30 0 56 0 49 1 17 7 7 00 0 52 0 44 1 16 8 6 00 0 43 0 39 1 8 9 5 00 0 36 0 34 1 2 10 4 40 0 25 0 29 1 2 Remarks upon the Table The Column of the Sun's Refractions I owe to that accurate observer of the celestial motions Mr Flamsteed Which Refractions altho in the Table the same yet do differ at different seasons of the year nay perhaps according to the different temperature of the air sometimes in the same day Thus Mr Flamsteed found the Refractions in February very different from those in April and it is observed that the Refractions are commonly greater when the Mercury is higher in the Barometer The Table therefore doth not shew what the Refractions always are but only about the middle quantity of them at every degree of the 10 first of the Sun's altitude And accordingly I have calculated the Variations thereby made in the hour of the day These Variations of the hour are greater or lesser according as the angle of the Sun 's diurnal motion is acuter with the horizon The reason is plain because as the Sun appears by refraction higher than really he is so this false height doth affect the hours in Winter more than the Summer half year There is no ray indeed of the Sun but what cometh refracted to a Sun dial and consequently there is no Dial but what goeth more or less false except at Noon in Dials that cast a Shade where the refraction makes no variation But the Refraction decreaseth apace as the Sun gets higher and causeth a variation of not above half a minute at 10 degrees of the Sun's altitude except when the Sun is in or near the Southern Tropick Nearer than half a minute few common Sun-dials shew the time And therefore partly for this reason and partly because Mr. Flamsteed's observations reach not much farther I have calculated my Table to only 10 degrees The Table needs little explication For having the Sun's height you have against it in the next Column the Refraction and in the 3 next the alterations of the hour at 3 times of the year Taking therefore by a Quadrant the Sun's altitude and observe at the same time the hour of the day by a Sun-dial by the Table you see how many minutes and seconds the Dial is too fast As at the Sun-rising a Sun-dial is too fast 4′ 34″ about June 11 and 3′ 32″ about Mar. 10. and Sept. 12 and 4′ 38″ about Dec. 11. Addenda TO the Fifth part of the Rule in § 6. p. 21. If you have occasion to lay the Pinion of Report upon any other Wheel and not the great-Wheel you may do it by this Rule As the Beats in one turn of any Wheel To the Beats in an hour So are the hours of the Dial To the Quotient of the Hour-wheel divided by the Pinion of Report To page 66. Suppose in altering an old Watch you would have it shew minutes as well as hours you may do it thus Divide the Beats in one turn of the Great-wheel by the Beats in an hour the Quotient will shew in how many hours the Great-wheel goeth round once If the Beats in the Great wheel exceed the Train you must chuse your Minute-wheel first and multiply it by the Quotient this will give the Pin. of Report But if the Train exceeds the Beats of the Great-wheel you must chuse the Pin. of Rep. and multiply the Quotient by it the product is the Minute-wheel But it often falls out that the Train and Beats of the Great-wheel will not exactly measure one another if so the best way is to half the two numbers as far as they will equally admit of halfing or divide them by some common divisor and so having brought them to as small numbers as you can you may suppose them to be a Wheel and Pinion and reduce them to lesser numbers by Chap. 2. Sect. 2. § 5. Thus suppose you would make the old dull Movement there mentioned a Minute-watch you may reduce the numbers of the Great-wheel 2188â— and the Train 9368 to a Pinion and Wheel 28 12. Which Pin. 28 being set upon the Spingle of the Gr. Wh. will drive a Wheel 12 round once in an hour to shew Minutes If you make this Wh. 12 drive another of 48 concentrical to which is a Pin. 12 driving a Wheel 36 which Wheel is concentrical with the Minute-wheel this will carry a Hand round in 12 hours But in this case you must place the Pin. 28 on the Spindle of the Gr. Wh. so as to slide round stiffly when you turn the Minute-hand to rectifie the Watch. FINIS Oughtred of Autom sect 4. 4 36 9 5 55 11 5 45 9 5 40 8   17 By the Quotients I commonly mean the â—umber of Turns which number is set on the right hand without a hook as is shewn in the last Paragraph Which I noâ—e â—ere now once for all 5 5â— 11 5 45 9 5 40 8 8 80 10 6 54 9 5 40 8   15 4 32 8 5 55 11 5 45 9 5 40 8   17 Sir J. Moor Mat. Com. p. 109. Ibid. p. 116. Oughtred Autom Sect. 14. 28 1440 Ought ib. Id. ib. 9  8 36 X 8 4  1 32 X 9 Id. ib. Oughtred Sect. 12. Sir J. Moor Ibid. p. 109. 4 36 9 5 55 11 5 45 9 5 40 8   17 Oughtred Sect. 21. § 8. 4 28 7 5 55 11 5 45 9 5 40 8   17 Id. ib. § 22. 24 20 20 24 6 60 10 6 48 8 5 40 8 5 33 6â…—   17 Horol Disq Sect. 1. § 6. 8 40 5   15 8 64 8 8 60 7½ 8 40 5   15 § 6. Par. 3. and § 7. â— 108 12 â— 64 8 â— 60 7½ â— 40 5   15 Sir J. Mooâ— Ibid. p. 116. V. Sect. 1. § 6. 8 96 12 8 64 8 8 60 7½   30 8 48 6 6 78 13 pins 6 60 10 6 48 8 § 1. Infer 2â— 15 195 13 13 195 15 10 65 6â— 8 48 6 6 48 8 pins V. Sect. 1 §. 3. 8 104 13 6 72 12. 24 pins 12 39 3¼ 10 120 12 8 96 12  78 26 pins 13 39 3 Ch. 2. Sect. 2. § 7. Oughtred § 26. 4 62 15½ 5 20 4 4 62 15½ 10 40 4 Id. ib. 10 5 9 â—9 4 40 10 4 59 14¾ 10 40 4 Id. ib. 4 73 18¼ 4 40 10 5 20 4 4 73 18¼ 4 32 8 4 20 5 Autom § 35. Id. ib. Mat. Com. p. 117. V. Sect. 1 § 4 5. De Subtil l. 17. 4 48 12 7 56 8 6 54 9   19 Horol Dis p. 54. 2736 9368 3½ 4 48 12 7 56 8 6 54 9 6 2â— 3½   19 V. Sect. 1 § 6. 4 48 12 7 56 8 6 54 9 6 36 6   11 6 30 5 7 56 8 6 54 9 6 48 8   19 4 39 â—¾ 7 56 8 pins 6 54 9 6 48 8 5 24 7 18 6 7 56 8. 16 pins 6 54 9 6 48 8 Sir J. Moor Mat. Com. R. 5. Id. ib. Rule 3. De Horol Oscil p. 10 11 12. Machina Pneumat Exp. 26. Ibid. Ibid. Fiugenius â—â—â—i supra p. 141. Sir J. Moor ibid. Hugen Moor ibâ— Horolog Disquis Ibid. Ibid. de Centro Oscil Prop. 23. 2 Kings â—0 11. Isai 38. 8. Lexic in verbo 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 De die Natali c. 23. Ibid. Nat. Hist l. 2. c. 76. De Archit l. 6. c. 48. In the Life of Dions Euseb Vit. Const l. 3. De Subtil l. 17. De Architect l. 9. c. 9â— Vâ—d Phiâ—â—nd not in Vitruv. Lib. 1. § 25. Edit Elâ—ivir Epigr. in Sphoer Archimed Vid. Card. de Subtil l. 17. De Nat. Deor. Lib. 2. § 34. Mâ—lyneaux Scioth Telescop Ep. Dedic Cosmog l. 2. Magia Univers P. 1. Proleg Magia Thaumaturg Hor. Oscil p. 3 Edit Paris p. 8. Exper made in the Acad del Cimento by Mr. Walâ—er p. 12. Hugen ib. Horolog Disquis p. 3.
