54 23 Athloon. 53 21 Bantry. 51 30 Belfast. 54 41 Cashell. 52 24 Casherlash. 52 46 Clare. 52 44 Corke. 51 43 Craven. 54 01 Droughdagh. 53 44 Dublin. 53 20 Dundalk. 54 02 Dungarvan. 51 57 Dunnagall. 54 40 Galloway. 53 12 James Town. 53 53 Kildare. 53 08 Kilkenny. 52 34 Kingsail. 51 30 Knockfergus. 54 50 Limrick. 52 33 Londonderry. 55 04 Longford. 53 42 Slego. 54 17 Waterford. 52 09 Wexford. 52 17

How to place an Horizontal Dyal upon a levell Plane, and to find the Meridian several wayes.

1. PRepare a smooth board or Stone, and place it truly Horizontal or levell, which may be done with such an Instrument as the Artificers call a Plumb-Rule, or otherwise, then find the hour of the day by such an Instrument as is before described, or by some other as true, or having a good Watch go to some Sun-Dyal that you know to go true, and set the Watch by it, afterwards turn the Dial (which you are to place) about, untill it shews the same hour with your Instrument or Watch, and there fasten it.

2. Or having prepared your plain as before, near the middle of it set up a wire which shall stand exactly perpendicular or upright, and the Sun Shining clear, observe a little before Noon when the shadow of the wire is at the shortest, and there make a point, and through that point and the center where the wire stood draw a line, upon which place the 12 a Clock line of your Dyal, and fix it.

3. And which is better, near the middle of your Plain choose a point as a center, and thereon describe a Circle of a convenient bigness, and erect a wire at Right Angles to your plain as before, then observe in the forenoon when the shadow of the top of the Pin just toucheth the Circle, and there make a mark, and again in the Afternoon watch when the shadow of the top of the Pin just toucheth the Circle, and there make another Mark, then with a pair of Compasses divide the space between those two Markes into two equal parts, and there make a third Mark, through this last point and the center of the Circle where the wire stood, draw a line and it shall be a true Meridian-line. This last conclusion may be done with more ease, if there be several Circles described one within another on the same center, also then you may make several observations for the doing it with more certainty.

4. The Meridian may be found by the help of a good magnetical needle, well made and fitted to a square Box, if in the useing of it there be an allowance made for the Variation, the use of which is so plain, even to those that have but seen them, that I think it needless here to treat of.

I shall set down only two ways more, which will require more knowledge in the Mathematicks than any of the Former, and so conclude. The first is in Dary's Misscellanies, page 22, thus.

1. Let a piece of Mettal or Wood be made a true Plain, then in some convenient point thereof (taken as a Center,) erect a Gnomon of sufficient length at right angles to the plain, this done, fix the Plain truly Horizontal; secondly if you take the Suns Co-altitude (that is his distance from the Zenith) 3 several times in one day, and according to the Stereographick Projection having a line of Tangents by you set off from the center of your plain or foot of the Gnomon, the Tangent of half each arch upon his respective Azimuth or Shadow (continued if need be) made by the Gnomon, at that Instant when the Co-altitude is taken, so shall you insert three points upon the plain. Thirdly if you find out the Center to those 3 inserted points, then a right line infinitely extended by this Center found and the foot of the Gnomon or the Center of the plain, is the true Meridian line.

2. The other way, is by the help of the Suns Azimuth, and it is hinted in most Books of Dyalling, thus, 1. Your plain being prepared as before, hold up a string and Plummet, so that the shadow of the string may fall a cross an assigned point in the plain, and in the same line of shadow make another point at a convenient distance from the first, then through these two points draw a right line, secondly at the same instant get the Suns Azimuth or Horizontal distance from the south part of the Meridian, and having a line of chords by you, set off the angle of the Azimuth from the assigned point, either on the west side of the line drawn, if your observation be made in the Morning, or on the east side if your observation be in the Afternoon, and draw the line. Thirdly this last line so drawn shall be in the true Meridian.

FINIS.

ERRATA.

PAge 4 line 9 read subivided and numbered. Page 8 line 15 dele the. Page 13 and 14 read Complement. Page 17 line 14 read Heavens. Page 19 line 14 read length.

All sorts of Mathematical Books are sold and Instruments made relating to Arithmetick. Trigonometry. Surveying. Stereometry. Gauging. Astronomy. Geography. Navigation. Opticks. Dyalling. Geometry. Architecture. Fortification. Gunnery. Mechanicks, &c. At reasonable rates: By Henry Wynne, near the Sugar-loaf in Chancery-Lane.