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! ARTIFICIAL 
 
 I Cloefe- maker* 
 
 A Treatife of 
 
 Watch, and Clock-work ^ 
 
 Wherein the Art of 
 
 Calculating Numbers 
 
 i For moft forts of 
 
 MOVEMENTS 
 
 Is explained to the capacity of 
 the Unlearned. 
 
 A L S O T H E 
 iHiflory of Clock-work , 
 Both Ancient and Modern. 
 
 With other ufeful matters never be- 
 , fore Publifhed. 
 
 By W. D. M. A. ~j 
 
 LON D 0 N, —"(j 1 
 
 Printed for James Kriaptort , at the Crow;'i in^ 
 St. Church-yard, 1696. 
 
The Preface 
 
 T He following Book was at foil drawii 
 up in a rude manner^ only to pleafemy 
 fcif, and divert the vacant hours of a Solitary 
 Countay Life. But it is now publiilied^ pure- 
 ly in hopes of its doing fome good in the 
 World, among fuck, whofe Genius and Lei- 
 iiire lead them to Mechanical Studies, 6r 
 thpfe vdiofe bufmefs and livelihoad it is. 
 
 Many there are, whofe fault, or calamity 
 ' it is, to have time lying upon their hands;: 
 and kr want of innocent, do betake them- 
 felves to hurtful pleafures. This is the too 
 common misfortune of Perfons of Quality. 
 Among fome of the courfer fort of thefe, il 
 this Book lliall find fon^c acceptance, it may 
 be a means to compofe their Ipofo Spirits ; 
 and by an innocent guile, initiate them int 
 other Studies, of greater ufe to themfelve^ 
 their family, and country. However it may 
 hinder their commiffion of many fms^ whicw 
 are the elFeds of idlenefs. 
 
 If there be any one perfon, in whom thefe 
 good effedls are produced, I’ foall think my 
 idle hours well bellowed, and blefs God f(» 
 it. However upon the account of the 
 cencc of my end in pubtilhing this Book, and 
 that it was written only as the ha^^mlefs (I ^ 
 
 A 2 may 
 
The Preface, 
 
 may add alfo the vertuous) fport of leifure 
 hours • I think my felf excufable to God and 
 the Worlds for the expence of fo muchtime^ 
 in a fubjec^ different from my Profeffion. 
 
 But befides, I think my ielf under fome 
 little obligations of Juftice and Charity^ to 
 publilh the cnfuing papers for the fake of 
 thofe^ whofe bufinefs the Mechanick part is. 
 I take it to be a Charity to the Trade ^ Ife- 
 caufe there are many (altho excellentv.rn the 
 working part) who are utterly uhskillednn 
 the artificial part of it. And theri^ it is a- 
 debt I pay ; becaufe I owe fomewhat of 
 health, as well as diverfion to the Study^ and 
 pradice of thefe fort of Mechanicks. ; And: 
 the beft requitall can make for my trefpafs, 
 is to publifh what I have had better oppor- ■ 
 tunities perhaps oF Tearning, th^v m 
 Workmen have. -Xi c : t 
 
 r And fuither yet, there is anothfe reafony 
 which much prevailed with me to publilh , 
 this Book, Becaufe no body, that I know 
 of, hath prevented me, by treating fo plain- . 
 ly and intelligibly of this fubjed, as to be i 
 ,^-iinderftood by a vulgar Workman. I have 
 often wondered at it, that fo ufeful and de-' 
 Kghtful a part of Mechanical Mathematicks 
 fhould lie in any obfcurity, in an age where- 
 in fuch vaft improvements have-' beeh made 
 therein, and when many Books are^ daily 
 publilhed upon every fubjed. I fpeak here 
 of this Art remaining in obfcurity ,* not as if 
 . nothing was ever written of it, and I the 
 
 1 
 
 I 
 
 I- 
 
 i 
 
 ■ 
 
Ihp. Preface, 
 
 inveiiter of Automatical Computat ion. 
 
 But altbo I cannot aflame the glory of 
 being tlie^ firS: Writer upon this fubjed:^ yet 
 very few have as yet donelq of which I lhail 
 next give feme account. 
 
 Car dap ^ Kirchtr^ and Scott us promi^d it ^ 
 but I do not find they ever publifhed any 
 thing to the purpofe ot it. Our great Ma 
 Oughtred I take to be the firft that ever wrote; 
 to any purpofe about the Calculation of 
 Automata : And I believe he was, the firfl: that 
 brought that Art under Rules/ in his little 
 treatife called Automtaa,, This Book was firft 
 furreptitioufly publifhed in Englifiy in a little 
 Book, called Horolog. Dialogues ^ in the year 
 1675* 5 and afterwards far more compleatly 
 in Latin ^ at the Theatre in , 0 :^ 67 ?, among Mr; 
 (^ghtreds Ofufe, Mathem, in the year 1677; 
 This laft edition it was my misfortune not to' 
 meet with, until it was too late, and there- 
 lore I have been forced to qaote-i the flrft 
 ’and worft in my. Book. . : ' 
 
 -What yis. Oughtred had Wrapt np. in 
 his Algebraick: „obfcure aiaradcrs:, was 
 afterwards put into plainer Language ^ 
 by that excellent Mathematician Sir Jon, 
 Moor^ withfome additions of his own • which 
 you have in his Math, Compend, and fince 
 
 him, by Mn Lejborne^ in his Tkajkre with 
 Trofit, . , . , i . 
 
 i hope I ^ail not be judged to have tranL 
 geffed the Rules of Modelty, in coming aP 
 ^ tte^^ fuch famous hjen* neither fliould 
 ^ ventur;? 
 