as 144 is To 170 So is 360 To 425. Or as 170 to 144 So is 360 To 305. In number thus 144. 170 360. 425. Or 170. 144 360. 305. Divide 360 and either of these two fourth and last numbers by 4 5 6 8 c. as is directed in the Rule last cited If you divide by 8 you will have for your numbers 1 14 74 â— 4 â—5 â— or 3 48 5. If you divide by 15 which will not bring it so near an integer you will have 2 24 8 or 2 â—0 4 which last are the numbers set down in the Margin where the numbers of the whole Movement are set down § 10. Having said enough I think concerning the Calculation of ordinary Watches to shew the hour of the day I shall next proceed to such as shew minutes and seconds The process whereof is thus First having resolved upon your beats in an hour you are next to find how many beats there will be in a minute by dividing your designed Train into 60 parts And accordingly you are to find out such proper numbers for your Crown-wheel and quotients as that the Minute-wheel shall go round once in an hour and the Second-wheel once in a minute An Example will make all plain Let us chuse a Pendulum of 6 inches to go 8 days with 16 turns of the Fusy By Mr Smith's Tables a Pendulum of 6 inches vibrates 9368 in an hour This divided by 60 gives 156 beats for a minute Half these summs are 4684 and 78. Now the first work is to break this 78 into good proportions which will fall into one quotient and the Crown-wheel First for the Crown-wheel let it have 15 notches Divide 78 aforeâ— by this 15 the quotient will be 5. Aâ— so this first work is done for a Crowâ— wheel of 15 and a Wheel aâ— Pinion whose quotient is 5 â— in the Margin will go rouâ— in a minute to carry a Haâ— to shew Seconds Next for a Hand to go round in â— hour to shew Minutes Now becauâ— there are 60 minutes in an hour 't is bâ— breaking 60 into two gooâ— quotients which may be â— and 6 or 8 and 7½ or c. and the work is done Thus your number 4684 broken as near as can be intâ— proper numbers But because it does not fall out exact into the above-mentioned numbers yoâ— must Correct as you were directed before and find out the true number â— beats in an hour by multiplying 15 by 5 which makes 75 and this by 6â— makes 4500 which is the half of the truâ— Train Then to find out the beats in on turn of thy Fusy operate as before viâ— As the number of turns 16 To the coâ—tinuanâ— 192 So is 4500 to 54000 which are half the beats in one turn of â—he Fusy In numbers thus 16. 192 4500. 54000. This 54000 must be diâ—ided by 4500 which are the true â—umbers already piâ—ched upon or beats â—n an hour The quotient of this division â—s 12 which being not too big for one single quotient needs not be divided into more The work will stand as you see in the Margin As to the Hour-hand the Great-Wheel which performs only one revolution in 12 turns of the Minute-wheel will shew the hour Or rather you may order it to be done by the Minute-wheel â—s shall be shew'd hereafter § 11. I shall add but one Example more and so conclude this Section and â—hat is To calculate the numbers of a â—iece whose Pendulum swings Seconds â—o shew the hour minutes and seconds â—nd to go 8 days which is the usual perâ—ormance of those Movements called â—oyal Pendulums at this day First cast â—p the number of seconds in 12 hours which are the beats in one turn of 〈◊〉 Great-wheel These are 12 times 〈◊〉 minutes and 60 times that gives 432â— which are the seconds in 12 hours Hâ— this number for the reasons before 21600. The Swing-wheel must neâ— be 30 to swing 60 seconds in one of 〈◊〉 revolutions Divide 21600 by it aâ— 720 is the quotient or number left to 〈◊〉 broken into quotients Of these quoâ—ents the first must needs be 12 for 〈◊〉 Great-wheel which moves round onâ— in 12 hours Divide 720 by 12 〈◊〉 quotient is 60 which may be conveâ— ently broken into two quotients as 〈◊〉 and 6 or 5 and 12 or 8 and 7 ½ whiâ— last is most convenient Aâ— if you take all the Pinions the work will stand as in 〈◊〉 Margin According to this compuâ— tion the Great-wheel will 〈◊〉 about once in 12 hours shew the hour if you please the Secoâ— wheel once in an hour to shew the 〈◊〉 nutes and the Swing-wheel once in a 〈◊〉 nute to shew the seconds Thus I have endeavour'd with all possible plainness to unravel this most mysterious as well as useful part of Watch-work In which if I have offended the more learned Reader by unartificial terms or multitude of words I desire the fault may be laid upon my earnest intent to condescend to the meanest capacity SECT III. To Calculate the Striking part of a Clock § 1. ALtho this part consists of many Wheels and Pinions yet respect needs to be had only to the Count-wheel Striking-wheel and Detent-wheel which move round in this proportion The Count-wheel moveth round commonly â—nce in 12 or 24 hours The Detent-wheel moves round every stroke the Clock striketh sometimes but once in two strokes From whence it follows 1. That as many Pins as are in the Pin-wheel so many turns hath the Detent-wheel in one turn of the Pin-wheel Or which is the same the Pins of thâ— Pin-wheel are the Quotient of that Wheel divided by the Pinion of the Detenâ—-wheel But if the Detent-wheel moveth but once round in two strokes oâ— the Clock then the said Quotient is buâ— half the number of Pins 2. As many turns of the Pin-wheel aâ— are required to perform the strokes of 1â— hours which are 78 So many turâ—â— must the Pinion of Report have to turn round the Count-wheel once Or thus Divide 78 by the number of Striking pins and the Quotient thereof shall bâ— the Quotient of the Pinion of Report Alâ— this is in case the Pinion of Report bâ— fixed to the arbor of the Pin-wheel as iâ— very commonly done All this I take to be very plain or 〈◊〉 it be not the example in the Margin wilâ— clear all difficulties Herâ— the Locking-wheel is 48â— the Pinion of Report is 8â— the Pin-wheel is 78 thâ— Striking-pins are 13. Anâ— so of the rest I need onlâ— to remark hero that 7â— being divided by the 13 pins gives 6â— which is the Quotient ofâ— the Pinionâ— of Report as was before hinted As for the Warning-wheel and Flying-Pinion it matters little what numbers they have their use being only to bridle the rapidity of the motion of the other Wheels Besides the last observation there are other ways to find out the Pinion of Report which
this caused several pieces of this nature to be made altho they did not take till after 1675. However he had before so far proceeded herein as to have a Patent drawn tho not sealed for these and some other Contrivances about Watches in the year 1660. But the reason why that Patent did no further proceed was some disagreement about some Articles in it with some Noble Persons who were concerned for the procuring it The same ingenious Dr. had also a Grant for a Patent for this last way of Spring Watches in the year 1675 but he omitted the taking it out as thinking it not worth the while § 7. After these Inventions of Dr. Hook and no doubt after the Publication of Mr. Hugens's book de Horolog Oscil at Paris 1673 for there is not a word of this tho of several other Contrivances after this I say Mr. Hugen's Watch with a Spiral Spring came abroad and made a great noise in England as if the Longitude could be now found One of these the Lord Bruncker sent for out of France where Mr Hugen â— had a Patent for them which I have seen This Watch of Mr. Zulichem's agreed with Dr. Hook's in the application of the Spring to the ballance only Mr. Zulichem's had a longer Spiral Spring and the Pulses and Beats were much slower That wherein it differs is 1. The Verge hath a Pinion instead of Pallets and a Contrate-wheel runs therein and drives it round more than one turn 2. The Pallets are on the Arbor of this Contrate-wheel 3. Then followeth the Crown wheel c. 4. The ballance instead of turning scarce quite round as Dr. Hook's doth turn several rounds every vibration § 8. As to the great abilities of Mr. Hugens no man can doubt that is acquainted with his Books and his share in the Philosophical Transactions c. But I have some reason to doubt whether his fancy was not first set on work by some Intelligence he might have of Dr Hook's Invention from Mr Oldenburgh or others his correspondents here in England But whether or no that ingenious person doth owe any thing herein to our ingenious Dr Hook it is however a very pretty and ingenious contrivance but subject to some defects viz. When it standeth still it will not vibrate until it is set on vibrating which tho it be no defect in a Pendulum Clock may be one in a Pocket-Watch which is exposed to continual jogs Also it doth somewhat vary in its Vibrations making sometimes longer sometimes shorter turns and so some slower some quicker vibrations I have seen some other contrivances of this sort which I mention not because they are of younger standing But these two of Dr Hook and Mr Hugens I have taken notice of because they were the first that ever appeared in the world CHAP. IX The Invention of Repeating Clocks § 1. THe Clocks I now shall speak of are such as by pulling of a String c. do strike the Hour Quarter or Minute at any time of the day and night § 2. These Clocks are a late Invention of one Mr Barlow of no longer standing than the latter end of K. Charles II. about the year 1676. This ingenious Contrivance scarce so much as thought of before soon took air and being talked of among the London Artists set their heads to work who presently contrived several ways to effect such a performance And hence arose the divers ways of Repeating work which so early might be observed to be about the Town every man almost practising according to his own Invention § 3. This Invention was practised chiefâ— if not only in larger Movements 〈◊〉 K. James II.'s Reign at which time it as transferred into Pocket-Clocks But â—ere being some little contest concernâ—g the Author hereof I