[Page] A SUPPLEMENT TO THE TREATISE OF Watch & Clock-work, CALLED The Artificial Clock-Maker.
Wherein is Contain'd,
- 1. The Anatomy of a Watch and Clock.
- 2. Monsieur Romer's Satellite-Instrument: with Observations concerning the Calculation of the Eclipses of Jupiter's Satellites, and to find the Longitude by them.
- 3. A nice way to correct Pendulum Watches.
- 4. Mr Flamsteed's Equation Tables.
- 5. To find a Meridian-Line for the Governing of Watches, and other Uses.
- 6. To make a Telescope to keep a Watch by the Fixed Stars.
By W. D. M. A.
LONDON, Printed for James Knapton, at the Crown in St Paul's Church-yard. 1700.
[Page 1] TO THE READER,
UPon a review of my Book, in order to another Edition, I have thought it necessary to add some things, and to make some small amendments in the body of the Book itself.
And because I think it a piece of justice owing to the Buyers of the first Edition, that I should endeavour, as much as I can, to make their Edition as compleat as this; therefore, instead of inserting what this Supplement contains into proper places of the Book, I have rather chosen to put it rhapsodically together; and taken care that it be printed so, as to be bought by itself at a small price.
[Page 2] Also I think my self obliged, to be at the pains to collect the most material alterations, and amendments which I have made in my Book, and here to insert them in this Supplement; whereby the Reader may supply with his Pen (if he pleaseth) what is wanting in the first Edition.
The Purchasers both of the first and of this Edition will (we hope) excuse both the Bookseller and me, for reducing this Edition into a lesser Volume, that it may be more portable for the Pocket, and (we hope) both Book and Supplement too, cheaper; at least, not dearer than the first Edition, for the benefit of poor workmen.
- PAge 5. line 2. after pocketwatches, add [and others] l. 4. after wheels, add [whence it hath its Name] l. penult. dele [somtimes.]
- P. 7. After l. 11. add [the Train is the Number of Beats which the Watch maketh in an hour, or any other certain time.]
- P. 10. l. 24. after Wheel 40, add [which runs concentrical, or on the same arbor with the second Pinion 5.]
- P. 12. l. 3. after has, add [as hath been said.]
- P. 15. l. 15. add in the Margin [see Sect. 1. §. 3.]
- L. 23. In the margin add [See Sect. 1▪ §. 4]
- P. 19. l. 6. add in the Margin [See §. 4.]
- P. 20. l. 20. for 2196. r. 20196.
- P. 25. l. 2. after Report add [fixed on the Great-wheel.]
- P. 28. l. 9. add in the Margin [Sect. 1. §. 3.]
- [Page 4] P. 30. l. 22. in the Margin add [§. 7]
- P. 34. l. 14. after Report add [and the Count-wheel.].
- P. 35. l. 12. after Rules, add [To find how many strokes the Clock striketh in one turn of the Fusy, or Barrel.
- L. 19. after Rule 2. add [To find how many days the Clock will go.]
- L. 27. after Rule 3. add [To find the number of turns of the Fusy or Barrel.]
- P. 36. l. 21. after Rule 4. add [To fix the Pin. of Report on the Spindle of the Great-wheel.]
- P. 38. l. 8. after turns, add [of the Fusy.]
- L. 25. after Then, add [(if you make the Great-wheel the Pin-wheel.)]
- P. 53. l. 9. after Motions, add [in Watch work]
- P. 57. l. 17. amend thus [10) 59 (5, 9]
- P. 58. l. 26. r. [round by a]
- P 75. l. penult. after To the, add [square▪ of the.]
- P. 112. l. 20. add [or thus with 16 turns.]
| 12)72 |
| 8)64 |
| 8)60 |
| 7)56 |
| 30 |
Fig. 1.
Fig. 1.
Page 5.th in the Appendix.
- [Page 5] P. 122, to § 3. add [if this Crown-wheel be too large you may use these numbers, viz.
12)48 6)48 6(45 6)48 Seconds-hand 15 - P. 126. l. 24 after Sextans, add [or any other Telescope.]
- P. 132. l. 15. after 2. add [by the directions in Chap. 2. Sect. 2. §. 5.]
- L. 18. after If add [as in the Movements in ch. 10.]
I.
An Explication of the Figures.
Fig. 1. Representeth the parts of a Watch and Clock described in the Book, Ch. 1.
The Wheels, &c. on the right hand, is the Watch-part. They on the left, the Clock-part.
A. A. A. A. The upper Plate of the Frame: which you may imagine to be transparent (as of glass) to admit of a Prospect of the Wheel-work underneath it.
B. B. B. The lower Plate of the Frame.
C. C. C. C. The Pillars.
D. D. The Spring-Boxes of the Watch, and Clock-part.
E. E. The Great-wheel of each part.
[Page 6] F. F. The Fusy of each part, about which the Chain, or String is wrapped.
g. g. g. g. g. g. g. The Ratchet of each part.
a. a. a. The Hoop, or Rim of the Second wheel.
b. b. The Cross thereof.
c. The Pinion.
H. The Contrate-wheel.
I. The Crown▪wheel.
d. d. The upper and lower Pevet thereof.
K. A piece of Brass, in which the Pevet-hole is, in which the Pevet d. playeth.
L. The Pin-wheel, with the Striking-Pins e. e. e. e. e.
M. The Detent-wheel.
N. The Warning wheel, or fourth wheel.
O The Detent.
P. The Lifting-piece.
Q. Q. The Fan, and Flying-Pinion.
R. The Bell.
S. The Hammer.
T. The Hammertail.
V. V. The Chain, or String of the Watch, and Clock.
x. The Verge or Spindle of the Ballance, or Pendulum.
y. y. y. The Rod of the Pendulum.
z. The Fork.