I he r ref ace. 
 
 venture that cenfure^ but for two reaforis. 
 One is, I find by experience, that what they 
 have written, is under flood by very few 
 W orkmen. And therefore I have endeavour- 
 ed, with all induftry, to make the matter as 
 plain as I could for luch. For which reafon, 
 
 I hope the more learned Reader will excufe 
 my ufing many words, when fewer would 
 have jferved ^^^rurn* and that I have con- .. 
 defcended to low things, (and to liifti rieed^ 
 lefs) as teaching the *Golden-rule, &c. The 
 other reafon is, that what thofe three have 
 written, relates only, or chiefly to the Watch- 
 part. To which I have added fevetal other 
 things of my own: particularly the Calcula- 
 tion of the Clock-part, &c. I haVe been for- 
 ced to reduce to Rules my felf, and to name 
 no more, the Hiflorical part hath not been fo 
 much as attempted before, that I know of. - 
 
 Thefe Reafons will, I hope, • excufe mO 
 with the moft cenforious Reader, not only 
 for prefuming to write after fo accurate a 
 piece, as Mr. Oughtreds is,- but alfo the No- 
 velty of the fubjedl, will I hope procure for 
 me a candid interpretation of the faults and ' 
 blunders, that I may have Unwittingly coni- 
 mitted. 
 
 To the preceeding account of what others 
 have, written (which fliews what help I have 
 had from printed Books) I fliall fubjoyn my 
 acknowledgments, and thanks to the princi- 
 pal of my friends^ who have given me tlieif 
 affiftance in compiling this Book. But their' ^ 
 
 names 
 
 I 
 
 !■ 
 
 I 
 
 I 
 
 
Ihe Preface., 
 
 names I j}iail not make more publick than mine 
 owo^ being unwilling to be difcovered rriy 
 fel£ ; .}n the -Chap, of the Terms of Art^ I 
 owe much to the affiftance of A, Br . ... a 
 judicious Workman in drevv 
 
 me up a Scheme of the .Clock-rnUker's I.an-. 
 guage. In the Hiftoryof the Modemlnven- 
 I have had (among fdhie Others) the 
 aiStonce chiefly of the ingenious T)f, fi, , . . 
 and Mr, T, : The former oeing the Au- 
 thor, of fome^ and well acquainted with Others^ 
 of the's^leclianicai Inventions of that fertile 
 Reign of King ChM&s the II. and the latter 
 concerned ini all^ ormoft of the late 
 inventions in Clock-work, by means of his 
 famed skill in that; and other Mechanick 
 operations. 
 
 There are fome other contrivances of this 
 laft age ( befides thofe. I have nieridoned ) 
 whichT have paffed over infilence ; becaufe 
 either they are only hFanches^ or improve- 
 ments: of the inventions"! have taken notice of^ 
 (fuch asfeveral ways of repeating 
 or elfe,.they only coll ater ally relkie to Watch- 
 work (as the invenrions of Cutting-Engines , 
 Fufy-Engines^ &c,) To treat df all thefe, 
 would fwell my Book far beyond its intended 
 bounds ,• which I have already fomewhat ex- 
 ceeded. I fhall therefore commk this task to 
 fome better Pen, hoping that no perfon will 
 take it amifs, that I have not me n tioned what 
 I have been beholcliing to him for the rela- 
 tion of. 
 
The Preface. 
 
 For tlic refons laft mentioned^ I have alfo 
 ^eft out of my Book, a Chapter of the Art 
 of making, and ufing many forts of Sodders, 
 the way of colo 4 ring Metals, ufeful iii 
 the pra<5lice of Clock-work. This I had pre- 
 pared for the fake of Mercurial Gentlemen, 
 but omitted printing it, and fome other things, 
 out of Charity to poor Apprentices and other 
 Workmen, whofe purles l am unwilling my 
 volun^e Ihould too much exceed. 
 
 If I have at any f invaded the Work- 
 man's province^ it v/as net becaufe I pretend 
 to teach him I ds Trade ; but either for Gen- 
 tlemen’s fakes, or v/hen the matter led me 
 hecelfarily to it. 
 
 I have nothing more to add, but that I 
 would have this little Treatife looked upon 
 only as an Elfay, which I hope will prompt 
 fome abler pen to perform the task better, 
 efpecially in the Hiftorical part. ForTince 
 Watch-work oweth fo nauch to our Age, and 
 Country, ’tis pity that it ihould not be re- 
 membred ; elpecially when we cannot but 
 lament the great defed of Hiftory, about the 
 beginning and improvements of this ingenw 
 
 ous and ufef'’C^^% 
 
THE 
 
 CONTENTS. 
 
 ^Hap. I. Of the Terms of Art. 
 
 The more .gemrd. Terms, 2. Names 
 hekngb.g properly to the Watch-part,^, Z, Names 
 of the Clock^part, p. f. ■ . 
 
 ‘hap, IL The Art of Calculation. 
 
 I. Preliminary Rules. 
 
 To find the turns of a Wheel or FlmonjS, The way 
 of writing down the Numbers ^ 9. To find the 
 I turns of any ^ or all the Wheels in the Movement ^ 
 
 1 10. To find the Beats of the Bdlance in all the 
 1 Watches going y or in one turn of any Wheely i r. 
 Two firokes to every tooth of theCr own-wheel yii^, 
 iB, 2. Calculation of the Watch-part. 
 
 Several ways of performing one and the fame 
 motion y 15*. A Rule to vary Numbers y 16. 
 The way of working the Golden Rulcy 17. A 
 very ujefut Rule to vary inconvenient Numbers ^ 
 
 1 8. Rules of perpetual ufe in proportioning the 
 p{irts of a Watch y 19, Examples of contriving 
 a piece of ordinary Watcb-worky 22. Examples 
 thereof for Minutes y and Seconds y 29. 
 
 B, Calculation of the Striking-part. 
 