shall relate the â—â—e matter of fact leaving the Reader to â—own judgment About the latter end of K. James II.'s â—gn Mr Barlow the ingenious Inventer â—ore-mentioned contrived to put his â—ention into Pocket watches and enâ—voured with the Lord Chief Justice â—bone and some others to get a Patent â—it And in order to it he set Mr Tomâ— the famous Artist to work upon it â—o accordingly made a Piece according â—is directions â—r Quare a very ingenious Watch â—er in London had some years before 〈◊〉 thinking of the like Invention but bringing it to perfection he laid by thoughts of it until the talk of Mr Barâ— Patent revived his former thoughts â—ch he then brought to effect This â—g known among the Watch-makers 〈◊〉 all pressed him to endeavour to hinâ— Mr Barlow's Patent And accordingly applications were made at Court and a Watch of each Invention produced before the King and Council The King upon tryal of each of them was pleased to give the preference to Mr Quare's of which notice was given soon after in the Gazette The difference between these two Inventions was Mr Barlow's was made to Repeat by pushing in two pieces on each side the Watch-box one of which Repeated the Hour the other the Quarter Mr Quare's was made to Repeat by aâ— Pin that stuck out near the Pendant which being thrust in as now 't is done by thrusting in the Pendant did Repeat both the Hour and Quarter with the samâ— thrust It would I think be very frivolous toâ— speak of the various contrivances and methods of Repeating work and the Inventers of them and therefore I shall saâ— nothing of them CHAP. X. Numbers for several sorts of Movements I Think it may be very convenient to set down some Numbers fit for several Movements partly to be as Examples to exercise the young Reader in the foregoing Art of Calculation and partly to serve such who want leisure or understanding to attain to this Art § 1. But first it may be requisite to shew the usual way of Watch-makers writing down their Numbers which is somewhat different from that in the preceding Book Their way representeth the Wheel and Pinion on the same Spindle not as they play in one another Thus the numbers of an old House-Watch of 12 hours is written thus My way The Watch-makers way 4 48 48 7 56 56 4 6 54 54 7 19 19 6 According to my way the Pin. of Report 4 drives the Dial-wheel 48 the Pinion 7 plays in the Great-wheel 56 c. But according to the other way the Dial-wheel stands alone the Great-wheel hath the Pinion of Report on the same arbor the Wheel 54 hath the Pin 7 and the Crown-wheel 19 the Pin 6 on the same Spindles This latter way tho very inconvenient in Calculation representeth a piece of work handsomely enough and somewhat naturally § 2. Numbers of an 8 day Piece with 16 turns the Barrel the Pend. vibrates Seconds the shews Minutes Seconds c. The Watch-part The Clock part 8 96 8 78 8 60 48 48 6 72 6 48 8 pins 7 56 6 48 30 6 48 In the Watch-part the Wheel 60 is the Minute-wheel which is set in the
middle of the Clock that its Spindle may go thro the middle of the Dial-plate to carry the Minute-hand Also on this Spindle is a Wheel 48 which driveth another Wheel of 48 which last hath a Pinion 6 which driveth round the Wheel 72 in 12 hours Note here two things 1. That the two Wheels 48 are of no other use but to set the Pinion 6 at a convenient distance from the Minute-wheel to drive the Wheel 72 which is concentrical with the Minute-wheel For a Pinion 6 driving a Wheel 72 would be sufficient if the Minute-hand and Hour-hand had two different centers 2. These numbers 60 48 48-6 72 set thus ought according to the last § be thus read viz. The Wheel 60 hath another Wheel 48 on the same Spindle which Wheel 48 divideth playeth in or turns round another Wheel 48 which hath a Pinion 6 concentrical with it which Pinion driveth or divideth a Wheel of 72. For a Line parting two numbers as 60-48 denoteth those two numbers to be concentrical or to be placed upon the same Spindle And when two numbers have a hook between them as 48 48 it signifies one to run in the other as hath before been hinted In the Striking-part there are 8 Pins on the Second wheel 48. The Count-wheel may be fixed unto the Great-wheel which goeth round once in 12 hours § 3. A Piece of 32 days with 16 or 12 turns both parts the Watch sheweth Hours Minutes and Seconds and the Pend. vibrateth Seconds The Watch-part With 16 turns With 12 turns 16 96 12 96 9 72 9 72 8 60 48 48 6 72 8 60 48 48 6 72 7 56 7 56 30 30 The Striking part With 16 turns With 12 turns 10 130 8 128 8 96 24 pins 8 104 26 pins 12 39 8 24 6 72 Double hoop 8 96 Double hoop 6 60 8 80 The Pinion of Report is fixed on the â—nd of the arbor of the Pin wheel This Pinion in the first is 12 the Count-wheel 39 thus 12 39. Or it may be 8 26. â—n the latter with 12 turns it may be 6 18 or 8 24. § 4. A two month Piece of 64 days with 16 turns Pend. vibrateth Seconds and sheweth Minutes Seconds c. Watch-part Clock-part 9 90 10 80 8 76 10 65 8 60 48 48 6 72 9 54 12 pins 7 56 8 52  5 60-Double Hoop 30 5 50 Here the third Wheel is the Pin-wheel which also carrieth the Pinion of Report 8 driving the Count-wheel 52. Or thus Watch-part Clock-part 8 80 6 144 8 76 6 78 26 pins 8 60 48 48 6 72 8 24 7 56 6 72-Double Hoop 30 6 60 § 5. A piece of 13 weeks with Pendulum Turns and Motions as before The Watch part 8 96 Or thus 6 72 8 88 6 66 8 60 48 48 6 72 6 48 48 48 6 72 7 56 6 45 30 30 The Clock part 8 72 Or thus 5 145 8 64 37 30 6 90 30 pins 8 48 12 pins 24 62 6 48 Double Hoop 6 72 5 40 6 60 § 6. A Seven Month Piece with Turns Pendulum and Motions as before The Watch. The Clock 8 60 8 96 8 56 8 88 27 12 8 48 8 64 16 pins 6 45 48 48 6 72 6 48 Double Hoop 5 40 6 48 30  § 7. A Year Piece of 384 days with Turns Pendulum and Motions as before The Watch. The Clock 12 108 10 120 9 72 8 96 36 9 8 64 6 78 26 pins 8 60 48 48 6 72 6 72 Double Hoop 7 56 6 60 30  If you had rather have the Pinion of Report on the Spindle of the Pin-wheel it must be 13 39. § 8. A Piece of 30 Hours Pendulum about 6 inches The Watch. The Clock 12 48 8 48 6 78 6 78 13 pins 6 60 6 60 6 42 6 48 15  § 9. A Piece of 8 days with 16 turns Pendulum about 6 inches to shew Minutes Seconds c. The Watch. The Clock may be the same with the 8 day piece before § 2. 8 96 8 64 48 48 6 72 8 60 8 40 The Seconds Wheel 15 § 10. A Month Piece of 32 days with Pendulum Turns and Motions as the last The Watch. The Clock may have the same numbers as the Clock § 3. 8 64 8 48 6 48 48 48 6 72 6 45 6 30 Seconds Wheel 15 § 11. A Year Piece of 384 days with Pendulum Turns c. as the last The Watch part 10 90 Or thus with a Wheel less and not to shew Minutes and Seconds 8 64  7 56 8 96 6 48 6 72 36 9 6 45 48 48 6 72 6 66 6 30 6 60 Seconds Wheel 6 54 15 19 In the latter of these two Numbers the Pinion of Report is 36 on the Second Wheel The Dial Wheel is 9. The Clock-part may have the same Numbers as the Year-piece before § 7. § 12. An 8 Day Piece to shew the Hour and Minute Pend. about 3 inches long 6 96 The Clock may have the same numbers as the 8 day piece before § 2. 8 64 6 72 7 49 6 36 19 Automata shewing the Motion of the Celestial Bodies § 1. Numbers for the Motion of the Sun and Moon See before in Chap. 2. Sect. 5. § 3 4. § 2. Numbers to shew the Revolution of the Planet Saturn which consists of 10759 days On the Dial-wheel If you would make it depend upon a Wheel going round in a year thus 5 69 4 52 4 48 10 59 or thus 4 118 4 40 6 30 Note The lowermost Pinion in these and the following numbers is to be fixed concentrical to the Wheel which is to drive the Motion viz. the Dial-wheel Year-wheel or c. § 3. Numbers for the Planet Jupiter whose Revolution is 4332 ½ days On the Dial-wheel 4 48 Or thus on the Year-wheel 4 40 6 71 4 36  4 32  Note here That the two last numbers of Saturn may be the two first of Jupiter also By the permission of my ingenious friend Mr Flamsteed I here insert a description of Mr Olaus Romer the French King 's Mathematician's Instrument to represent the Motion of Jupiter's Satellites a copy of which he sent to Mr Flamsteed in 1679. Upon an axis which turns round once in 7 days are four Wheels fixed one of 87 teeth a second of 63 the third 42 and the last of 28 teeth On another axis run 4 other Wheels or Pinions you may call them which are driven by the asoresaid Wheels The first is a Wheel or Pinion of 22 leaves driven by the Wheel 87 which carrieth round the first Satellite The second is 32 driven by the Wheel 63 which carrieth round the second Satellite The third hath 43 leaves driven by the Wheel 42 which carrieth the third Satellite And lastly is the Pinion 67 driven by the Wheel 28 which carrieth round the fourth Satellite On the first axis is an Index that pointeth to a circle divided into 168 parts which are the hours in 7 days On