[Page 7] 2. The Flatt.
3. The Great-Ball.
4. The Corrector or Regulator.
5. 5. The Pallets.
II.
Fig. 2.
Rerpresenteth the Satellite Instrument of Mons. Olaus Romer, described in the Book, page 109.
A. B. the upper Plate of the Instrument.
C. D. The lower Plate.
K. L. An Axis, or Spindle, on which four wheels are fixed, and turn round with it, and with the Hand L. once in 7 days. E. F. G. H. are the Sockets, or hollow Arbors of 4 wheels running concentrically.
The hollow Arbor H. carrieth round the First-Satellite p. and belongeth to the Wheel, or Pinion 22, which is driven by the fixed Wheel 87.
The hollow Arbor G. carrieth round the Second-Satellite S. and belongeth to the Wheel 32 which is driven by the wheel 63. And the like of the Arbors F. and E.
Within all these hollow Arbors is another fixed one included, on the top of which is a Ball (I) representing the Planet Jupiter: round which the Satellites move, represented by the little Balls p. s. t. q.
[Page 8] This Satellite-Instrument may be added to a Watch, by causing the Great-wheel or Dial-wheel to drive round the Arbor K. L. once in 7 days. To do which there are sufficient directions given in the preceding Book.
The use of the foregoing Instrument.
This Satellite-Instrument may be of good use both at Sea and Land to assist in finding the longitude by Jupiter's Satellites: partly, by giving notice when an approaching Eclipse is, that we may be ready with a Telescope to observe it; and partly, when any Eclipse happeneth, to shew which Satellite it is that is eclipsed, which is difficult to be seen in the Heavens: and partly, to supply the place of Tables, or Calculation of the Satellite-Eclipses, which it may do for a little while, but it must not long be trusted unto.
It may seem foreign to my subject, to shew how the Longitude may be found by Jupiter's Satellites: but because I would with all my power advance this way (which far transcends all others yet known, especially that of the Logline) therefore I hope the Reader will excuse this Digression.
The way to find the Longitude, by an Eclipse of any of Jupiter's four Satellites [Page 9] is briefly this: knowing by Tables of the Satellite-Eclipses (suppose such as Mr Flamsteed published in the Philos. Transact. No 177, and afterwards gave Parker leave to publish in his Almanacks, knowing I say) the time when an Eclipse happeneth in any one part of the World; observe by a Telescope, at what time the same Eclipse happeneth in any other part of the World, the difference of time giveth the difference of Meridians. Thus a total Immersion Philos. Trans. Dec. 1685. No. 117.of the first Satellite was observed at Rome, at 10 h. 07′ 53″ p. m. Which Mr Flamsteed notes at 9 h. 15′ 41″. The difference is 52′ 12″, or 13 deg. 03′ distant from the Meridian of the English Observatory, where Mr Flamsteed observ'd it.
I once had thoughts of shewing the way to calculate the Eclipses of Jupiter's Satellites, and to make Tables thereof, by the help of my very good Friend Mr Flamsteed's, and some other observations: but considering that it would be too great a digression, and especially that Monsieur Cass [...]ni hath very ingeniously, and well done it for the First, I shall therefore refer the Reader to his Tables, reduced to the Meridian and Style of London, by that very judicious Mathematician Mr Halley; in Philos. Trans. No 214.
[Page 10] The Reader, I hope will pardon me, if (before I leave this digression) I observe a few things which may be of use, not only in the Calculation of the Eclipses of the 3 outermost Satellites, but also may contract the labour of Calculation in the first.
The first thing to be observed is Jupiter's place. For if he be on his Aphelion, he moves slowest, and consequently the Satellites make their returns to him somewhat sooner, than when he is on his Mean distance and Perihelion. By Mr Flamsteed ▪s first Tables the first Satellite makes 13 revolutions to Jupiter, when he is on his▪
| days | h▪ | ′ | ″ | |
| Aphelion in— | 23 | 00 | 10 | 30 |
| Mean distance— | 23 | 00 | 11 | 48 |
| Perihelion— | 23 | 00 | 13 | 08 |
The Second Satellite makes 10 Revolutions when Jupiter is on his
| days | h. | ′ | ″ | |
| Aphelion in— | 35 | 12 | 55 | 10 |
| Mean-distance— | 35 | 12 | 59 | 00 |
| Perehelion— | 35 | 13 | 03 | 15 |
The Third Satellite makes 5 Revolutions when Jupiter is on his
| days | h. | ′ | ″ | |
| Aphelion in— | 35 | 19 | 50 | 15 |
| Mean-distance— | 35 | 19 | 58 | 00 |
| Perihelion— | 35 | 20 | 06 | 42 |
[Page 11] The Fourth, or furthermost Satellite makes 5 Revolutions to Jupiter in his
| days | h. | ′ | ″ | |
| Aphelion in— | 82 | 17 | 42 | 55 |
| Mean-distance— | 83 | 18 | 25 | 15 |
| Perihelion— | 82 | 19 | 12 | 57 |
From this account it is easy to compute in what time one Revolution of any Satellite is at any time performed: which is the next thing to be observed. Thus in Jupiter's Mean-distance the Revolution of the
| days | h. | ′ | ″ | |
| First Satellite is— | 1 | 18 | 28 | 36 |
| Second— | 3 | 13 | 17 | 54 |
| Third— | 7 | 3 | 59 | 36 |
| Fourth— | 16 | 18 | 05 | 03 |
The Reader may himself, from what hath been said, compute the Periods of the Satellites in Jupiter's other places.