 Gem^ 
 
The Contents. 
 
 General Ohfervations and Rules relating to u 
 Wheel-work of a Clock^ p. Rules of perpe' 
 V tualufe m proportioning 4 ke- farts of a Glook^ ti, fi 
 •^fyamples of Calculating the Numbers of a fmak 
 Ciock^ ^8. Examples of Clocks of longer conti- 
 nuance., 59. An ufeful Rule to find the number 
 of Strokes in one turn of the Fufy^ ^7^, Exam- 
 ples of fixing the Vinipn of Rfport^ ^4* 
 
 Seh. 4. pf uarters and Chime.^, 
 
 Notes concerning the Quarters^ 45'. Of making 
 the Chime-barref 4 6 , Of dividing it ^ and jet- 
 ting on the Chime-pins^ Af], Chimes 
 • loOj md of a Song-tune^ 5*0. Another way oj 
 fitting Chimes on the Barref 5* 2. 
 
 SeSf, To calculate . Numbers to reprefen 
 the Celellial Motions. 
 
 Contrivance of Movements only to fhew thefe Mi ; 
 tions^ 5* . To add it to a Watch that .fie^s .tl 
 hmr cf the .day^ ^ y 5’, A motion to Jhew: we di 
 of the month y fS, To .Jhew the Agexof tk 
 Moony ^7. To Jhew tbe day of the. Teary m^ 
 Su^ns place in the Eclipticky his p.ifng.oAS.ettm^ 
 ;6cc.. j8. ToJhew theTydcSy ib. To\reprefei 
 the motion of the Flanets^ fixed Starsy See. 6( 
 ChaprEl. To alter Clock- work^ p. .62. Ei 
 ample of converting a 12 hour BaUanc e-clock m 
 aFendulumy 63. To 7 nake.itgar}y<^hoursyh 
 To change the Clock-part y 67. ' I 
 
 Chap^ TV. . Eo fize Wheels and PLoIoiis. 
 
 ' To do it Arithmetically y 69. MtchankaUyy ^ ■ 
 
 ’Cjhap,Y, Of Pendulums. 
 
 Irregularities of Fendular motions remediedy 7 ^ 
 Caufe of the difference of the m.otim. of the. fa 
 
The Contents. 
 
 Tetidiilitm, 72. True length of a Tendtilum 
 that ‘vihrateth Seconds ^ 7^. I'd find the Center 
 of Ofcillationy 74. To calcnlate the Lengths^ or 
 Vihmtltns f Pendulums ^ ' A Table of 
 
 Lengths and Swings^ 78 . To cor reft the iHdthon 
 of a Pendulum^ 7^.. 
 
 haf,yi. The Antiquity^ and general Hfiftd- 
 ry of Watch-work. . . . \ 
 
 The ancient eji Tmei^e)dgin'ey 82, TheCjit^ 6 v^h. 
 and Roman ways of 7 neafur mg Time^ 8 ^. Sorhz 
 hoi^ohgical Infirume^tts nkntidMd^ by Mcteiii Ak^ 
 thorsy 84. Watch^ or Clbck-Tldofk^ no fie^ Qkt^ 
 mzi). TkHjentlon^ 86 . The Sfhere' df hfd^i- 
 nlede^j 87. Of Pofidonius^ 89.‘ "The bf 
 ginning of our prefent Clock-Worh,^ 91. 'CIqc%s , 
 that perform fir ange feats ^ 92. — ^7" ' 
 
 "hap, VII. The Invention oF. Pehdurum 
 •Watches. . 
 
 Mr, Hngehs the Ihventer ^ P** 9 ?* 
 
 ■ eMfhi^ip^ 94. Tid’dr begiriningan England, 
 9 V*’ contriver of their carrying a heavy 
 Bally See, 96. Their ujcy ibid. TlkCirtu^ 
 lar Pendulumy 97. 
 
 ihap, VIII. Of the Invention of Pocket Pen- 
 dulum Watches. 
 
 The Inventer y p 99. Several ways ofthemyih. 
 The Time when invented y 105. Mr, Hugens’^ 
 Whtchy 1 04. 
 
 'llhap, IX. The Invention of Repeating Clocks. 
 The Inventer y p. 106. When and by whom 
 firfi ujed in Pocket Clocks y 107. 
 
 Chap, XL Numbers for various Movements. 
 The way of Wat^h-mahrs writing down their 
 
 Num- 
 
The Contents. 
 
 Numbers^ 109. Numbers of an 8 day Viece^ 
 iio. A Month Tiece^ 112. AN^o Month 
 Tiece^ 11:5. A Quarter of Tear pecey 11 4.* An] 
 Half Tear Viece^ ib. A Tear Piece^ ^ 
 
 lejfer 30 hours Piece ^ ib. A fmall Week Piece ^ ib.. : 
 A fmall Month Piece ^ 116. A fmall Tear \ 
 Tiece^ ib. An 8 day Piece Pend, 3 inches , 
 117, Numbers refrefenting the Motion of the . 
 Planet Saturn^ 118. Jupiter^ ib. Mon^ \ 
 fieur Romer’^ hflrument for ]\x^\.tQps Satel‘ 
 lites^ 119. Numbers for Mars^ Venus^ and \ 
 Mercury, 120. For the Dragons Head and 
 Tail^ 12 1, Numbers for Pocket Watches of S 
 iays^ ib. Of hours ^ 122, 123. The way 
 
 to amend the Numhm j 2 ^ . 
 
 G%. XI. TabiesofTime. , 
 
 A Table for feady cafiing up the parts of TimCy 
 124. A Table to fet a Watch by the Fixed 
 Stars ^ 125'. A Table of the Variations of the ' 
 Hour by the Sms Rcfra^ion^ tlj, Obferva- 
 Hons concerning RfraHions, and the Variations 
 128, 
 
 till 
 
The Artificial 
 
 G L O C K-M A K E R. 
 