the other axis all the Pinions run concentrically by means of their being hollow in the middle In the midst of them all the axis of Jupiter himself is fixed with a little Ball at the top representing Jupiter's body On the ends of 4 small Wires fixed in the four several Sockets of the aforesaid Pinions may 4 lesser Globules be placed at their due distance from Jupiter's Globule to represent the 4 Satellites going round that Planet § 4. Numbers for Mars whose Revolution is 1 year 322 days On the Dial-wheel  4 48 The two last Numbers of Saturn may be the two first of Mars also 4 40 4 45 § 5. Numbers for Venus whose Revolution is in 224 days On the Dial-wheel  4 32 Note The last number of Jupiter may be the first of Venus 4 32 4 28 § 6. Numbers for Mercury whose Revolution is near 88 days On the Dial-wheel 4 56 4 52 § 7. Numbers to represent the Motion of the Dragon's Head and Tail near 19 years to shew the Eclipses of the Sun and Moon On the Dial-wheel On the Year-wheel 4 48 4 76 4 40 Note The two last numbers of Saturn may be the two first of this on the Dial-wheel 4 44 4 42 As to the placing these several Motions on the Dial-plate I shall leave it wholly to the Work-mans contrivance He may perhaps make them to represent the Copernican or some other Sysâ—em Numbers for Pocket Watches § 1. A Watch to go 8 Days with 1â— turns to shew Minutes and Seconds the Train 16000. 6 96  6 48 12 48 12 36. 6 45 On the Wheel 42 is the Second's hand placed and on the Wheel 48 the Minute hand 6 42 19 § 2. Another of the same without Minutes and Seconds to go with only 8 turns 20 10 6 66 6 60 5 50 5 45 19 § 3. A Pocket-Watch of 32 Hours with 8 turns to shew Minutes and Seconds Train as the last 12 48 6 48 12 48 12 36 6 45 6 42 Seconds Hand 19 § 4. The usual Numbers of 30 hours Pendulum Watches with 8 turns to shew the Hour and Minute 12 48 6 54 12 48 12 36 6 48 6 45 15 § 5. The usual Numbers of the old 30 hours Pocket-watches With 5 Wheels With 4 Wheels 10 30 6 32 7 63 6 66 6 42 5 50 6 36 5 45 6 32 13 15 If any of the Numbers of the preceding Wheels and Pinions should not please the Reader he may easily correct them to his mind by the Instructions in the foregoing Book The way in short is this Divide the Wheel by the Pinion and so find the number of turns according to Chap. 2. Sect. 1. § 2. Multiply the Pinion you like better by this number of turns and the Product is the Wheel Thus in the 8 day Pocket-watch § 1 if you think the Great-wheel too large you make it instead of 6 96 16 thus viz. 5 80 16 i. e. chusing the Pinion only 5 and multiplying it by 16 the turns the Wheel will be 80. CHAP. XI Tables of Time relating to Watch-work A Table of Time Seconds       60 Minutes      3600 60 Hours     86400 1440 24 Day    604800 10080 168 7 Week   2592000 43200 720 30 4 Month.  31536000 525600 8760 365 52 12 Year The foregoing Table will be of good use in Calculation for the ready finding out the parts of Time which is thus Find the parts of time you seek for the number in the concurrence of Squares is the answer to your question Thus suppose you seek for the number of Seconds â—n a Year in the Square under Seconds and in the same line with Year which is the â—owermost Square on the left hand is the number sought viz. 315 c. So Minutes in a Month are 43200. If you would know any number where there is the addition of an odd number to it as the Seconds in a Month and one day add the Seconds in a month which are 259 and the Seconds in a Day which are 86 and you have the number sought viz. 2678400. A Table to set a Watch by the Fixed Stars Night Hour Min. Sec. Night Hour Min. Sec. 1 0 3 57 16 1 3 20 2 0 7 54 17 1 7 17 3 0 11 51 18 1 11 14 4 0 15 47 19 1 15 11 5 0 19 44 20 1 19 8 6 0 23 41 21 1 23 5 7 0 27 38 22 1 27 1 8 0 31 35 23 1 30 58 9 0 35 32 24 1 34 55 10 0 39 29 25 1 38 52 11 0 43 26 26 1 42 49 12 0 47 23 27 1 46 46 13 0 51 29 28 1 50 43 14 0 55 26 29 1 54 40 15 0 59 23 30 1 58 36 Explanation of the Table This Table shews how much the Sidereal goeth faster than the Solar day in any number of nights for a month So that observing by your Watch the nice time when any fixed Star cometh to the Meridian or any other point of the Heavens if after one Revolution of that same Star to the same point your Watch goeth 3′ 57″ â—lower than the Star or after two nights 7′ 54″ or 16 nights 1 h. 3′ 20″ c. then doth your Watch keep time rightly with the Mean motion of the Sun If it vary from the Table you must alter the length of your Pend to make it so keep time To observe the time nicely when the Star cometh again to the same point of the heavens 't is necessary to make the observation with a Telescope that hath cross threads in the focus of the object-glass and so leaving the Telescope fixed in the same posture till a second Observation You may do this with the telescopular sights of a Quadrant or Sextans and so leaving it standing until anoher night of Observation Or for want of this more nice way you may do it by looking along by the edge of two Strings suspended with Plumbets in a room at some distance from one another Or by looking at the edge of a Chimney c. as Mr Watson hath directed at the end of Mr Smith's Horoâ— Disquis But to make a tolerable observation any of these last ways 't is necessary to have a Candle shine upon the edge of the furthermost String or Chimney without which you cannot see exactly when the Star cometh thereto A Table shewing the Variations made in the true Hour of the Day by the Refraction of the Sun in the Equator and both the Solstices Sun's altitude Deg. Sun's Refraction Variation at the N. Solstice Variation at the Equator Variation at the S. Solstice ′ ″ ′ ″ ′ ″ ′ ″ 00 33 00 4 34 3 32 4 38 1 23 00 2 34 2 28 3 19 2 17 00 2 24 1 49 2 31 3 13 30 1 46 1 27 2 3 4 11 30 1 29 1 12 1 40 5 9 30 1 12 1 1 1 33 6 7
exceeded I shall therefore commit this task to some better Pen hoping that no person will take it amiss that I have not mentioned what I have been beholding to him for the relation of For the resons last mentioned I have also left out of my Book a Chapter of the Art of making and using many sorts of Sodders the way of colouring Metals c. useful in the practice of Clock-work This I had prepared for the sake of Mercurial Gentlemen but omitted printing it and some other things out of Charity to poor Apprentices and other Workmen whose purses I am unwilling my volume should too much exceed If I have at any time invaded the Workman's province it was not because I pretend to teach him his Trade but either for Gentlemen's sakes or when the matter led me necessarily to it I have nothing more to add but that I would have this little Treatise looked upon only as an Essay which I hope will prompt some abler pen to perform the task better especially in the Historical part For since Watch-work oweth so much to our Age and Country t is pity that it should not be remembred especially when we cannot but lament the great defect of History about the beginning and improvements of this ingenious and useful Art THE CONTENTS CHap. I. Of the Terms of Art The more general Terms p. 2. Names belonging properly to the Watch-part p. 8. Names of the Clock-part p. 5. Chap. II. The Art of Calculation Sect. 1. Preliminary Rules To find the turns of a Wheel or Pinion 8. The way of writing down the Numbers 9. To find the turns of any or all the Wheels in the Movement 10. To find the Beats of the Ballance in all the Watches going or in one turn of any Wheel 11. Two strokes to every tooth of the Crown wheel 14. Sect. 2. Calculation of the Watch-part Several ways of performing one and the same motion 15. A Rule to vary Numbers 16. The way of working the Golden Rule 17. A very useful Rule to vary inconvenient Numbers 18. Rules of perpetual use in proportioning the parts of a Watch 19. Examples of contriving a piece of ordinary Watch-work 22. Examples thereof for Minutes and Seconds 29. Sect. 3. Calculation of the Striking-part General Observations and Rules relating to the Wheel-work of a Clock p. 33. Rules of perpetual use in proportioning the parts of a Clock 35. Examples of Calculating the Numbers of a small Clock 38. Examples of Clocks of longer continuance 39. An useful Rule to find the number of Strokes in one turn of the Fusy 33. Examples of fixing the Pinion of Report 34. Sect. 4. Of Quarters and Chimes Notes concerning the Quarters 45. Of making the Chime-barrel 46. Of dividing it and setting on the Chime-pins 47. Chimes of Psal 100 and of a Song-tune 50. Another way of setting Chimes on the Barrel 52. Sect. 5. To calculate Numbers to represent the Celestial Motions Contrivance of Movements only to shew these Motions 53. To add it to a Watch that shews the hour of the day 55. A motion to shew the day of the month 56. To shew the Age of the Moon 57. To shew the day of the Year and Sun's place in the Ecliptick his Rising or Setting c. 58. To shew the Tydes ib. To represent the motion of the Planets fixed Stars c. 60. Chap. III. To alter Clock-work p. 62. Example of converting a 12 hour Ballance-clock into a Pendulum 63. To make it go 30 hours 65. To change the Clock-part 67. Chap. IV. To size Wheels and Pinions To do it Arithmetically 69. Mechanically 70. Chap. V. Of Pendulums Irregularities of Pendular motions remedied 71. Cause of the difference of the motion of the same Pendulum 72. True length of a Pendulum that vibrateth Seconds 73. To find the Center of Oscillation 74. To calculate the Lengths or Vibrations of Pendulums 75. A Table of Lengths and Swings 78. To correct the motion of a Pendulum 79. Chap. VI. The Antiquity and general History of Watch-work The ancientest Time-engine 82. The Grecian and Roman ways of measuring Time 83. Some horological Instruments mentioned by ancient Authors 84. Watch or Clock-work no new German Invention 86. The Sphere of Archimedes 87. Of Poâ—idonius 89. The beginning of our present Clock-work 91. Clocks that perform strange feats 92. Chap. VII The Invention of Pendulum Watches Mr. Hugens the Inventer p. 93. Others claiming it 94. Their beginning in England 95. The contriver of their carrying a heavy Ball c. 96. Their use ibid. The Circular Pendulum 97. Chap. VIII Of the Invention of Pocket Pendulum Watches Inventer p. 99. Several ways of them ib. The time when invented 103. Mr. Hugens's Watch 104. Chap. IX The Invention of Repeating Clocks The Inventer p. 106. When and by whom first used in Pocket Clocks 107. Chap. XI Numbers for various Movements The way of Watch-makers writing down their Numbers 109. Numbers of an 8 day Piece 110. A Month Piece 112. A Two Month Piece 113. A Quarter of Year piece 114. An Half Year Piece ib. A Year Piece 115. A lesser 30 hours Piece ib. A small Week Piece ib. A small Month Piece 116. A small Year Piece ib. An 8 day Piece Pend. 3 inches 117. Numbers representing the Motion of the Planet Saturn 118. Of Jupiter ib. Monsieur Romer's Instrument for Jupiter's Satellites 119. Numbers for Mars Venus and Mercury 120. For the Dragons Head and Tail 121. Numbers for Pocket Watches of 8 days ib. Of 30 hours 122 123. The way to amend the Numbers 123. Chap. XI Tables of Time A Table for ready casting up the parts of Time 124. A Table to set a Watch by the Fixed Stars 125. A Table of the Variations of the Hour by the Sun's Refraction 117. Observations concerning Refractions and the Variations of the Hour 128 The Artificial CLOCK-MAKER CHAP. I. Of the Terms of Art or Names by which the parts of an Automaton are called IT is necessary that I should shew the meaning of those Terms which Clock-makers use that Gentlemen and others unskilful in the Art may know how to express themselves properly in speaking and also understand what I shall say in the following Book I shall not trouble the Reader with a recital of every name that doth occur but only such as I shall have occasion to use in the following discourse and some few others that offer themselves upon a transient view of a piece of work I begin with the more general Terms as the Frame which is that which contains the Wheels and the rest of the work The Pillars and Plates are what it chiefly consists of Next for the Spring and its appurtenances That which the Spring lies in is the Spring-box that which the Spring laps about in the middle of the Spring-box is the Spring-Arbor to which the Spring is hooked at one end At the top of the Spring-Arbor is the Endless-Screw and its Wheel That which the Spring draweth and about