From these things laid down, it is easy from an Eclipse known, to find the next that will follow. For if you add one, or more Revolutions, you have the Eclipses following. Thus for
| days | h. | ′ | ″ | |
| July | 12 | 14 | 18 | 00 |
| 1 Revol. | 1 | 18 | 28 | 36 |
| July | 14 | 8 | 46 | 36 |
| 4 Revol. | 7 | 1 | 54 | 24 |
| July | 21 | 10 | 41 | 00 |
example, July 12 this year 1700, according to Mr Flamsteed's computation, the first Satellite comes out of Jupiter's [Page 12] shadow at 14 h. 18′ p. m. (according to Mr Cassini's at 14 h. 20′ 56″ p m.) consequently the next Emersion is on Jul. 14th past 8 of Clock in the evening▪ If you add 4 Revolutions, another Emersion is on Jul. 21 at 10 h. 41′ nearly p. m. as here is exemplified in the Margin.
The last thing I shall take notice of concerning the Satellite Eclipses is their Durations. This varies according as Jupiter is nearer unto, or remoter from the 10th degree of ♒ or ♌ (as Mr Flamsteed says.) About which points are the Nodes, or intersections of the plane of the Satellite Orbit and Jupiter's, or the Jovial Ecliptick. Mr Cassini makes it in 150 of ♒ or ♌, and varies in the length of the Duration of the Eclipses. But according to Mr Flamsteed (the accuracy of whose observations is not to be distrusted) the greatest Semiduration of the
| h | ′ | ″ | |
| First Satellite is | 1 | 9 | 28 |
| Second— | 1 | 27 | 38 |
| Third— | 1 | 48 | 55 |
| Fourth— | 2 | 26 | 19 |
But as Jupiter removeth from his Nodes, the Semidurations diminish. And when▪ he is gotte n 55 degrees from either of his Nodes, the Fourth Satellite passeth clear of the shadow, and falleth [Page 31] not into it again, until he comes within 55 degrees of the opposite Node.
When Jupiter is on the Limit, or 90 degrees from his Nodes, the Least Semiduration of the Eclipse of the
| h | ′ | ″ | |
| First Satellite is | 1 | 6 | 49 |
| Second— | 1 | 18 | 59 |
| Third— | 1 | 17 | 33 |
From this account of the Duration of the Satellite Eclipses, we may, having the Immersion into Jupiter's shadow, compute the Emersion of any Satellite out of his shadow: or contrariwise, which will be of use to see both the beginning and end of any Eclipse, when visible; I mean, when not hindred by Clouds, day light, or Jupiter's body. Or if by some of these means we are hindred from seeing the one, we may perhaps hereby see the other. Thus (for instance) this August 6. 1700. the first Satellite immerges at 6 h. 44′ p. m. which cannot be seen, not only by reason of day light, but also because Jupiter's shadow lieth a little to the left of his body; but if you add one whole obscuration (viz. twice 10h. 9′ 28″ the emersion you will find visible at 9 h 3′ according to Mr Flamsteed; at 9 h. 4′ according to Monsieur Cassini's Tables. Another instance will make all [Page 14] yet more plain, Oct. 19. at 9 h. 50′ p▪ m. the 3d Satellite will emerge; from which substracting one Obscuration (viz. twice 1 h. 48) you will find the immersion fall at 6 h▪ 13▪ p. m. Which may be seen, by reason that Jupiter▪ is at a good distance from his Opposition to the Sun, so that the shade lies so far on the left hand, as to admit of seeing the 3d and 4th Satellite between Jupiter's body and his shade.
I might to these have added divers other remarks, particularly concerning the Equation of Light, or the 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 [Page 15] 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.