 C H A P. I. 
 
 Of the Terms of Art^ or Names bj, 
 which the farts of an Automa^ 
 ton are called. 
 
 I T i$ necefliry that I fhopid lliew, thq 
 meaning of thofe Terms which 
 Clock-makers ufe, that Gentlemen 
 Had ethers^ unskilful in the Aft, may 
 know how to exprefs themfelves properly^- 
 infpeaking ; and alfo upcjerflarid whar I 
 lhall fay in the following Book, 
 
 I rtiall not trouble the Reader \Vith a 
 recital of every name that doth occur, 
 but only fuchas I fliall have c^cafion to 
 
2 Evaluation of the Gh. I, I 
 
 life in the following difcourfe, and feme | 
 lew others that offer themielves, upon a I 
 tranfient view of a piece of work. 
 
 I begin W'ith the more general Terms : 
 as, the Frame ; which is that w hich con- 
 tains the Wheels, and the reft of the 
 work. The Pillars^ and Plates, are what 
 it chiefly confifts of. 
 
 Next for the Spring, and its appurte- 
 nances. 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 Endlefs-Screw, 
 and its Wheel. 
 
 That which the Spring draweth, and 
 about which the Chain or String is wrap- 
 ped, and w hich is commonly taper, is i 
 the Fufy. In larger work, going w'ith { 
 weights, where it is cylindrical, itiscal- 
 \ed th& Barrel. The fmall Teeth at the 
 bottom of the Fufy, or Barrel, thatftop 
 it in winding up, is the Ratchet. That 
 which flops it when wound up, and is 
 for that end driven up by the String, is 
 the Garde-cant, ox Guard C«;k, asothers; 
 and Garde-du’Cerd, and Gard’du’Gut, as 
 others call it. The 
 
Ch. T. Temi of Art. 3 
 
 The parts of a Wheel are, the Hoop, 
 or fi/w ; the Teeth: thcCrofs : and the 
 Collet, or piece of Brafs, foddered on the 
 Arbor, or Spindle, on which the Wheel 
 is rivetted. 
 
 A Pinion \s that little Wheel, which- 
 plays in the teeth of the Wheel. Its 
 teeth (which are commonly 4, y, 6 , 8, 
 are called Levei, not Teeth. 
 
 The ends of the Spindle, are called 
 Pevetts : the holes in which they run, 
 Pevet-holes- 
 
 The guttered Wheel, with Iron fpikes 
 at the bottom, in which the line of or- 
 dinary Houfe-Clocks doth run, is called 
 the Pttlly. 
 
 I need not fpeak of the Dial-plate, the 
 Hand, Screws, Wedges, Stops, &c. 
 
 Thus much for genera! Names, which 
 are common to all parts of a Movement. 
 
 The parts of a Movement, which 1 
 fliall confider, are the Watch, and Clock: 
 
 The Watch- part of a Movement is that 
 which fervethto the meafuring the hours. 
 
 In which the firft thing I ihall confider is 
 the Ballance : whole parts are, the pHno, 
 which is the circular part ofit : the Terge, ^ 
 is it5 Spindle : to which belong the two 
 B 2. pallets. 
 
i. Exfiicatim of the Gh. L | 
 
 falkts, OF Nuts^ which play in the fangs I 
 of the Crown^ Wheel : in Pocket- Watches, | 
 
 that ftrong Stud in which the lower Pe- 
 vct of the Verge plays, and in the mid- 
 dle of which one Pevet of the Crown- 
 
 Wheel runs, is called the 'Pott am : the 
 wrought piece which covers the BallanCe, 
 and in which the upper Pevet of the Bal^ 
 lance plays, is the Cock, The fmall Spring 
 in the new Pocket- Watches is the Regu^ 
 lator. 
 
 The parts of a Pendulum are, the Verges 
 Pallets and Cocks^ as before. The Ball 
 in long Pendulums, the Boh in Ihort 
 ones, is the Weight at the bottom. The 
 Rod^ or Wire is plain. The terms pe- 
 culiar to the Royal Swings are the Pads^ 
 which are the Pallets in others, and are 
 fixed on the Spindle, The Fork is alfo 
 fixed on the Spindle, and about 6 inches 
 below, catcheth hold on the Rod, at a 
 flat piece of Brais, called the Flatt,^ in 
 which the lower end of the Spring is 
 faftened. 
 
 ^ The names of the Wheels next follow. 
 The Crown-Wheel in Small pieced, and 
 Swmg-Wheel in Royal Pendulums, isthat 
 Wheel which drives the Rallancc, or Pen- 
 
 dalurn.,' - The 
 
 ■j 
 
 ( 
 
 ■I 
 
 i< 
 
 ii 
 
 (( 
 
 i 
 
 c 
 
 ii 
 
 if 
 
 Ti 
 
 tt 
 
[2h. !• Terns cf Art. 
 
 The CiHirate-Wheel, is that Wheel in 
 Pocket-Watches, which is next to the 
 Crown-Wheel, whofe Teeth and Hoop 
 lye contrary to thofe of other Wheels. 
 
 The Great-Wheel, or Firft-Wheel, is 
 that which the Fufy, immediately 
 driveth. Next it, are the Second-Wheel, 
 Third-Wheel, &c. 
 
 Next followeth the Work between the 
 Frame and Dial Plate. . And firft, is the 
 •piaioH of Report', which is that Pinipn 
 which is commonly fixed on the Arbor 
 of the Great-Wheel, and in old Watcher 
 lufed to have commonly but four Leaves; 
 which driveth ^he Dial-Wheel, arid this 
 carrieth about the //aW. 
 