which the Chain or String is wrapped and which is commonly taper is the Fusy In larger work going with weights where it is cylindrical it is called the Barrel The small Teeth at the bottom of the Fusy or Barrel that stop it in winding up is the Ratchet That which stops it when wound up and is for that end driven up by the String is the Garde-caut or Guard-Cock as others and Garde-du-Cord and Gard-du-Gut as others call it The parts of a Wheel are the Hoop or Rim the Teeth the Cross and the Collet or piece of Brass soddered on the Arbor or Spindle on which the Wheel is rivetted A Pinion is that little Wheel which plays in the teeth of the Wheel Its teeth which are commonly 4 5 6 8 c. are called Leves not Teeth The ends of the Spindle are called Pevetts the holes in which they run Pevet-holes The guttered Wheel with Iron spikes at the bottom in which the line of ordinary House-Clocks doth run is called the Pully I need not speak of the Dial-plate the Hand Screws Wedges Stops c. Thus much for general Names which are common to all parts of a Movement The parts of a Movement which I shall consider are the Watch and Clock The Watch-part of a Movement is that which serveth to the measuring the hours In which the first thing I shall consider is the Ballance whose parts are the Rim which is the circular part of it the Verge is its Spindle to which belong the two Pallets or Nuts which play in the fangs of the Crown Wheel in Pocket-Watches that strong Stud in which the lower Pevet of the Verge plays and in the middle of which one Pevet of the Crown-Wheel runs is called the Pottans the wrought piece which covers the Ballance and in which the upper Pevet of the Ballance plays is the Cock The small Spring in the new Pocket-Watches is the Regulator The parts of a Pendulum are the Verge Pallets and Cocks as before The Ball in long Pendulums the Bob in short ones is the Weight at the bottom The Rod or Wire is plain The terms peculiar to the Royal Swing are the Pads which are the Pallets in others and are fixed on the Spindle The Fork is also fixed on the Spindle and about 6 inches below catcheth hold on the Rod at a flat piece of Brass called the Flatt in which the lower end of the Spring is fastened The names of the Wheels next follow The Crown-Wheel in Small pieces and Swing-Wheel in Royal Pendulums is that Wheel which drives the Ballance or Pendulum The Contrate-Wheel is that Wheel in Pocket-Watches which is next to the Crown-Wheel whose Teeth and Hoop lye contrary to those of other Wheels The Great-Wheel or First-Wheel is that which the Fusy c. immediately driveth Next it are the Second-Wheel Third-Wheel c. Next followeth the Work between the Frame and Dial-Plate And first is the Pinion of Report which is that Pinion which is commonly fixed on the Arbor of the Great-Wheel and in old Watches used to have commonly but four Leaves which driveth the Dial-Wheel and this carrieth about the Hand The last Part which I shall speak of is the Clock which is that part which serveth to strike the Hours In which I shall First speak of the Great or First-Wheel which is that which the Weight or Spring first drives In 16 or 30 hour Clocks this is commonly the Pin-Wheel in 8 Day pieces the Second-Wheel is commonly the 〈◊〉 This Wheel with Pins is sometimes called the Striking-Wheel or Pin-Wheel Next to this Striking-Wheel followeth the Detent-Wheel or Hoop-Wheel having a Hoop almost round it in whicâ— is a vacancy at which the Clocâ— locks The next is the Third or Fourth Wheel according as it is distant froâ— the First-Wheel called also the Warning Wheel And lastly is the Flying-Pinion with a Fly or Fan to gather Air and so bridle the rapidity of the Clock's motion Besides these there are the Pinion oâ— Report of which before which driveth round the Locking-Wheel called also the Count-Wheel with 11 Notches in it commonly unequally distant from one another to make the Clock strike the hourâ— of 1 2 3 c. Thus much for the Wheels of the Clock part Besides which there are the Rash or Ratch which is that sort of Wheel of twelve large Fangs that runneth concentrical to the Dial-Wheel and serveth to lift up the Detents every hour and make the Clock strike The Detents are those Stops which by being lifted up or let â—all down do lock and unlock the Clock in striking The Hammers sâ—rike the Bell The Hammer-tails are what the Striking-pins draw back the Hammers by Latches are what liâ—t up and unlock the Work Catches are what hold by hooking or catching hold of The Lifting-pieces do lift up and unlock the Detents in the Clock part CHAP. II. The Art of Calculation SECT I. General preliminary Rules and Directions for Calculation § 1. FOR the more clear understanding this Chapter it must be observed that those Automata whose Calculation I chiefly intend do by little Interstices or Strokes measure out longer portions of Time Thus the strokes oâ— the Balance of a Watch do measure ouâ— Minutes Hours Days c. Now to scatter those strokes among Wheels and Pinions and to proportionatâ— them â—so as to measure Time regularly is the design of Calculation For thâ— clearer discovery of which it will be necessary to proceed leisurely and gradually § 2. And in the first place you are to know that any Wheel being divided by its Pinion shews how many turns that Pinion hath to one turn of that Wheel Thus a Wheel of 60 teeth driving a Pinion of 6 will turn round the Pinion 10 times in going round once From the Fusy to the Ballance the Wheels drive the Pinions and consequently the Pinions run faster or go more turns than the Wheels they run in But it is contrary from the Great-Wheel to the Dial Wheel Thus in the last Example The Wheel drives round the Pinion 10 times but if the Pinion drove the Wheel it must turn 10 times to drive the Wheel round once § 3. Before I proceed further I must shew how to write down the Wheels and Pinions Which may be done either as Vulgar Fractions or in the way of Division in Vulgar Arithmetick E. C. A Wheel of 60 moving a Pinion of 5 may be set down thus 60 3 or rather thus 5 60 where the first figure is the Pinion the next without the hook is the Wheel The number of Turns which the Pinion hath in one turn of the Wheel is set without a hook on the right hand as 5 60 12 i. e. a Pinion 5 playing in a Wheel of 60 moveth round 12 times in one turn of the Wheel A whole Movement maâ— be noted thus 4 â—â— 55 5 45 5 40 5 17 Notches in the Crown Wheel Or rather as you see here in the Margin where the
of the new Pendulum Pocket Watches or any other Train Having thus pitched upon your Train you must next resolve upon the number of turns you intend your Fusy shall have and also upon the number of Hours you would have your Piece to go As suppose 12 turns and to go 30 hours or 192 hours which is 8 days or c. These things being all soon determined you next proceed to find out the beats of the Ballance or Pendulum in one turn of the Fusy by the last § 6. part 3. viz. As the turns of the Fusy To the hours of the Watch's going So is the Train To the number of beats in one turn of the Fusy In numbers thus 12. 16 20000. 26666. Which last number are the beats in one turn of the Fusy or Great-Wheel and by Sect. I. § 5. of this Chap. are equal to the Quotients of all the Wheels unto the ballance multiplied together This number therefore is to be broken into a convenient parcel of Quotients which you are to do after this manner First half your number of beats viz. 26666 for the reasons in Sect. I. § 6. of this Chap. the half whereof is 13333. Next you are to pitch upon the number of your Crown-wheel as suppose 17. Divide 13333 by 17 the Quotient will be 784 or to speak in the language of one that understands not Arithmetick divide 13333 into 17 parts and 784 will be one of them This 784 is the number left for the Quotients or turns of the rest of the Wheels and Pinions which being too big for one or two Quotients may be best broken into three Chuse therefore 3 numbers which when multiplied all together continually will come nearest 784. As suppose you take 10 9 and 9. Now 10 times 9 is 90 and 9 times 90 is 810 which is somewhat too much You may therefore try again other numbers as suppose 11 9 and 8. These multiplied as the last produce 792 which is as near as can be and convenient Quotients Thus you have contrived your Piece from the Great-Wheel to the Ballance But the numbers not falling out exactly according as you at first proposed you must correct your work thus First to find out the true number of beats in one turn of the Fusy you must multiply 792 aforesaid which is the true product of alâ— the Quotients by 17 the notches of the Crown-wheel the product of this iâ— 13464 which is half the number of true beats in one turn of the Fusy by Sect. ◠§ 5. of this Chap. Then to find the truâ— number of beats in an hour say by § 6 part 4. of this Section as the hours oâ— the Watch's going viz. 16 to the 1â— turns of the Fusy So is 13464 the haâ—â— beats in one turn of the Fusy to 1009â— the half beats in an hour the numbeâ— will stand thus 16. 