[Page 16] 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, 'tis 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
| 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 | 27 | too | 2 | 41 | too | 3 | 33 | too | 2 | 11 | too | 5 | 46 | too | 1 | 5 | fast. * * | 9 | 3 | too | 15 | 47 | too | 11 | 40 | too | 1 | 56 | Watch. |
| 17 | 13 | 30 | 13 | 7 | 5 | 9 | 2 | 51 | 3 | 26 | 2 | 23 | 5 | 45 | 0 | 48 | 9 | 23 | 15 | 51 | 11 | 20 | 2 | 25 | ||||||||||||
| 18 | 13 | 41 | 12 | 56 | 4 | 50 | 3 | 0 | 3 | 19 | 2 | 35 | 5 | 44 | 0 | 31 | 9 | 42 | 15 | 54 | 10 | 59 | 2 | 34 | ||||||||||||
| 19 | 13 | 51 | 12 | 44 | 4 | 31 | 3 | 8 | 3 | 11 | 2 | 47 | 5 | 42 | 0 | 13 | 10 | 2 | 15 | 57 | 10 | 37 | 3 | 23 | ||||||||||||
| 20 | 14 | 0 | 12 | 32 | 4 | 13 | 3 | 16 | 3 | 3 | 2 | 59 | 5 | 40 | 0 | 5 | 10 | 21 | 15 | 59 | 10 | 14 | 3 | 52 | ||||||||||||
| 21 | 14 | 9 | fast. | 12 | 18 | fast. | 3 | 54 | fast. | 3 | 24 | slow. | 2 | 54 | slow. | 3 | 10 | fast. | 5 | 37 | fast. | 0 | 22 | too | 10 | 3 | slow. | 16 | 00 | slow. | 9 | 50 | slow. | 4 | 21 | too |
| 22 | 14 | 17 | 12 | 5 | 3 | 36 | 3 | 32 | 2 | 46 | 3 | 22 | 5 | 33 | 0 | 40 | 10 | 5 [...] | 16 | 01 | 9 | 26 | 4 | 40 | ||||||||||||
| 23 | 14 | 24 | 11 | 51 | 3 | 17 | 3 | 39 | 2 | 37 | 3 | 33 | 5 | 29 | 0 | 59 | 11 | 15 | 16 | 00 | 9 | 2 | 5 | 16 | ||||||||||||
| 24 | 14 | 30 | 11 | 36 | 2 | 59 | 3 | 45 | 2 | 27 | 3 | 44 | 5 | 25 | 1 | 19 | 11 | 32 | 15 | 59 | 8 | 37 | 5 | 43 | ||||||||||||
| 25 | 14 | 35 | 11 | 21 | 2 | 40 | 3 | 50 | 2 | 17 | 3 | 54 | 5 | 19 | 1 | 39 | 11 | 4 [...] | 15 | 57 | 8 | 11 | 6 | 11 | ||||||||||||
| 26 | 14 | 39 | 11 | 5 | 2 | 22 | 3 | 54 | 2 | 6 | 4 | 4 | 5 | 13 | 1 | 58 | slow. | 12 | 6 | 15 | 54 | 7 | 45 | 6 | 37 | fast. | ||||||||||
| 27 | 14 | 43 | 10 | 50 | 2 | 5 | 3 | 58 | 1 | 56 | 4 | 13 | 5 | 07 | 2 | 17 | 12 | 22 | 15 | 50 | 7 | 19 | 7 | 3 | ||||||||||||
| 28 | 14 | 46 | 10 | 34 | 1 | 47 | 4 | 2 | 1 | 45 | 4 | 22 | 5 | 0 | 2 | 37 | 12 | 37 | 15 | 46 | 6 | 52 | 7 | 29 | ||||||||||||
| 29 | 14 | 47 | 10 | 17 | 1 | 30 | 4 | 5 | 1 | 34 | 4 | 31 | 4 | 52 | 2 | 57 | 12 | 5 [...] | 15 | 40 | 6 | 24 | 7 | 54 | ||||||||||||
| 30 | 14 | 49 | 1 | 13 | 4 | 8 | 1 | 22 | 4 | 39 | 4 | 44 | 3 | 18 | 13 | 8 | 15 | 34 | 5 | 57 | 8 | 18 | ||||||||||||||
| 31 | 14 | 49 | 0 | 57 | 1 | 11 | 4 | 35 | 3 | 38 | 15 | 27 | 8 | 41 | ||||||||||||||||||||||
| Jan. | Febr. | Marc. | April. | May | June. | July | Aug. | Sept. | Octob. | 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 | 9 | 4 | 14 | 48 | 10 | 4 | 0 | 45 | *I* | 4 | 10 | 1 | 2 | * | 4 | 45 | 4 | 2 | Watch | 3 | 53 | 13 | 18 | 15 | 21 | 5 | 35 | too | ||||||||
| 2 | 9 | 26 | 14 | 46 | 9 | 47 | 0 | 28 | 4 | 1 [...] | 0 | 50 | 4 | 53 | 4 | 18 | 4 | 14 | 13 | 32 | 15 | 13 | 5 | 6 | ||||||||||||
| 3 | 9 | 48 | 14 | 44 | 9 | 30 | 0 | 12 | 4 | 12 | 0 | 37 | 5 | 0 | 4 | 8 | 4 | 34 | 13 | 46 | 15 | 3 | 4 | 38 | ||||||||||||
| 4 | 10 | 10 | 14 | 41 | 9 | 13 | 0 | [...] | 4 | 13 | 0 | 25 | 5 | 7 | 3 | 57 | 4 | 55 | 13 | 59 | 14 | 53 | 4 | 9 | ||||||||||||
| 5 | 10 | 31 | 14 | 37 | 8 | 55 | 0 | 1 [...] | 4 | 12 | 0 | 13 | 5 | 13 | 3 | 46 | 5 | 15 | 14 | 11 | 14 | 41 | 3 | 40 | ||||||||||||
| 6 | 10 | 50 | 14 | 32 | 8 | 37 | 0 | 3 [...] | 4 | 11 | 0 | 0 | * | 5 | 18 | 3 | 34 | too | 5 | 36 | 14 | 23 | 13 | 29 | 3 | 10 | slow. | |||||||||
| 7 | 11 | 9 | 14 | 27 | 8 | 19 | 0 | 4 [...] | 4 | 10 | 0 | 13 | 5 | 24 | 3 | 2 [...] | 5 | 56 | 14 | 34 | 14 | 17 | 2 | 40 | ||||||||||||