 The laft Part which I fliall fpeak of, 
 is theCWF, which is that part which 
 lerveth to ftrike the Hours : In which I 
 fhall 
 
 Firft fpeak of the Great, or Firfl- 
 Wheel ; which is that which the Weight 
 or Spring firft drives. In or 30 
 hour Clocks, this is commonly the Pin- 
 Wheel ; in 8 Day pieces, the Second- 
 Wheel' is commonly the Pin-Wheel- 
 This Wheel with Pins isforaetimes called 
 the StrikinfyWheel, or Pin-Wheel. - 
 
 Next 
 
Explication of the Cb. I. 
 
 Next to this Striking- Wheel, foHow- 
 eth the Detent-Wheel^ or Hoop-Wheel^ it 
 having a Hoop almofl: round it, in which 
 is a vacancy, at which the Clock 
 locks. 
 
 The next is the Thirdy or Fourth^ 
 Wheel (according as it is diftant fromi 
 the Firft* Wheel) called alio the Warnings 
 Wheel 
 
 i 4 nd laftly is the Flying-Pinion^ with 
 a Fly or Fan to gather Air, and fo bridle 
 the rapidity of the Clock’s motion. 
 
 Behdes thefe, there are the Pinion of 
 Report^ of which before ; which driveth 
 round the Locking-Wheel^ called alfo the 
 Count-Wheel^ with ii Notches in it com- 
 monly, unequally diftant from one ano- 
 ther, to make the Clock ftrike the hours 
 of I, 2, 3, 
 
 Thus much for the Wheels of the 
 Clock part. 
 
 Befides which there are the Rajh^ .or 
 Ratch ; which is that fort of Wheel, of 
 twelve large Fangs, chat runneth conceo:- 
 trical to the Dial-Wheel, and ferveth to 
 lift up the Detents every hour, and 
 make the Clock ftrike. 
 
 The Detents are thofe Stops, which 
 
 by 
 
Ch, II. Term^ of Art. 
 
 by being lifted up, or let fall down, do 
 lock and unlock the Clock in ftriking. 
 
 The Hammers ftrike the Bell : The 
 Hammer»tails are what the Striking- 
 pins draw back the Hammers by. 
 
 Latches are what lift up, and unlock 
 the Work. 
 
 Catches are w^hat hold by hooking, 
 or catching hold of. 
 
 The Lifthg-pkces do lift up, and un- 
 lock the Detents, in the Clock part. 
 
 C H A P. IL 
 
 The Art of Calculation. 
 
 SECT. I. 
 
 General preliminary Rules and Direilions 
 for Calculation. 
 
 5 i-lTOR the more clear iinderftand- 
 ing this Chapter it muft be ob- 
 lerved, that thofe Automata CaU 
 
 culation I chiefly intend) do by little In- 
 terflices, or Strokes, me^fure cut longer 
 ' ' portions 
 
8 General Rules Chap. 2 , 
 
 portions of Time. Thus the ftrokes ol 
 the BaUance of a Watch, do meafureout 
 Minutes, Hours, Days, &c. 
 
 Now to fcatter thole ftrokes among 
 Wheels and Pinious, and to proportionat e 
 them, fo as to meafure Time regularl>', 
 is the defign of Calculation. For the 
 clearer difcovery of which, it will be ne- 
 ceflary to proceed leifurely, and gradu- 
 ally. 
 
 ^ place, you are to 
 
 [cS.^. know, that any Wheel being divided by 
 its Pinion, fhews how matiy turns that 
 Pinion hath to one turn of that Wheel. 
 Thus a Wheel of 60 teeth driving a Pi- 
 nion of 6, will turn round the Pinion .10 
 times in going round once. 
 
 ? From the Fufy to the Ballance the 
 Wheels drive the Pinions ; and confe- 
 quentiy the Pinions run fafter, dr go more 
 turns, than the VVheels they run in. But 
 it is contrary from the Great-Wheel to 
 the Dial - Wheel. Thus in the laft Exam- 
 ; pie. The Wheel drives round the Pinion 
 10 times: but if the Pinion drove the 
 Wheel it muft turn 10 times to- drive 
 the Wheel round once. 
 
 § Beiore i proceed further, I muft 
 
 ftew 
 
Se<5t* I. for Calculation. 
 
 fhew how to write down the Wheels and 
 Pinions. Which may be done, either as 
 Vulgar FraAions, or in the way of Oivi- 
 'fion in Vulgar Arithmetick. E. C A 
 Wheel of 6o moving a Pinion of 5*, may 
 be fet down thus, ^T: or rather tijus, 
 5 j 60 : where the hrft figure is the Pini- 
 on, the next without the hook, is the 
 Wheel. 
 
 The number of Turns, which the 
 nion hath in one turn of the Wheel, is fet 
 without a hook on the right hand : as 
 5) 60 (iz, Le a Pinion 5” playing in a 
 Wheel of 60, itioveth round iz times, ia 
 j one turn of the Wheel. 
 
