great exactness You may see nicely when the very edge of the Sun or Moon toucheth the Meridian and whilst all their body is passing it 2. You may see what Stars are at any time on the Meridian either Northward or Southward and so find the hour of the night 3. You may with all exactness continue your Meridian-line for many Miles if you please by looking thro either Sight and seeing what objects the Plumb-lines intersect 4. If you would be still more nice you may apply a Telescope to this Meridian Instrument by placing for the Eye-glass a Convex glass of a convenient Focus at a due distance between the Plumb-line and either Sight so as thro the Sight to see the Plumb-line thro the Convex glass or Eye-glass And at a convenient distance from the Instrument place another Convex-glass for the Object-glass 5. If I am not much mistaken this Meridian-Instrument may as well and being made Telescopulous much better serve the design of trying whether the Meridian differeth or not which some have experimented with more trouble and expence than this instrument comes to 6. This Instrument is very easily brought to the Meridian For whether it stands upright aside or any other way still the Plumb-lines may be brought easily to their due place 7. This instrument is prepared with little cost or trouble it may be carried from place to place or imitated where-ever there is occasion to correct either Sun Dial or Watch. A Table shewing the Time when the Pole-Star is on the Meridian M. January February March April August Septemb. October Novemb. Decemb. D. Hour Min.  Hour Min.  Hour Min.  Hour Min.  Hour Min.  Hour Min.  Hour Min.  Hour Min  Hour Min.  5 4 45 Morning 2 40 Morning 0 51 Morn 10 55 Evening 2 54 Morning 1 1 Morn 11 8 Evening 9 6 Evening 6 57 Evening 10 4 23 2 21 0 33 10 37 2 34 0 42 10 49 8 46 6 35 15 4 3 2 2 0 15 10 18 2 17 0 24 10 30 8 25 6 13 20 3 42 1 43 11 54 Even 9 59 1 58 0 6 10 11 8 3 5 5◠25 3 22 1 24 11 35 9 40 1 40 11 47 Even 9 50 7 41 5 29 30 3 00   11 17 9 21 1 22 11 29 9 30 7 20 5 7 This Table is intended for the unskilful Reader to whom it may be of use for some years But it will in time run out by reason of the increase of the Pole-star's R. Ascention Leap year c. The Hour and Minute when the Pole-star comes on the Meridian is shewn every fifth day But in May June and July it cannot be seen when it is on the Meridian by reason of Daylight The Table will be sufficiently explained by an Example or two Jan. 5. The Pole-star comes to the Meridian at 45 minutes after 4 of clock in the morning at which time you may set your Meridian-Instrument So you may do the same on Mar. 20th at 54 after 11 of clock at night at which time also the Pole-star is on the Meridian VI. To make a Telescope for the Government of Watches In chap. 11. I mentioned a Telescope for the governing a Watch by the Fixed Stars And because it is the nicest way I have mentioned by reason you may see a Star pass at one Beat of a Pendulum therefore I shall here describe the way to make such a Telescope as is needful for this purpose Prepare your self with two Convex glasses the one for the Object-glass to have its Focus or Cons about 6 feet or according to the length you intend your Telescope the other glass for the eye glass about 2 or 3 inches Lodge these Glasses in a Tube of thin boards pastboard or what you think fit Between the Object and Eye-glass at the focal distance of the Eye-glass viz. about 3 inches place two fine Hairs or Threads across so as to be seen clearly when you look thro the Eye-glass Let there be an aperture near these cross hairs that the light of a Candle may shine on them in the night when you look at a Star It is convenient that the Eye-glass and Cross-Hairs or Threads should be lodged in a short lesser Tube by themselves so as to go into and slide backward and forward in the end of the larger Tube whereby you may set the Eye-glass and Cross-Strings nearer unto or farther off from the Object-Glass Also there must be a conical Socket of Wood before the Eye-glass such as is usual in all Telescopes to look thro but its perforation must be very small so as only to give you leave to see the Star through it Your Telescope being thus prepared you must plant it for observation as is directed in the foregoing Book BOOKS printed for James Knapton at the Crown in St Paul's Church-yard A New Voyage round the World Describing particularly the Isthmus of America several Coasts and Islands in the West-Indies the Isles of Cape Verd the Passage by Terra del Fuego