12 13464. 1009â— Then to know what Quotient is to bâ— laid upon the Pinion of Report say by 〈◊〉 6. part 5. of this Sect As the hours 〈◊〉 the Watch's going viz. 16 to the turâ— of the Fusy viz. 12 So are the houâ—â— of the Dial-plate viz. 12 To the Quotient of the Pinion of Report In numbers thus 16. 12 12. 9. Having thus found out all your Quotients 't is easie to determine what numbers your Wheels shall have for chuse what numbers your Pinions shall have and multiply the Pinions by their Quotients and that produceth the numbers for your Wheels as you see in the Margin Thus 4 is the number of your Pinion of Report and 9 its quotient therefore 4 times 9 which makes 36 is the number for the Dial-wheel So the next Pinion being 5 and its quotient 11 this multiplied produces 55 for the Great-wheel And the like of the rest of the following numbers Thus as plain as words can express it I have shewed how to Calculate the numbers of a 16 hour Watch. § 8. This Watch may be made to go a longer time by lessening the Train and altering the Pinion of Report Suppose you could conveniently slacken the Train to 16000 the half of which is 8000. Then say by § 6 part 2. of this Sect. As the halfed Train or Beats in an hour viz. 8000 To the halfed beats in one turn of the Fusy viz. 13464 So are the turns of the Fusy viz. 12 To the hours of the Watch's going in numbers thus 8000. 13464 12. 20 So that this Watch will go 20 hours Then for the Pinion of Report say by the same § part 5 As 20 the Continuance To 12 the turns of the Fusy So are 12 the hours of the Face To 7 the quotient of the Pinion of Report In numbers thus 20. 12 12. 7. The work is the same as before as to the numbers only the Dial-wheel is but 28 because its quotient is altered to 7 as appears in the Margin by the Scheme of the work § 9. I shall give the Reader one example more for the sake of shewing him the use of some of the foregoing Rules not yet taken notice of in the former operations Suppose you would give numbers to a Watch of about 10000 beats in an hour to have 12 turns of the Fusy to go 170 hours and 17 notches in the Crown-wheel This work is the same as in the last Example § 7. In short therefore thus As the turns 12 are To the Continuance 170 So is the Train 10000 To 141666 which are the beats in one turn of the Fusy The numbers will stand thus 12. 170 10000 14â—666 Half this last is 70â—33 Divide this half into 17 parts and 4167 will be for the quotients And because this number is too big for 3 quotients therefore chuse 4 as suppose 10 8 8 and 6 â…— i. e. 6 and 3 fifths These multiplied together as before and with 17 maketh 71808 which are half the true beats in one turn of the Fusy By this you are to find out your true Train first saying as in the former example As 170 to 12 So 71808 to 5069 which last is the half of the true Train of your Watch. Then for the Pinion of Report say as 170 to 12 So 12 to 1 â—4 74 â— Which Fraction ariâ—eth thus If you multiply 12 by 12 it makes 144 and divide 144 by 170 you cannot but setting the 144 the dividend over 170 the Divisor and there ariâ—eth this fraction â— 24 â—4 â— which is a Wheel and Pinion the lower is the Pinion of Report and the upper is the Dial-wheel according to Sect. I. § 3. of this Chapter Or which perhaps will be more plain to the unlearned Reader you may leave those two numbers in their Divisional posture thus 170 144 which does express the Pinion and Wheel in the way I have hitherto made use of But to proceed These numbers being too big to be cut in small Wheels may be varied as you see a like Example is § 5. of this Section viz. Say
will fall under the next § § 2. These following Rules will be of great use in this part of Calculation viz. Rule 1. As the number of turns of the Great-wheel or Fusy To the days of the Clock's continuaucâ— So is the number of strokes in 24 hours viz. 156 To the strokes in one turn of the Fusy or Great-wheel Rule 2. As the number of strokes in 24 hours which are 156 To the strokes in one turn of the Fusy or Great-wheel So are the turns of the Fusy or Great-wheel To the days of the Clock's continuance or going Rule 3. As the strokes in one turn of the Fuâ—y To the strokes of 24 hours viz. 156. So is the Clock's continuance To the number of turns of the Fusy or Great-wheel These two last Rules are of no great use as the first is but may serve to correct your work if need be when in breaking your Strokes into Quotients of which presently you cannot come near the true number but a good many strokes are left remaining In this case by Rule 2. you may find whether the continuance of your Clock be to your mind And by Rule 3 you may enlarge or diminish the number of turns for this purpose The praxis hereof will follow by and by The 2 following Rules are to find fit numbers for the Pinion of Report and the Locking-wheel besides what is said before § 1. Inference 2. Rule 4. As the number of Strokes in the Clock's continuance or in all itâ— turns of the Fusy To the turns of the Fusy So are the Strokes in 12 hours which are 78 To the Quotient of the Pinion of Report fixed upon the arbor of the Great-wheel But if you would fix it to any other Wheel you may do it thus as is before hinted viz. Rule 5. First find out the number of Strokes in one turn of the Wheel you intend to fix your Pinion of Report upon which I shall shew you how to do in the following § Divide 78 by this number and the number arising in the Quotient is the Quotient of the Pinion of Report Or thus Take the number of Strokes inâ—â—e turn of the Wheel for the number of the Pinion of Report and 78 for the Count or Locking wheel and vary them to lesser numbers by Sect. 2. § 5. of this Chapter Rule 6. The foregoing Rules are of greatest use in Clocks of a larger continuance altho where they can be applied they will indifferently serve all But this Rule which will serve larger Clocks too I add chiefly for the use of lesser Pieces whose continuance is accounted by hours The Rule is to find the Strokes in the Clock's continuance viz. As 12 is to 78 So are the hours of the Clocks continuance To the number of Strokes in that time This Rule I said may be made use of for the largest Clock but then you must be at the trouble of reducing the Days into Hours Whereas the shortest way is to Multiply the strokes in one turn of the Great-wheel by the number of Turns Thus in an 8 day piece the Strokes in one turn are 78. These multiplied by 16 the turns produce 1248 which are the Strokes in the Clock's continuance If you work by the foregoing Ruled the hours of 8 days are 192. Then say 12 78 192. 1248. § 3. In this Paragraph I shall shew the use of the preceding Rules and by examples make all plain that might seem obscure in them I begin with small Pieces of which but briefly And first having pitched upon the number of turns and the continuance you must find by the last Rule how many Strokes are in its continuance Then divide these Strokes by the number of turns and you have the number of Striking-pins Or divide by the number of Pins and you have the number of Turns Thus a Clock of 30 hours with 15 turns of the Great-wheel hath 195 strokes For by the last Rule 12. 78 30. 195. Divide 195 by 15 it gives 13 for the Striking-pins Or if you chuse 13 for your number of Pins and divide 195 by it it gives 15 for the number of â—urns as you see in the Margin As for the Pinion of Report and the rest of the Wheels enough is said in the § 1. But suppose you would calculate the numbers of a Clock of much longer continuance which will necessitate you to make your Pin-wheel further distant from the Great-wheel you are to proceed thus Having reâ—olved upon your turns you must find out the number of strokes in one turn of the Great-wheel or Fusy by § 2 Rule 1. Thus in an 8 day piece of 16 turns 16. 8 156. 78. So in a piece of 32 days and 16 turns 16 32 156. 312. These strokes so found out are the number which is to be broken into a convenient parcel of Quotients thus First resolve upon your number of Striking-pins divide the last named number by it The quotient arising hence is to be one or more quotients for the Wheels and Pinions As in the last examples Divide 78 by 8 the usual pins in an 8 day piece and the quotient is 9â— which is a quotient little enough So in the Month-piece if you take your Pins 8 divide 312 by it the quotient is 39. Which being too big for one must bâ— broken into two quotients for Wheels and Pinions or as near 〈◊〉 can be which may bâ— 7 and 5 or 6 and 6½ Thâ— latter is exactly 39 and may thereâ—oâ— stand as you see is done in the Margin The quotients being thus determined and accordingly the Wheels and Pinioâ—â— as you see the next work is to find 〈◊〉 quotient for the Pinion of Report to â—â—ry round the Count or Locking whâ—â— once in 12 hours or as you please â— you fix your Pinion of Report on thâ— Great-wheel arbor you must operate 〈◊〉 the Rule 4. of the last paragraph As 〈◊〉 the last example in the Month-piece 〈◊〉 Rule 6. before the strokes in the contiâ—â—ance are 4992. Then by Rule 4 say 4992. 16 78. 499â— 124â— or thus 4992 1248. The first of which two numbers is the Pinion the next is the Wheel Which being too large may be varied to â—â— 9 or 36 9 or to â—4 6 or 24 6 by Sect. 2 § 5. before These numbers being not the usual numbers of a Month-piece but only made use of by me as better illustrating the foregoing Rules I shall therefore for the fuller explication of what has been said briefly touch upon the calculation of the more usual numbers They commonly encrease the number of Striking-pins and so make the Second-wheel the Striking-wheel Suppose you take 24 Pins Divide 312 by it and the Quotient is 13. Which is little enough for one Quotient and may therefore stand as you see is done in the Margin where the Quotient of the first Wheel is 13. In the second Wheel of 72 teeth are the 24 pins altho its quotient is but 12