 A whole Movement mav 
 I 4^36^9 be noted thus, 
 
 'dStcCxi ^7 Notches in the Grower* 
 ^r\c(Q Wheel. Or rather as you fee 
 Oaof 8 Margin : where 
 
 — the uppermoil number, above 
 17 the line, is the Pinion of Be- 
 port 4, the Dial-whcei 
 and 9 turns of the Pin. of Report. The 
 fecond number (under the iine) is 5* the 
 Pinion, ^5*151^6 Great-wheel, and ii 
 turns of the Pinion it driveth. Thethi^d 
 numbers, are the Second-wheel, &c, 
 C Tha 
 
I o General Rules Chap. IL 
 
 The fourth the Contrate-wheel^ (Sc, And 
 tiK fmg e number 17 under. s^II, is the 
 
 C rown wheel 
 
 4 by tlic ^ before, knowing the 
 niaril er of turns, which any Pinion hath 
 in G!!e turn of the Wheel it worketh in, 
 you may aik) find out how many turns a 
 Wiieel or Pinion hath, at a greater di- 
 flance,* as 'he CoiitratG wheel, Crowm- 
 wheef or For it is but multiplying 
 together the Qmitents^ and 
 riie number produced, is the 
 niimbcr of Turns. An Ex- 
 will make what 1 fay 
 Ictus chufe 
 thefe 5 numbers 
 here fee down ; the yj45C9 
 firfl of W'hich hath 5740:^8 
 1 1 turns, the next 9; and the 
 I’ili 8 .. If you rnuitiply ii and 9 it pro- 
 duceth 99, for ^ times ii is 99, that is, 
 in<>ne lurn of the Wheel 5-5, there are 
 99 iurnGof thefecond Pin.on 5, or of the 
 W heol 40. It you multiply 99 by the !aft 
 Quotient 8 (that it, 8 r.mes 99 is 79x) 
 it fbews the number ol turns, wWch the 
 third andiafi^ Pinion 5 hath. So that this 
 thad, and iall Pinion turns 791 times m 
 
 one 
 
 Iv (he Qaotients I com' 
 lonly Hjean the number 
 f fur-is , which nurrj- 
 er let. ou the ripJ'^t 
 and, a hook, 
 
 ha 
 
 s is ihewn in rhe 
 'asagi 3r>i't. Which 
 
 ample 
 
 plain: 
 
 o enerjuow once for 
 
Sedt. !• for Calculation- i 
 
 one turn of the firft Wheel 5-5. Another 
 Example will make ir iiill 
 8^8o(io more plain. The Example is 
 6}54C9 in the Margin The turns are 
 5)40i^8 10, 9, and 8 Thefe multiphed 
 
 2S b^Toic run thus, viz. jo 
 
 ^ 15 times 9 is 90, that is, the Pi- 
 nion 6 fwhich is the Pm, oF 
 the third Wheel turns 90 tunes in erne 
 turn of tae Firit wheel, 80, Ihis Lift 
 produd: 90 being multiplied by 8, pro- 
 duces 710 5 that is, the. Pinion y ( Inch 
 is the Pin of the Cre wivwheel 15) ni ns 
 720 times in one turn of Fiu -vUieel, 
 of 80 teeth 
 
 § We may now proceed to that, 
 whxh is the very groundwork oi all ; 
 which is, not only to find out the turns, 
 •but the Beats aHo of the Ballance is thole 
 turns of the Wheels. By the laft Para- 
 graph, having found out the nurnber of 
 turns, which the hath in one 
 
 turn of the Wheel you kek for, you mull 
 then multiply thole turns of the Crown- 
 vwheel by its number of Notches, and this 
 will give you half the nurirjihej:i,of BeatSy 
 in that one turn of t, e Whdbl. Half the 
 number, I fay^ for the reafons in the fol- 
 C 2 iov/inti 
 
General Rules Ch* II. . 
 
 lowing 6 § For the Explication of what . 
 hath been faid, we will take the example 
 in the laft ^ : the Crowo'-wheel there, has 
 72p turns in one turn of the firft Wheel : 
 This number multiplied by 15' , the 
 Notches m the Crown-wheel, produceth 
 icSoo, which are half the number of 
 flrokes of the Baliance, in one turn of the 
 firft w heel 80 . The like may be done for 
 any of the other Wheels ; as the Wheel 
 54. or 40 : but I lhail not infift upon 
 thefe, having faid enough. 
 
 I lhail give but one Example more, 
 which will fully , and very plainly illu- 
 ftrate the whole matter. The example is 
 in the margin, and ’tis of a 16 
 4^32^^ hour Watch, wherein the Pir 
 ^ 1 1 nion of Report is 4, t?'ie Dial- 
 
 5^45(9 wheel 32, theGreat^wbeeJ is 
 5)40^8 5'5^ the Pinion of the fecond 
 
 - — Wheel Ls the number ; 
 
 17 of Notches in the Crown- 
 w hetl are 17 : the quotients, 
 or rumber oi turns in each, are 8, Ti, 
 
 9, 8 . All which being multiplied as be- | 
 fore, make 6336 : this number multipli- ( 
 • ed by 17, produceth 10771^; whichlaft c 
 Ipmrn is half the number of Beats in one i 
 i turn I 
 
Sc 6 t» I- for Calculation. 15 
 
 turn cf the Dial-wheel. The half num« 
 ber of Beats m one turn of the Great- 
 wheel, >ou will find to be 13464: For 
 8 times' 1 7 is 136, which is the half num- 
 ber of Beats in one turn of the Contrate- 
 w heel 40 : and 9 times 136, is 12x4, 
 the hah beRts in one turn of the Second- 
 wheel : and 1 1 times 1224, ^ 34^4? 
 
 half beats in one turn of the Great-wheel 
 55'. /\nd 8 times this laft, is 10771?, 
 before named. It you multiply this by 
 the two Pdlets, that is, double it, it is 
 215424, which is the number of Beats 
 in one turn of the Dial-wheel, or 12 
 hours. If you w ould know how many 
 beats this Watch hath in an hour, 'tis but 
 dividing thq beats in 12 hours, into i2 
 parts, and it gives 17952, the Train of the 
 Watch, or beats in an hour. If you di- Maf Com. 
 vide this into 60 parts, it gives 299 andP-^®^* 
 a little more, for the beats in a minute. 
 
 And fo you may go on to feconds and 
 thirds, if you pleafe. 
 
 Thus I have delivered my thoughts as 
 plainly as I can, that I may be w dl un- 
 derftood ; this being the very foundation 
 of all the artificial part of Clock-work. 
 