| 8 | 11 | 27 | 14 | 21 | 8 | [...] | 1 | 2 | 4 | 8 | 0 | 26 | 5 | 29 | 3 | [...] | 6 | 17 | 14 | 44 | 14 | 3 | 2 | 10 | ||||||||||||
| 9 | 11 | 45 | 14 | 15 | 7 | 43 | 1 | 1 [...] | 4 | 6 | 0 | 39 | 5 | 33 | 2 | 5 [...] | 6 | 38 | 14 | 54 | 13 | 49 | 1 | 40 | ||||||||||||
| 10 | 12 | 2 | 14 | 7 | 7 | 2 [...] | 1 | 2 [...] | 4 | 3 | 0 | 52 | 5 | 36 | 2 | 4 [...] | 6 | 58 | 15 | 4 | 13 | 34 | 1 | 11 | ||||||||||||
| 11 | 12 | 18 | Watch. | 13 | 59 | Watch | 7 | 6 | Watch | 1 | 4 [...] | Watch | 4 | 0 | Watch | 1 | 4 | Watch | 5 | 39 | Watch | 2 | 27 | fast. | 7 | 19 | Watch | 15 | 13 | Watch | 13 | 17 | Watch | 0 | 41 | *I* |
| 12 | 12 | 34 | 13 | 50 | 6 | 47 | 1 | 54 | 3 | 56 | 1 | 17 | 5 | 42 | [...] | 13 | 7 | 39 | 15 | 22 | 13 | 0 | 0 | 11 | ||||||||||||
| 13 | 12 | 47 | 13 | 41 | 6 | 28 | 2 | 6 | 3 | 51 | 1 | 30 | 5 | 44 | 1 | 58 | 7 | 59 | 15 | 28 | 12 | 43 | 0 | 19 | ||||||||||||
| 14 | 13 | 2 | 13 | 31 | 6 | 10 | 2 | 1 [...] | 3 | 46 | 1 | 4 [...] | 5 | 45 | 1 | 4 [...] | 8 | 19 | 15 | 34 | 12 | 24 | 0 | 49 | ||||||||||||
| 15 | 13 | 15 | 13 | 21 | 5 | 51 | 2 | 2 | 3 | 40 | 1 | 56 | 5 | 46 | 1 | 26 | 8 | 38 | 15 | 40 | 12 | 5 | 1 | 19 | ||||||||||||
| 16 | 13 | 27 | too | 13 | 10 | too | 5 | 32 | too | 2 | 38 | too | 3 | 4 | too | 2 | 8 | too | 5 | 46 | too | 1 | 9 | *I* | 8 | 58 | too | 15 | 45 | too | 11 | 45 | too | 1 | 49 | Watch |
| 17 | 13 | 38 | 12 | 59 | 5 | 14 | 2 | 4 [...] | 3 | 8 | 2 | 20 | 5 | 45 | 0 | 52 | 9 | 18 | 15 | 50 | 11 | 25 | 2 | 18 | ||||||||||||
| 18 | 13 | 48 | 12 | 47 | 4 | 55 | 2 | 5 [...] | 3 | 21 | 2 | 32 | 5 | 44 | 0 | 35 | 9 | 37 | 15 | 53 | 11 | 4 | 2 | 47 | ||||||||||||
| 19 | 13 | 58 | 12 | 35 | 4 | 36 | 3 | [...] | 3 | 13 | 2 | 44 | 5 | 42 | 0 | 17 | 9 | 57 | 15 | 56 | 10 | 42 | 3 | 16 | ||||||||||||
| 20 | 14 | 7 | 12 | 22 | 4 | 17 | 3 | 14 | 3 | 5 | 2 | 56 | 5 | 40 | 0 | 1 | 10 | 16 | 15 | 58 | 10 | 20 | 3 | 45 | ||||||||||||
| 21 | 14 | 15 | fast. | 12 | 8 | fast. | 3 | 58 | fast. | 3 | 22 | slow | 2 | 56 | slow. | 3 | 7 | fast. | 5 | 38 | fast. | 0 | 18 | too | 10 | 34 | slow. | 15 | 59 | slow. | 9 | 56 | slow. | 4 | 14 | too. |
| 22 | 14 | 22 | 11 | 54 | 3 | 42 | 3 | 30 | 2 | 48 | 3 | 19 | 5 | 34 | 0 | 36 | 10 | 5 [...] | 16 | 1 | 9 | 32 | 4 | 42 | ||||||||||||
| 23 | 14 | 28 | 11 | 40 | 3 | 22 | 3 | 37 | 2 | 39 | 3 | 30 | 5 | 30 | 0 | 55 | 11 | 10 | 16 | 0 | 9 | 8 | 5 | 9 | ||||||||||||
| 24 | 14 | 3 | 11 | 24 | 3 | 3 | 3 | 4 | 2 | 28 | 3 | 41 | 5 | 26 | 1 | 14 | 11 | 28 | 15 | 59 | 8 | 43 | 5 | 36 | ||||||||||||
| 25 | 14 | 3 | 11 | 2 | 45 | 3 | 4 | 2 | 19 | 3 | 51 | 5 | 20 | 1 | 34 | 11 | 45 | 15 | 57 | 8 | 17 | 6 | 4 | |||||||||||||
| 26 | 14 | 4 | 10 | 54 | 2 | 26 | 3 | 53 | 2 | 9 | 4 | 1 | 5 | 14 | 1 | 53 | slow. | 12 | 2 | 15 | 55 | 7 | 51 | 6 | 30 | fast. | ||||||||||
| 27 | 14 | 4 | 10 | 38 | 2 | 3 | 57 | 1 | 59 | 4 | 11 | 5 | 8 | 2 | 12 | 12 | 18 | 15 | 51 | 7 | 25 | 6 | 57 | |||||||||||||
| 28 | 14 | 47 | 10 | 21 | 1 | 51 | 4 | 1 | 1 | 48 | 4 | 2 [...] | 5 | 2 | 2 | 32 | 12 | 33 | 15 | 47 | 6 | 59 | 7 | 33 | ||||||||||||
| 29 | 14 | 48 | 1 | 34 | 4 | 4 | 1 | 37 | 4 | 29 | 4 | 54 | 2 | 52 | 12 | 49 | 15 | 41 | 6 | 31 | 7 | 48 | ||||||||||||||
| 30 | 14 | 49 | 1 | 17 | 4 | 7 | 1 | 25 | 4 | 37 | 4 | 46 | 3 | 13 | 13 | 4 | 15 | 35 | 6 | 3 | 8 | 12 | ||||||||||||||
| 31 | 4 | 49 | [...] | 1 | 1 | 1 | 14 | 4 | [...]7 | 3 | 33 | 1 [...] | 2 [...] | 8 | 35 | |||||||||||||||||||||
Place these Tables in the Appendix between Page 18 and 19.