the South Sea Coasts of Chili Peru and Mexico the Isle of Guam one of the Ladrones Mindanao and other Philippine and East-India Islands near Cambodia China Formosa Luconia Celebes c. New Holland Sumatra Nicobar Isles the Cape of Good Hope and Santa Hellena Their Soil Rivers Harbours Plants Fruits Animals and Inhabitants Their Customs Religion Government Trade c. By William Dampier Vol. the first illustrated with particular Maps and Draughts The Fourth Edition Corrected Voyages and Descriptions Vol. II. In Three Parts viz. 1. A Supplement of the Voyage round the World describing the Countries of Tonquin Achin Malacca c. their Product Inhabitants Manner Trade Policy c. 2. Two Voyages to Campeachy with a Description of the Coast Product Inhabitants Logwood Cutting Trade c. of Jucatan Campeachy New Spain c. 3. A Discourse of Trade-winds Breezes Storms Seasons of the Year Tides and Currents of the Torrid Zone throughout the World with an Account of Natal in Africk its Product Negro's c. By Captain William Dampier Illustrated with particular Maps and Draughts To which is added A General INDEX to both Volumes The second edition A Short view of the Principal Duties of the Christian Religion With plain Arguments to perswade to the sincere and speedy practice of them To which is added a Prayer suited to the whole to be used Morning and Evening By a Divine of the Church of England for the Use of his Parishioners Price 3 d. or 20 s. per Hundred The God-Fathers Advice to his Son Shewing the necessity of performing the Baptismal Vow and the danger of neglecting it With general instructions to young persons to lead a Religious life and prepare them for their Confirmation and worthy receiving the Blessed Sacrament Very necessary for Parents c. to give their Children or others committed to their care By John Birket Vicar of Milford and Hordle in Hampshire The Second Edition with a Preface Price 3 d. or 20 s per Hundred Mr. Wingate's Arithmetick containing a plain and familiar Method for attaining the Knowledge and Practice a common Arithmetick The tenth edition very much enlarged By John Kersey late Teacher of the Mathematicks Octavo FINIS
time in which Light passeth from the Sun to Jupiter which is at last settled by that sagacious Observer so often before mentioned Mr Flamsteed But I must forbear fearing that I have already wearied the Readers patience and shall need his pardon for detaining him so long on this subject from so small an occasion as only a Satellite Instrument of Watch-work But I was willing from a small occasion rather than not at all to say something to excite the observations and enquiries of others concerning this matter which may be of vast use in Navigation making and correcting Maps of Countries c. Many of those to whom this matter would be of greatest use scarce ever heard of it and others except Monsieur Cassini have been backward in favouring the World with their observations necessary to Calculation It is indeed a novel subject and full of difficulties on which little hath been written and concerning which the first material observations to be relied on were Hodierna's and Mr Rook's Those of the former were published but not very accurate those of the latter were more accurate but not published and neither of them are yet 50 years old But neither Novelty nor Difficulty ought to discourage the curious and the diligent to excite whom is partly the design of this digression III. To correct the motion of Royal Pendulums IN Chap. 5. of the preceding Book I judged it to be a good expedient to bring a Pendulum to vibrate nicely to add a Bob underneath the Pendulum Ball. This I have since found to succeed so much according to expectation that I think it frivolous to attempt by any of the usual ways to bring a large single Ball to vibrate to one single Beat in any considerable quantity of Time But when the Great Ball is brought pretty near its due length the little Regulating Bob will nicely perform the rest The Great Ball being of the usual weight and form to swing Seconds I would have the Corrector or Regulating Bob to be about 10 ounces Troy to scrw up and down beneath the Ball as is directed in Chap. 5 before But after all endeavours of this kind it must be expected that the Movement will still be exposed to the influences of the weather and the alterations caused by foulness For the more easy and quick bringing of a Pendulum that should swing Seconds to its true length I have composed the following Table which sheweth the