 And therefore let the young praclifer ex- 
 
 creifc 
 
Calculation of Ch ^ 
 
 ercife himfelf thorowly in it, in more * ' 
 than one example. ■- 
 
 If I have offended the more learned, 
 quick-fighted Reader, by ufing many . 
 words: mv dtfire to inflrudi the moft • ' 
 ignorant Aruft, mart plead my exc.ufe. , ' 
 § 6 . The Balance or Swing hath two 
 . n^. ftrokes to every tooth of the Crown- 
 wheeJ. For each or the two Pallets hath 
 its blow againflteach tooth of the Crown- ' 
 wheel : Wherefore a Pendulum that 
 fwings Seconds , hath its Crown-wheel 
 but 30. 
 
 SECT. n. 
 
 way to Calculate^ or contrive the Num~ 
 hers vf a piece of irVatch work. ; 
 
 I 
 
 H Aving in the laft Se<3:ion led on the 
 Reader to 3 general knowledge of 
 Calculation ; I may now venture him 
 further into the more obfeure, and uieful 
 parts of that Aft : Which 1 lhall explain 
 with all poffible plainnefs, tho kis brevi- 
 ty, than I could wilh. I 
 
 tughtfei I. The fame motion may be per- j 
 formed either with one Wheel and one 1 
 
 •eci* 14. . 
 
 Pini- 
 
Se( 5 t. 2. Watch-vpork- 15 
 
 Pinion ; or by •^i'tanv Wheels and many 
 Pinions: provided thar the number of 
 turns of all thofe Wheels bear the fame 
 proportion to all thofe Pinions, which 
 that one Wheel bears to us Pinion. Or 
 (which is the fame thihg) that the 
 number pro uccd by multiplying all the 
 Wheels together , be to the number- 
 produced by multiplying afl the Pini- 
 ons together; as that one Wheel is to 
 that one Pinion. Thus fup- 
 28)1440 pofe you had nfe for a Wheel 
 of 1440 teeth, with a Pin. of 
 28 leaves, you may make it into 5 Wheels 
 and Pinions, viz. 4^36, 7^ 8, and 
 
 For if you multiply the three 
 Wheels together, viz. 3(5. 8 and 5 ; and 
 the three Pinions together by themfelves, 
 viz 4, 7 and 1, you will find 1440 
 to arile lor the WTiCels, and 28 for the 
 Pinions. Or if you try the example by 
 the number of turns, it will be the fame. 
 
 For 28)1440 (j I And the quotients 
 and turns of the 3 Wheels and Pinions 
 multiplied together, are 51 \ alfo, as in 
 the lafl example. 
 
 It matters not in what order the Wheels 
 and Pinions are fet, or which Pinion runs 
 
 in 
 
6 Calculation of Ch, II*| 
 
 in which Wheel:’ On^y for convenience .;j 
 fake, they commonly-fet the biggeft num- j! 
 bers to drive the reft. ‘ i 
 
 § 1 Two Wheels and Pinions of difle- 
 ib. Tcnt numbers may perform the fame mo-. 
 tion. As, a Wheel of ^6 drives a Pinion 
 of all one as a Wheel of 45* drives a 
 Pin. of 5 ; or as a Wheel of 90 drives a ; 
 Pin. of 10, The turns of each are 9. 
 
 § 3. If in breaking your Train into ""J 
 •parcels (of which by and by) any of your 
 Quotients fhould not pleafe you ; or if j' 
 you would alter any other two numbers^^ 
 which are to be muhipl ed togi;ther, you ' 
 may vary them by this Rule: Divide 
 your two numbers by any two other '| 
 numbers which will mealure them; then i 
 multiply the Quotients by the alternate 
 divifors, the produd: of thelc two laft 
 numbers found, fliall be equal to the pro- ■ 
 dud of the ^wo numbers firft given. . 
 Thus if you would vary 36 times 8, dl- '| 
 vide thefehy any two numbers that wull f 
 evenly meafure them, as 36 by 4, and 8 
 by I. The fourth part ct 36 is 9, and 8 
 divided by i gives 8. Multiply 9 by f, 
 the produd is 9 ^ and 8 multiplied bv 4 
 produceth 31. So that for 3^. times 8, ; 
 
 you 
 
Sedt* 2. the Watch-part. i 
 
 9 8 you fliall have found 3 x times 
 
 36 X 8 9. The operation is in the Mar-; 
 
 4 I gin, that you may fee, and ap- 
 
 prehend it the better. Thefe 
 
 3a X 9 numbers are equal, 36 times 
 8 is equal to times 9 ; both 
 producing zZS. If you divide 35 by 6, 
 and 8 by ^ , and multiply as before is 
 faid, you will have for 36 times 8 , 14 
 times iz, equal to 288 alio. 
 
 If this Rule feem to the unsltifful Rea^ 
 dcr hard to be underflnod, let him not 
 be difcouraged, becaule he may do with*- 
 out it, altho it may be of good ufe to him 
 that would Sjfa more compjeat Artift. 
 
 § 4. Becaule in the following Para- 
 grapljf, 1 fhall have -frequeDt occafion to 
 ufe the Rule of Thr^ee, or Rule of Proper- 
 tioui it will be necefTary to Ihew the un- 
 skilful Reader, how to work this noble 
 Rule. 
 
 If you find 3 or 4 nu.mbers thus let, 
 vtuth four fpots after the fecond of them, 
 
 ’tis the Rule of Proportion : as in this ex* 
 ample, x. 4 :: 3. 6. i.e. As x is to 43: 
 
 So is 3 to G. 
 
 The way to work this Rule,; viz. by 
 the 3 fifft numbers to find a fourth, is, 
 
 B To 
 
1 8 Calculation of Chap. II. 
 