| Jan. | Feb. | Marc | April▪ | May▪ | June. | July. | Aug. | Sept. | Octob. | 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 | 59 | 14 | 48 | 10 | 8 | 0 | 49 | *l* | 4 | 9 | 1 | 5 | 4 | 43 | 4 | 30 | 3 | 48 | 13 | 14 | 15 | 23 | 5 | 42 | too | ||||||||||
| 2 | 9 | 21 | 14 | 47 | 9 | 5 | 0 | 32 | 4 | 11 | 0 | 53 | 4 | 51 | 4 | 20 | 4 | 9 | 13 | 28 | 15 | 15 | 5 | 13 | ||||||||||||
| 3 | 9 | 43 | 14 | 45 | 9 | 3 [...] | 0 | 16 | 4 | 12 | 0 | 40 | 4 | 58 | 4 | 10 | 4 | 29 | 13 | 42 | 15 | 5 | 4 | 45 | ||||||||||||
| 4 | 10 | 5 | 14 | 42 | 9 | 17 | 0 | 1 | 4 | 13 | 0 | 28 | 5 | 5 | 4 | 0 | 4 | 50 | 11 | 56 | 14 | 55 | 4 | 16 | ||||||||||||
| 5 | 10 | [...]6 | 14 | 38 | 8 | [...] | 0 | 14 | 4 | 12 | 0 | 16 | 5 | 11 | 3 | 49 | 5 | 10 | 14 | 8 | 14 | 44 | 3 | 47 | ||||||||||||
| 6 | 10 | 45 | Watch | 14 | 33 | Watch | 8 | 42 | Watch | 0 | 29 | Watch | 4 | 11 | Watch | 0 | 3 | *I* | 5 | 17 | Watch | 3 | 37 | Watch | 5 | 31 | Watch | 14 | 20 | Watch | 14 | 32 | Watch | 3 | 17 | slow. |
| 7 | 11 | 4 | 14 | 28 | 8 | 24 | 0 | 44 | 4 | 10 | 0 | 10 | 5 | 23 | 3 | 24 | 5 | 51 | 14 | 31 | 14 | 20 | 2 | 47 | ||||||||||||
| 8 | 11 | 23 | 14 | 23 | 8 | 0 | 58 | 4 | 8 | 0 | 23 | 5 | 28 | 3 | 11 | 6 | 12 | 14 | 41 | 14 | 6 | 2 | 17 | |||||||||||||
| 9 | 11 | 40 | 14 | 14 | 7 | 47 | 1 | 12 | 4 | 6 | 0 | 36 | 5 | 32 | 2 | 58 | 6 | 33 | 14 | 51 | 13 | 52 | 1 | 47 | ||||||||||||
| 10 | 11 | 57 | 14 | 9 | 7 | 29 | 1 | 26 | 4 | 4 | 0 | 49 | 5 | 35 | 2 | 44 | 6 | 53 | 15 | 1 | 13 | 38 | 1 | 18 | ||||||||||||
| 11 | 12 | 14 | too | 14 | 1 | too | 7 | 10 | too | 1 | 38 | too | 4 | 1 | too | 1 | 1 | Watch | 5 | 38 | too | 2 | 30 | too | 7 | 14 | too | 15 | 11 | too | 13 | 21 | too | 0 | 48 | *I* |
| 12 | 12 | 30 | 13 | 52 | 6 | 52 | 1 | 51 | 3 | 57 | 1 | 14 | 5 | 41 | 2 | 16 | 7 | 34 | 15 | 20 | 13 | 4 | 0 | 18 | ||||||||||||
| 13 | 12 | 44 | 13 | 43 | 6 | 33 | 2 | 3 | 3 | 52 | 1 | 27 | 5 | 43 | 2 | 2 | 7 | 54 | 15 | 26 | 12 | 47 | 0 | 12 | ||||||||||||
| 14 | 12 | 58 | 13 | 34 | 6 | 15 | 2 | 14 | 3 | 47 | 1 | 40 | 5 | 45 | 1 | 46 | 8 | 14 | 15 | 32 | 12 | 28 | 0 | 42 | ||||||||||||
| 15 | 13 | 12 | 13 | 24 | 5 | 56 | 2 | 24 | 3 | 41 | 1 | 53 | 5 | 46 | 1 | 30 | 8 | 33 | 15 | 38 | 12 | 9 | 1 | 12 | ||||||||||||
| 16 | 13 | 24 | fast. | 13 | 13 | fast. | 5 | 37 | fast. | 2 | 35 | slow. | 3 | 35 | slow | 2 | 5 | too | 5 | 46 | fast. | 1 | 13 | fast. | 8 | 53 | slow. | 15 | 44 | slow. | 11 | 50 | slow. | 1 | 42 | Watch |
| 17 | 13 | 35 | 13 | 2 | 5 | 18 | 2 | 46 | 3 | 29 | 2 | 17 | 5 | 45 | 0 | 56 | 9 | 13 | 15 | 49 | 11 | 30 | 2 | 11 | ||||||||||||
| 18 | 13 | 46 | 12 | 50 | 5 | 0 | 2 | 56 | 3 | 23 | 2 | 29 | 5 | 44 | 0 | 39 | 9 | 32 | 15 | 52 | 11 | 9 | 2 | 40 | ||||||||||||
| 19 | 13 | 56 | 12 | 37 | 4 | 41 | 3 | 4 | 3 | 15 | 2 | 41 | 5 | 42 | 0 | 21 | 9 | 52 | 15 | 55 | 10 | 47 | 3 | 9 | ||||||||||||
| 20 | 14 | 5 | 12 | 25 | 4 | 22 | 3 | 12 | 3 | 7 | 2 | 53 | 5 | 40 | 0 | 3 | 10 | 11 | 15 | 57 | 10 | 25 | 3 | 38 | ||||||||||||
| 21 | 14 | 1 [...] | 12 | 12 | 4 | 3 | 3 | 20 | 2 | 58 | 3 | 4 | fast. | 5 | 38 | 0 | 14 | too | 10 | 30 | 15 | 59 | 10 | 2 | 4 | 7 | too | |||||||||
| 22 | 14 | 20 | 11 | 57 | 3 | 44 | 3 | 28 | 2 | 50 | 3 | 16 | 5 | 35 | 0 | 31 | 10 | 48 | 16 | 1 | 9 | 38 | 4 | 35 | ||||||||||||
| 23 | 14 | 27 | 11 | 43 | 3 | 26 | 3 | 35 | 2 | 41 | 3 | 27 | 5 | 31 | 0 | 50 | 11 | 6 | 16 | 0 | 9 | 14 | 5 | 2 | ||||||||||||