should happen to be such double Notes on every Bell instead of 8 you must have 16 Hammers and accordingly you must divide your Barrel and strike 16 strokes round it opposite to each Hammer-tail Thus much for dividing your Barrel from end to end In the next place you are to divide iâ— round about into as many divisions as there are Musical Barrs Semibriefs Minums c. in your Tune Thus the 100th Psalm-tune hath 20 Semibriefs the Song-tune following hath 24 Barrs of triple time and accordingly their Barrels are divided Each division therefore of the 100th Psalm Barrel is a Semibrief â—nd of the Song-tune 't is three crotchets And therefore the intermediate Spaces serve for the shorter notes as one third of a division is a Crotchet in the Song-tune One half a division is a Minum and one quarter a Crotchet in the Psalm-tune Thus the first note in the 100th Psalm is a Semibrief and accordingly on the Barrel 't is a whole division from 5 to 5. The second is a Minum and therefore 6 is but half a division from 5 and so of the rest And so also for the Song-tune which is shorter time The two first notes being Quavers are distant from one another and from the third pin but half a third part of one of the divisions But the two next pins of the bell 3 3 being Crotchets are distant so many third parts of a division And the next pin of the bell 1 being a Minum is distant from the following pin 4 two thirds of a division A Table of Chimes to the 100 Psalm The Musical Notes of Psalm 100. The Musical Notes of Such Command o're my Fate c A Song The Chimes of the Song Such Command o're my Fate c. Pins to be set on the Barrel You may observe in the Tables that from the end of each Table to the beginning is the distance of two or near two divisions which is for a Pause between the end of the Tune and its beginning to Chime again I need not say that the Dotts running about the Tables are the places of the Pins that play the Tune If you would have your Chimes compleat indeed you ought to have a set of Bells to the Gamut notes so as that each Bell having the true sound of Sol La Mi Fa you may play any Tune with its Flats and Sharps Nay you may by these means play both the Bass and Treble with one Barrel If any thing going before appears gibberish I can't help it unless I should here teach the skill of Musick too As to setting a Tune upon the Chime-barrel from the number of Bells viz. 1 2 3 4 I shall here give you a specimen thereof Such Command o're my Fate in numbers 775 3 3 1. 4 5 6 4. 4 2. 4 3 2 3 4 6 3 5 7 7 7. ‖ 5 6 8 8 4. 4 4 3 5 4. 6 5 7 5 3 41 3 5 5 5. 3 3 1 3 5. 554 2 4 6. 4 3 23 3 53 5 7 7 7. Note In these numbers a Comma signifies the note before it to be a Crotchet A prick'd Comma or Semi-colon denoteth a prick'd Crotchet And a Period is a Minum Where no punctation is those Notes are Quavers I shall only add further that by setting the Names of your Bells at the head of any Tune as is done in the Tables before you may easily transfer that Tune to your Chime-barrel without any great skill in Musick But observe that each line in the Musick is three notes distant i. e. there is a Note between each line as well as upon it as is manifest by inspecting the Tables SECT 5. To Calculate any of the Celestial Motions The Motions I here chiefly intend are the Day of the Month the Moons age the Day of the Year the Tides and if you please the slow motion of the Suns Apogaeum of the Fixed Stars the motion of the Planets c. § 1. For the effecting these Motions you may make them to depend upon the Work already in the Movement or else measure them by the beats of a Ballance or Pendulum If the latter way you must however contrive a Piece as before in Watch-work to go a certain time with a certain number of turns But then to Specificate or determine the Motion intended you must proceed one of these two ways either 1. Find how many beats are in the Revolution Divide these beats by the beats in one turn of the Wheel or Pinion which you intend shall drive the intended Revolution and the Quotient shall be the number to perform the same Which if too big for one may be broken into more Quotients Thus if you would represent the Synodical Revolution of the Moon which is 29 days 12 ¾ hours with a Pendulum that swings Seconds the Movement to go 8 days with 16 turns of the Fusy and the Great-wheel to drive the Revolution Divide 2551500 the Beats in 29 days 12 ¾ hours by 43200 the Beats in one turn of the Great-wheel and you will have 59 in the Quotient which being too big for one may be put into two Quotients Or 2. You may proceed as is directed before in the Section of Calculating Watch-work viz. Chuse your Train turns of the Fusy Continuance c. And then instead of finding a Quotient for the Pinion of Report find a number which is all one as a Pin. of Report to Specificate your Revolution by this following Rule Rule As the Beats in one turn of the Great-wheel To the Train So are the Hours of the Revolution To the Quotient of the Revolution Thus to perform the Revolution of Saturn which is 29 years 183 days with a 16 hour Watch of 26928 Beats in one turn of the Fusy and 20196 the Train the quotient of the Revolution will be 193824. For As 26928 To 20196 So 258432 the Hours in 29 y. and 183 d. To 193824. Note here That the Great-wheel Pinion is to drive the Revolution work But if you would have the Revolution to be driven by the Dial-wheel and the Work already in the Movement which in great Revolutions is for the most part as nice as the last way and in which I intend to treat of the particular Motions in this case I say you must first know the Days of the Revolution And because the Dial-wheel goeth round twice in a day therefore double the number of the days in the Revolution and you have the number of turns of the Dial-wheel in that time This number of turns is what you are to break into a convenient number of quotients for the Wheels and Pinions as shall be shewed in the following examples § 2. A Motion to shew the Day of the Month. The days in the largest Month are 31. These doubled are 62 which are the turns of the Dial-wheel which may be broken into these two quotients 15 ½ and 4 which multiplied together make 62. Therefore chusing your Wheels and Pinions as
hath been directed in the former Sections your work is done The Wheels and Pinions may be as you see done in the Margin Or if a larger Pinion than one of 5 be necessary by reason it is concentrick to a Wheel you may take 10 for the Pinion and 40 for the Wheel as in the Margin The work will lye thus in the Movement viz. Fix your Pinion 10 concentrical to the Dial-wheel or to turn round with it upon the same Spindle This Pinion 10 drives the Wheel 40 which Wheel has the Pinion 4 in its center which carrieth about a Ring of 62 teeth divided on the upper side into 31 days Or you may without the trouble of many Wheels effect this motion viâ— By a Ring divided into 30 or 31 days and as many Fangs or Teeth like a Crown wheel teeth which are caught and pushed forward once in 24 hours by a pin in a Wheel that goeth round in that time This is the usual way in the Royal Pendulums and many other Clocks and therefore being common I shall say no more of it § 3. A Motion to shew the age of the Moon The Moon finisheth her course so as to overtake the Sun in 29 days and a little above an half This 29 ½ days not regarding the small excess makes 59 twelve hours or turns of the Dial-wheel which is to be broken into convenient quotients which may be 5 9 and 10 as in the first example or 14¾ and 4 as in the second example in the Margin So that if you fix a Pinion of 10 concentrical with your Dial-wheel to drive a Wheel of 40 according to the last example which Wheel 40 drives a Pinion 4 which carries about a Ring or Wheel of 59 teeth divided on the upper side into 29 ½ 't will shew the Moons age § 4. A Motion to shew the day of the Year the Sun's place in the Ecliptick Sun's Rising or Setting or any other annual motion of 365 days The double of 365 is 730 the turns of the Dial-wheel in an year which may be broken into these quotients viz. 18 ¼ and 10 and 4 according to the first example or 18 ¼ 8 and 5 according to the second So that a Pinion of 5 is to lead a Wheel of 20 which again by a Pinion of 4 leadeth a Wheel of 40 which thirdly by a Pinion of 4 carrieth about a Wheel or Ring of 73 divided into the 12 months and their days or into the 12 signs and their degrees or into the Sun's Rising and Setting c. For the setting on of which last you have a Table in Mr. Oughtred's Opuscula § 5. To shew the Tides at any Port. This is done without any other trouble than the Moon 's Ring before mentioned § 3. to move round a fixed circle divided into twice 12 hours and numbered the contrary way to the age of the Moon To set this to go right you must find out at what Point of the Compass the Moon makes full Sea at the place you would have your Watch serve to Convert that point into hours allowing for every point North or S. lost 45′ of an hour Thus at London-bridge 't is vulgarly thought to be high Tide the Moon at N. E. and S. W which are 4 Points from the N. and S. Or you may do thus by Tide-tables learn how many hours from the Moon 's Southing 