alterations which will be made in 24 hours by screwing up or letting down the great Ball. If therefore the Ball runs upon a Rule divided into inches and tenths of an inch 't is easy to see how much or how little the Ball needeth to be altered Pendul length Variation of Vibrat  in ten Min. Sec.  38 0 22 33 Faster 38 1 20 38 38 2 18 43 38 3 16 48 38 4 14 55 38 5 13 2 38 6 11 9 38 7 9 16 38 8 7 25 38 9 5 32 39 0 3 42 39 1 1 51 39 2 00 00  39 3 1 50 Slower 39 4 3 40 39 5 5 29 39 6 7 19 39 7 9 7 39 8 10 57 39 9 12 42 40 0 14 29 This Table will need little explication If your Ball should be at 39 inches 2 tenths it would swing Seconds If you alter it to 39 inches 1 tenth it would go 1′ 51″ faster if to 39 inches 3 tenths it would go 1′ 51″ slower And so of the rest of the Table IV. Of the Equation of Natural Days BY reason that the Sun's motion in his Orbit is not equal and that although he moved equal arches of the Ecliptick in equal times yet he would come to the Meridian with unequal arches of the Equator by whose equal Revolutions the Equal Time is measured hence I say it will happen that altho a Clock should go so exactly as at the years end to agree with the Sun yet it will vary from the times shewed by the exactest Sun-Dials The quantity of which Variations may be seen in the following Tables for every day in the year For which Tables I am greatly obliged to that most accurate Astronomer Mr Flamsteed so often mentioned These Tables need but little explication If you would keep your Watch to the Middle or Equal motion of the Sun it must go so many minutes and seconds faster or slower than the Sun-Dial as the Tables shew But if you would keep your Watch to go by the Sun-Dial you may conclude it goes well if it loseth or gaineth every day so many Seconds as you will find in the Table Thus for example Jan. 1. in Leap year the Watch ought to be 8 min. 47 Sec. faster than Mr Flamsteed's Tables of Aequation of Natural-Days The Bissextile or Leap-year  Jan. Febr. Marc. April May. June July Aug. Sept Octo. Nov. Dec.  M. S.  M. S  M S  M S  M S  M S  M S  M S  M S  M S  M S  M S  1 8 47  14 49  10 00  0 41 * l* 4 10  0 59 * 4 47  4 26  8 58  13 22  15 19  5 28 too 2 9 10 14 48 9 43 0 24 4 11 0 47 4 55 4 16 4 19 13 36 15 10 4 59 3 9 32 14 46 9 26 0 8 4 12 0 34 5 2 4 5 4 39 13 49 15 01 4 31 4 9 54 14 43 9 9 0 7 4 13 0 22 5 9 3 54 5 00 14 2 14 50 4 2 5 10 15 14 40 8 51 0 22 4 12 0 10 5 15 3 43 5 20 14 14 14 38 3 33 6 10 36  14 36  8 33  0 37  4 11  0 03 * 5 20  3 31 Watch 5 41  14 26  14 26  3 3 slow 7 10 55 14 31 8 15 0 52 4 10 0 16 5 25 3 18 6 1 14 37 14 13 2 33 8 11 14 14 26 7 57 1 6 4 8 0 29 5 30 3 5 6 22 14 47 14 00 2 3 9 11 32 14 20 7 39 1 19 4 5 0 42 5 34 2 52 6 43 14 57 13 45 1 33 10 11 49 14 13 7 20 1 31 4 2 0 55 5 37 2 38 7 3 15 6 13 30 1 4 11 12 5 Watch 14 5 Watch 7 1 Watch 1 44 Watch 3 59 Watch 1 7 Watch 5 40 Watch 2 24 too 7 24 Watch 15 15 Watch 13 13 Watch 0 34 * I* 12 12 22 13 57 6 43 1 57 3 54 1 20 5 43 2 9 7 44 15 24 12 56 0 4 13 12 37 13 48 6 24 2 9 3 50 1 33 5 45 1 54 8 4 15 30 12 38 0 26 14 12 51 13 39 6 05 2 19 3 45 1 46 5 45 1 38 8 24 15 36 12 19 0 56 15 13 5 13 29 5 46 2 30 3 39 1 59 5 46 1 22 8 43 15 42 12 00 1 26 16 13 18 too 13 18 too 5
4 28 23 14 25 11 47 3 31 3 33 2 43 3 25 5 32 0 46 11 1 16 1 9 20 4 56 24 14 31 11 32 3 1â— 3 40 2 34 3 36 5 28 1 5 11 19 16 0 8 55 5 23 25 14 36 11 16 2 54 3 46 2 2 3 5 23 1 24 11 37 15 58 8 30 5 50 26 14 40  11 1  2 31  3 51  2 14  3 57  5 17  1 44 slow 11 54  15 56  8 4  6 17 fast 27 14 43 10 46 2 17 3 55 2 4 4 7 5 11 2 3 12 10 15 53 7 38 6 44 28 14 46 10 30 2 0 3 59 1 53 4 16 5 5 2 22 12 26 15 49 7 12 7 10 29 14 47   1 42 4 3 1 42 4 25 4 58 2 42 12 4â— 15 44 6 45 7 36 30 14 48   1 25 4 6 1 31 4 33 4 50 3 3 12 5â— 15 38 6 17 8 0 31 14 49     1 9     1 19     4 41  3 23     15 32     8 24  the Sun Dial on Jan. 2. it ought to be 9′ 10″ c. If you would know on the same days whether your Watch goes well when kept to go by the Sun-dyal if set on Jan. 1. it hath gained on Jan. 2. as much as 8′ 47″ wanteth of 9′-10″ viz. 23″ you may conclude your Watch goes well Otherwise you must screw up or let down the Ball or Corrector until it loseth or gaineth according to the Equation Tables The Tables will serve for many years being mede for Bissextile and the 3 years following By an Almanack therefore or any other way knowing the Year you may find what Table you are to use all that year By reason of the Refractions or some error in the Sun-Dial it may be convenient to compare or set your Watch at some certain