| 24 | 14 | 32 | 11 | 28 | 3 | 8 | 3 | 42 | 2 | 31 | 3 | 38 | 5 | 27 | 1 | 9 | 11 | 24 | 15 | 59 | 8 | 49 | 5 | 29 | ||||||||||||
| 25 | 14 | 37 | 11 | 13 | 2 | 49 | 3 | 47 | 2 | 21 | 3 | 48 | 5 | 22 | 1 | 29 | 11 | 41 | 15 | 57 | 8 | 23 | 5 | 57 | ||||||||||||
| 26 | 14 | 41 | 10 | 58 | 2 | 31 | 3 | 52 | 2 | 11 | 3 | 59 | 5 | 16 | 1 | 49 | slow. | 11 | 58 | 15 | 55 | 7 | 57 | 6 | 23 | fast. | ||||||||||
| 27 | 14 | 44 | 10 | 42 | 2 | 13 | 3 | 56 | 2 | 1 | 4 | 9 | 5 | 10 | 2 | 7 | 12 | 14 | 15 | 52 | 7 | 31 | 6 | 50 | ||||||||||||
| 28 | 14 | 47 | 10 | 25 | 1 | 55 | 4 | 0 | 1 | 51 | 4 | 18 | 5 | 3 | 2 | 27 | 12 | 29 | 15 | 48 | 7 | 5 | 7 | 16 | ||||||||||||
| 29 | 14 | 48 | 1 | 38 | 4 | 3 | 1 | 40 | 4 | 27 | 4 | 56 | 2 | 47 | 12 | 45 | 15 | 43 | 6 | 38 | 7 | 41 | ||||||||||||||
| 30 | 14 | 49 | 1 | 22 | 4 | 6 | 1 | 28 | 4 | 35 | 4 | 48 | 3 | 8 | 13 | 0 | 15 | 37 | 6 | 10 | 8 | 6 | ||||||||||||||
| 31 | 14 | 49 | 1 | 5 | 1 | 17 | 4 | 39 | 3 | 28 | 15 | 31 | 8 | 29 | ||||||||||||||||||||||
| M | Jan. | Feb. | Marc. | April. | May | June. | July. | Aug. | Sep. | Octob. | Nov. | Dec. | ||||||||||||||||||||||||
| D | 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 | 53 | 14 | 49 | 10 | 12 | 0 | 53 | *l* | 4 | 9 | 1 | 8 | 4 | 41 | 4 | 32 | 3 | 43 | 13 | 11 | 15 | 25 | 5 | 49 | too | ||||||||||
| 2 | 9 | 15 | 14 | 47 | 9 | 54 | 0 | 36 | 4 | 10 | 0 | 56 | 4 | 49 | 4 | 23 | 4 | 4 | 13 | 25 | 15 | 17 | 5 | 20 | ||||||||||||
| 3 | 9 | 37 | 14 | 45 | 9 | 38 | 0 | 20 | 4 | 12 | 0 | 43 | 4 | 57 | 4 | 13 | 4 | 24 | 13 | 39 | 15 | 8 | 4 | 52 | ||||||||||||
| 4 | 9 | 59 | 14 | 42 | 9 | 21 | 0 | 4 | 4 | 13 | 0 | 31 | 5 | 4 | 4 | 2 | 4 | 45 | 13 | 53 | 14 | 58 | 4 | 23 | ||||||||||||
| 5 | 10 | 20 | 14 | 39 | 9 | 4 | 0 | 11 | 4 | 12 | 0 | 19 | 5 | 10 | 3 | 51 | 5 | 5 | 14 | 5 | 14 | 4 [...] | 3 | 54 | ||||||||||||
| 6 | 10 | 41 | Watch | 14 | 34 | Watch | 8 | 46 | Watch | 0 | 26 | Watch | 4 | 12 | Watch | 0 | 6 | *l* | 5 | 13 | Watch | 3 | 40 | Watch | 5 | 26 | Watch | 14 | 17 | Watch | 14 | 35 | Watch | 3 | 25 | slow. |
| 7 | 11 | 00 | 14 | 29 | 8 | 28 | 0 | 41 | 4 | 11 | 0 | 7 | 5 | 22 | 3 | 27 | 5 | 46 | 14 | 28 | 14 | 23 | 2 | 55 | ||||||||||||
| 8 | 11 | 18 | 14 | 24 | 8 | 10 | 0 | 55 | 4 | 9 | 0 | 20 | 5 | 27 | 3 | 14 | 6 | 7 | 14 | 39 | 14 | 10 | 2 | 25 | ||||||||||||
| 9 | 11 | 36 | 14 | 18 | 7 | 52 | 1 | 9 | 4 | 7 | 0 | 33 | 5 | 31 | 3 | 01 | 6 | 28 | 14 | 49 | 13 | 50 | 1 | 55 | ||||||||||||
| 10 | 11 | 54 | 14 | 11 | 7 | 34 | 1 | 22 | 4 | 4 | 0 | 46 | 5 | 35 | 2 | 48 | 6 | 48 | 14 | 59 | 13 | 41 | 1 | 25 | ||||||||||||
| 11 | 12 | 10 | too | 14 | 3 | too | 7 | 15 | too | 1 | 35 | too | 4 | 1 | too | 0 | 58 | Watch | 5 | 38 | too | 2 | 34 | too | 7 | 9 | too | 15 | 9 | too | 13 | 25 | too | 0 | 56 | *l* |
| 12 | 11 | 26 | 13 | 54 | 6 | 56 | 1 | 48 | 3 | 58 | 1 | 11 | 5 | 41 | 2 | 20 | 7 | 29 | 15 | 18 | 13 | 8 | 0 | 26 | ||||||||||||
| 13 | 12 | 41 | 13 | 45 | 6 | 38 | 2 | 0 | 3 | 53 | 1 | 24 | 5 | 43 | 2 | 5 | 7 | 49 | 15 | 25 | 12 | 51 | 0 | 4 | ||||||||||||
| 14 | 12 | 55 | 13 | 36 | 6 | 19 | 2 | 11 | 3 | 48 | 1 | 7 | 5 | 45 | 1 | 50 | 8 | 9 | 15 | 31 | 12 | 33 | 0 | 34 | ||||||||||||
| 15 | 13 | 9 | 13 | 26 | 6 | 0 | 2 | 22 | 3 | 43 | 1 | 30 | 5 | 46 | 1 | 34 | 8 | 29 | 15 | 37 | 12 | 14 | 1 | 4 | ||||||||||||