't is High-water Or thus find at what hour it is High-water at the Full or Change of the Mâ—on as at London-bridge the full Tide is commonly reckoned to be 3 hours from the Moon 's Southing or at 3 of clock at the Full and Change The day of Conjunction or New-Moon with a little stud to point being set to the hour so found will afterwards point to the hour of full Tide This is the usual way but it being always in motion as the Tides are not a better way may be found out viz. By causing a Wheel or Ring to be moved forward only twice a day and to keep time as near as can be with Mr. Flamsteed's most correct Tables But this I shall commit to the Readers contrivance it being easie and more of curiosity than use § 6. To Calculate Numbers to shew the Motion of the Planets the Slow Motion of the Fixed Stars and of the Sun's Apogeum c. Having said enough before that may be applied here and they being only curiosities seldom put in practice I shall not therefore trouble the Reader or swell my Book with so many words as would be required to treat of these Motions distinctly and compleatly Only thus much in general Knowing the years of any of these Revolutions you may break this number into quotients if you will make the Revolution to depend upon the year's Motion which is already in the Movement and described § 4. before Or if you would have it depend upon the Dial-wheel or upon the Beats of a Penduluâ— enough is said before to direct in mis matter In all these Slow motions you may somewhat â—â—â—â—ten your labour by endless Screws to serve for Pinions which are but as a Pinion of one tooth Sir Jonas Moor's account of his large â—phere going by Clock-work will suffiâ—ently illustrate this paragraph In this â—phere is a Motion of 17100 years for â—he Sun's Apogeum performed by six â—heels thus as Sir Jonas relates it For the Great-wheel fixed is 96 a Spindle-wheel of 12 bars turns round it 8 times in 24 hours that is in 3 hours after these there are four Wheels 20 73 24 and 75 wrought by endless Screws that are in value but one therefore 3 20 73 24 and 75 multiplied together continually produceth 7884000 hours which divided by 24 gives 3285000 days equal to 900 years Now on the last wheel 75 is a pinion of 6 turning a great Wheel that carrieth the Apogeum number 114 and 114 divided by 6 gives 19 the quotient and 900 times 19 is 17100 years Thus I have with all the perspicuity I â—ould led my Reader through the whole â—rt of Calculation so much of it at least â—at I hope he will be master of it all not â—ly of those motions which I have parâ—cularly treated about but of any other â—t mentioned Such as the Revolution of the Dragons Head and Tail whereby the Eclipses of the Sun and Moon are found the Revolution of the several Orbs according to the Ptolemaick System or of the celestial bodies themselves according to better Systems with many other such curious performances which have made the Sphere of Archimedes of old famous and since him that of William of Zeland and another of Janellus Turrianus of Cremona mentioned by Cardan and of late that elaborate piece of Mr. Watson late of Coventry now of London in her late Majesties Closet CHAP. III. To alter Clock-work or convert one Movement into another THis Chapter I design for the use of such as would convert old
and is as an Architect of so great a work as the World is as the Collocutor expresseth himself His words so far as they relate to my present purpose are these Cum Solarium vel descriptum aut ex Aqua contemplere intelligere declarari horas arte non casu c. And a little after Quod si in Scythiam aut in Britanniam Sphaeram aliquis tulerit hanc quam nuper familiaris noster effecit Posidonius cujus singulae Conversiones idem efficiunt in Sole in Luna in quinque Stellis errantibus quod efficitur in coelo singulis diebus noctibus quis in illa barbarie dubitet quin ea Sphaera sit perfecta ratione The sum of the Authors meaning is That there were Sun-dials described or drawn with Lines after the manner as our Sun-dials are and some made with Water which were the Clepsydrae or Hour-glasses before-mentioned That Posidonius had lately contrived a Sphere whose Motions were the same in the Sun Moon and 5 Planets as were performed in the heavens each day and night The age wherein this Sphere was inâ—ented was Cicero's time which was aâ—out 80 years before our Saviours birth And that it was a piece of Clock-work â—s not I think to be doubted if it be â—onsidered that it kept time with those â—elestial bodies imitating both their anâ—ual and diurnal motions as from the â—escription we may gather it did It may be questioned whether those Machines were common or not I believe â—hey were rarities then as well as Mr Watâ—n's and others are accounted now But â—nethinks it is hard to imagine that so â—seful an Invention should not be reduced â—to common use it being natural and â—sie to apply it to the measuring of â—ours tho unequal especially in two â—â—ch Ages as those of Archimedes and â—ully were in which the Liberal Arts so greatly flourished § 6. After the times last mentioned I â—nd little worth remark till the last Age 〈◊〉 which Clock-work was revived or â—holly invented anew in Germany as is â—enerally thought because the ancient â—ieces are German work But who was â—e Inventer or in what time I cannot discover Some think Sever. Boethius invented it about the year 510. Perhaps it was in Regiomontanus his time if not so early as Boethius which was above 200 years ago It is very manifest it was before Cardan's time because he speaketh of it as a thing common then And he lived about 150 years since § 7. As to those curious contrivances in Clock-work which perform strange surprizing feats I shall say little Dr. Heylin tells us of a famous Clock and Dial in the Cathedral Church of Lunden in Denmark In the Dial saith he are to be seen distinctly the Year Month Week-day and Hour of every day throughout the Year with the Feasts both moveable and fixed together with the Motion of the Sun and Moon and their passage thro each degree of the Zodiack Then for the Clock it is so framed by artifical Engines that whensoever it is to strike two Horse-men encounter one another giving as many blows apiece as the Bell sounds hours And on the opening of a door there appeareth a Theatre the Virgin Mary on a Throne with Christ in her arms and the three Kings or Magi with their several trains marching in order doing humble reverence and presenting severally their Gifts two Trumpeters sounding all the while to adorn the Pomp of that Procession To this I might add many more such curious performances but I rather chuse to refer the Reader to Schottus where he may find a great variety to please him CHAP. VII Of the Invention of Pendulum Watches § 1. THe first that invented the way of applying Pendulums to Watch-work was Mr Christian Hugens of Zulichem as he affirmeth of himself with very cogent reasons This excellent invention he says he put first in practice in the year 1657 and in the following year 1658 he printed a delineation and description of it Others have claimed the honour of this Invention among which the great Galileo hath the most to be said on his side Dr. John Joachim Becher who printed a Book when he was in England entituled De Nova Temporis dimetiendi ratione Theoria c. which he dedicated to the English Royal Society Anno 1680. he I say tells us That the Count Magalotti the Great Duke of Tuscany's Resident at the Emperors Court told him the whole History of these Pendulum Clocks and denied Mr Zulichem to be the Author of them Also That one Treffler Clock-maker to the Father of the then G. Duke of Tuscany related to him the like History and said moreover That he had made the first Pend. Clock at Florence by the command of the Great Duke and by the direction of his Mathematician Galilaeus a Galilaeo a pattern of which was brought into Holland And further he saith That one Caspar Doms a Fleming and Mathematician to John Philip a Schonborn the late Elector of Mentz told him that he had seen at Prague in the time of Rudolphus the Emperor a Pend. Clock made by the famous Justus Borgen Mechanick and Clock-maker to the Emperor which Clock the great Tycho-Brahe used in his Astronomical observations Thus far Becher To which I may add what is said by the Academie del Cimento viz. It was thought good to apply the Pendulum to the Movement of the Clock a thing which Galilaeo first invented and his Son Vincenzio Galilei put in practice in the year 1649. As to these matters thus related by hear-say by Becher and so expressly affirmed by the Academy I have little to reply but that Mr Hugens does expressly say He was the Inventer and that if Galilaeo ever thought of any such thing he never brought it to any perfection It is certain that this Invention never flourished till Mr Hugens set it abroad § 2. After Mr Hugens had thus invented these Pendulum Watches and caused several to be made in Holland Mr Fromantil a Dutch Clock-maker came over into England and made the first that ever were made here which was about the year 1662. One of the first Pieces that was made in England is now in Gresham-Colledg given to that Honorable Society by the late eminent Seth Lord Bishop of Salisbury which is made exactly according to Mr Zulichem's directions § 3. For several years this way of Mr Zulichem was the only method viz. Crown-wheel Pendulums to play between two cycloidal cheeks c. But afterwards Mr W. Clement a London Clock-maker contrived them as Mr Smith saith to go with less weight an heavier Ball if you please and to vibrate but a small compass Which is now the universal method of the Royal Pendulums But Dr Hook denies Mr Clement to have invented this and says that it was his Invention and that he caused a piece of this nature to be made which he shewed before the R. Society soon after the Fire