hour of the day Noon is a good time for it if you have a nice Meridian-line or any way to see when the Sun is exactly South because the time of the Day is not at all then varied by the Refractions in Dials that cast a shade V. To find a Meridian-Line It may happen that we may be at a Place where there is no Sun Dial or not one to be relied upon or indeed where we have a good one it may be of great use to us to have a Meridian-Line For the finding of which there are divers ways but I shall shew only two The first is draw one or more Circles on some plain as on the bottom of a Southern Window Or you may make the center on the Southern edge of the Window and draw only half circles Hang up a Thread and Plumbet exactly over or in the center of the Circles By a Bead or two sliding up and down the Thread mark out exactly the points of the Circles touched by the Shade of the Beads in some of the Morning Hours the longer before Noon the better In the afternoon when the same shade of the Beads toucheth the circles mark that point or points also A line drawn thro the Center and in the middle between these two points in the Circle is the Meridian-line or near so If you can't hang up a Plumbet a Pin set exactly upright will do the matter Another and better way is by the Pole star when it is exactly upon the Meridian Or if but near so the error will not be great You may find the time when the Pole-star comes to the Meridian by Substracting the Suns Right Ascention from right Ascention of the Pole-star and turning the remainder into hours minutes and seconds allowing to every degree four minutes of time whereby you will have the Apparent time when the Pole-star comes on the Meridian above the Pole I scarce need to observe that the time when it comes under the Pole is 12 hours distant You may shorten your labour by using Tables of the Sun 's right ascention in Time which you may find in Sir J. Moor's Mathem Compendium Note If the Sun's R. Ascention exceeds the Pole-stars R. A. you must add 24 hours to the Pole-star's R. A. then substract The right ascention of the Pole-Star is determined by Mr Flamsteed 0 h 33′ 44″ of time in the year 1690 and the increase of its R. Ascention 1′ 16″ of time in 10 years Therefore this present Year 1700 its true R. Ascention is 0 h 35′ 00″ of time If the unlearned Reader should think this way difficult he may see when the Pole-Star comes near the Meridian by hanging up a Line and Plumbet and observing when the first Star in the Great-Bear's tail next her Rump comes under the Line on one side of the Pole or when the Plumb-line intersects the Star in Cassiopeia's Knee on the other side of the Pole When the Pole-star is found to be on the Meridian if you hang up two strings with Plumbets between the Pole-Star and your eye this will be a Meridian-line to see when the Sun comes to the Meridian Or you may do it with a Crevis between two boards or plates of Metal almost touching one another Or which is a better way with a pair of Sights such as Surveyors use but much longer with a Crevis in one Sight next the eye and a large aperture in the other with a fine Caâ—s gut string down the middle These should be counter-changed so as to look either at the Pole-star by night or the other way at the Sun by day Page 22d Appendix Fig. 3. Fig. 2. Your instrument being thus prepar d plant it in some convenient place where you may see the Pole star by night and the Sun by day When the Pole-star is on the Meridian look thro the Sight with the bigger Hole and turn the whole instrument about until you see the opposite Plumb line intersect the Pole-star Take care at the same time that the Plumb-lines hang so as to intersect the Sights Your instrument thus plac'd standeth nicely in the Meridian so as to see when either Sun Moon or Stars come on the Meridian When you look by night 't is necessary that a Candle should shine on the Plumb-line that you may see it If you look at the Sun you must guard your eye against the Sun-beams with a coloured Glass or one blackened with the smoak of a Candle I had almost forgotten to say that it matters not much what length the bottom piece A. B. is of but the longer the better provided that the Plumb-lines are high enough to see the Pole-star and the Sun in the Summer Solstice or any time of the Year If the bottom piece be 2 feet long the Plumb-lines had need to be near 4 feet This instrument is very serviceable to several purposes particularly 1. To see the Southing of the Sun or Moon which you may do with