| 16 | 13 | 21 | fast | 13 | 15 | fast | 5 | 41 | fast. | 2 | 33 | slow. | 3 | 37 | slow. | 2 | 2 | too | 5 | 46 | fast. | 1 | 17 | fast. | 8 | 48 | slow. | 15 | 43 | slow | 11 | 55 | slow | 1 | 34 | Watch |
| 17 | 13 | 33 | 13 | 4 | 5 | 23 | 2 | 43 | 3 | 31 | 2 | 14 | 5 | 45 | 1 | 0 | 9 | 8 | 15 | 48 | 11 | 35 | 2 | 4 | ||||||||||||
| 18 | 13 | 43 | 12 | 53 | 5 | 4 | 2 | 52 | 3 | 24 | 2 | 26 | 5 | 44 | 0 | 43 | 9 | 28 | 15 | 52 | 11 | 14 | 2 | 33 | ||||||||||||
| 19 | 13 | 53 | 12 | 41 | 4 | 45 | 3 | 1 | 3 | 17 | 2 | 38 | 5 | 43 | 0 | 26 | 9 | 47 | 15 | 5 [...] | 10 | 53 | 3 | 2 | ||||||||||||
| 20 | 14 | 03 | 12 | 28 | 4 | 26 | 3 | 10 | 3 | 9 | 2 | 50 | 5 | 41 | 0 | 9 | 10 | 7 | 15 | 57 | 10 | 31 | 3 | 31 | ||||||||||||
| 21 | 14 | 11 | 12 | 15 | 4 | 7 | 3 | 18 | 3 | 0 | 3 | 2 | fast | 5 | 39 | 0 | 9 | * too | 10 | 25 | 15 | 59 | 10 | 8 | 4 | 0 | too | |||||||||
| 22 | 14 | 18 | 12 | 1 | 3 | 49 | 3 | 26 | 2 | 52 | 3 | 13 | 5 | 36 | 0 | 27 | 10 | 43 | 16 | 0 | 9 | 44 | 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 | 1 [...] | 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 | 4 [...] | 15 | 44 | 6 | 45 | 7 | 36 | ||||||||||||||
| 30 | 14 | 48 | 1 | 25 | 4 | 6 | 1 | 31 | 4 | 33 | 4 | 50 | 3 | 3 | 12 | 5 [...] | 15 | 38 | 6 | 17 | 8 | 0 | ||||||||||||||
| 31 | 14 | 49 | 1 | 9 | 1 | 19 | 4 | 41 | 3 | 23 | 15 | 32 | 8 | 24 | ||||||||||||||||||||||
[Page 19] 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 Sundyal 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 [Page 20] 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 [Page 21] 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 0h 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 0h 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.
[Page 22] 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 Ca [...]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.
But much the best way which I have yet thought of, and which is exceedingly nice, is with the instrument, Fig. 3. which is thus made. At each end of a board, or rather small flat Iron-bar (A. B) fix two upright sights: one with a very small Hole (a. b.) to look through to the Sun; the other (c. d.) with a larger hole, to look at the Pole-star. Not far from the Sights, on the same bar, fix two arms (C. D, C. D) to bend off, so as to be out of the way of the Sights, when you look through them. On the top of these arms, place a small rod of Iron or Wood, to turn with a joynt at D. which rod is to
Fig. 3.
Fig. 2.
[Page 23] bear the Plumb-lines (E. F.) and to turn backward and forward, so as to bring the Plumb-lines to the Sights at any time. Place this instrument on a Pedestal (G. H.) to turn round on it stiffly.
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, 'tis 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, [Page 24] and the Sun in the Summer Solstice, or any time of the Year. If the bottom piece be 2 feet long▪ the Plumblines 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 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.
[Page 25] 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 whereever there is occasion to correct either Sun Dial or Watch.
| 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 | |||||||||||
[Page 27] 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.
[Page 28] 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.
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