 To j6Sitiply the fecond number and" the 
 third together, and ^divide their produ( 3 : 
 by the firfl:. Thus 4 times 9 is la, which 
 iz divided by z, gives 6; which is the 
 number fought for , and flands in the 
 fourth place. 
 
 You will find the great ufe of this Rule 
 hereafter ; only take care to bear it in 
 mind all alocg. 
 
 § y. To proceed. If in feeking for 
 your Pinion of Report, or by any other 
 means, you happen to have a Wheel and 
 Pinion fall out with crofs numbers,too big 
 to be cut mW heels, and yet not to be alter- 
 ed by the former Rules, you may find out 
 two numbers of the fame, or a near pro- 
 portion, by this following Rule, m.'’‘As 
 either of the two numbers given, is to 
 ib. the other ;; So is 360 to a tourth: Di- 
 vide that fourth number, as alfo 36o by 
 4. y. 6. 8. 9. 10. iz. ly. (each of which ; 
 numbers doth exactly meafure 360) or j 
 by any one of thofe numbers that bring- ' 
 eth a quotient neareft to an integer (or ; 
 whole number. ) Thus if you had thefe : 
 two numbers, 147 the Wheel, and 170 i 
 the Pinion, which are too great to be cut I 
 in fmall Wheels, and yet can’t be reduced i 
 
 inta- 
 
Se(5t. 2 . the Watch-farP ip 
 
 into le's, becaufe they ha ve no other com- 
 mon m*";afurc, but unity: lay therefore 
 according to the lall paragraph, As lyo 
 is to 147; or as 147 is to 170:: So is 
 3<5 o to a fourth number fought. In 
 numbers thus, 170 147 :: 360. ^ ir. or 
 147. 170 :: 360. 416. Oivnde the fourth 
 number and 360 by one of the foregoing 
 numbers ; as 31 1 and 360 by 6, it giires ’ 
 yx and 60. In numbers ’tis tl^us , 
 
 Divide by 8 Yis thbs,'8 )^ ” (39 
 
 If you divide 360 and 416 by 8, it will 
 
 fall out exadly to be 4^ and yx 
 
 Wherefore for the two numbers 147 and 
 170, you may take yx and 60 ; or 39 
 and 45’; or 45 and yx, or 
 
 § 6. I (hall add but one Rule more, be- 
 fore I come to the pradlice of what hath 
 been laid down 5 which Rule will be of 
 perpetual ufe, and confifts of thefe five 
 particulars. 
 
 !• To find what number of turns the , . 
 Fufy will have, thus, As the Beats of the^ea-^Is. 
 ^allaace in one turn of the Great- Wheel sir^. 
 or Fufy (fuppofe x69x8) To the Beats of 
 the Ballancein one hour (fuppofe xoi96)^' 
 
 D z ; : So 
 
20 
 
 Calculation of Ch* II* 
 
 ; : So is the continuance of the Watches 
 going in hours (fuppofe 16) To the num- 
 ber of the turns of the Fufy' iz. Jn num- 
 bers ’twill ftand thus, z6^zB. 201^6 : ; 
 16. ii. By ^ 4. you may remember that 
 you are to multiply 20195 by 16, the 
 produdfcis Divide this by 26928, 
 
 and there will arife 12 in the Quotient, 
 which muft be placed in the fourth place, 
 and is the number of turns which the Fufy 
 hath. 
 
 2. By the Beats and turns of the Fufy, 
 to find how many hours the Watch will 
 go, thus, 
 
 As the Beats of the Ballance in one 
 hour, are to the Beats in one turn of the 
 Fufy : : So is the number of the turns of 
 the Fufy , to the continuance of the 
 Watches going. Jn numbers thus, 
 
 2196. 26928:: 12,16. 
 
 3. To find the ftrokes of the Ballance, 
 
 in one turn of the Fufy, fay. As the num- 
 ber of turns of the Fufy, to the continu- 
 ance of the Watch’s going in hours : : So 
 are the Beats in one hour, to the Beats of 
 one turn of the Fufy. In numbers it is 
 thus, • ' 
 
 12. i6;: 20196. 26928. 
 
 4. To 
 
Se< 9 :* 2. the Watch-pan. 2 
 
 4. To find the Beats of the Ballance ia 
 an hour, fay thus. As the hours of the 
 Watch’s going, To the number of turns 
 of the Fufy a : So are the Beats in pne 
 turn of the Fufy, To the Beats in an hour, 
 in numbers thus, . .. 
 
 i 6 ‘ II :: ^ 59 ^ 8 . 10196. 
 
 y. To find what Quotient is to be laid *■ 
 [upon the Pinion of Report, (ay thus, A|. 
 the beats in one turn of the Great«wheel,- 
 To the beats in an hour : : So are ther- ? . 
 hours of the Face of the Clock (viz. ri 
 or 14) To the Quotient of the Hour- 
 Wheel divided by the Pinion of Report, 
 i. e. the number of turns, which the Pi- 
 nion of Report hath in one turn of the 
 Dial-Wheel. In numbers thus, 
 
 16918. 10196 :: 12. 9. 
 
 Or rather (to avoid trouble^ fay thus, 
 
 As the hours of the Watch’s going. Are 
 to the numbers of the turns ot the Fufy :: 
 
 So are the hours of the Face, To the Quo- 
 tient of the Pinion of Report, In num- 
 bers thus, 16. II : : ii. 9. If the hours 
 of the Face be 24, the Quotient will be . 
 1 8 ; thus, 16. 1 1 : : 14. 1 8. 
 
 S 7. Having given a full account of all 
 things necefiary to the underlhnding the 
 
 Art 
 
22 
 
 Calculation of Cb. II* 
 
 Art of Calculation, I (hall now reduce 
 what hath been faid into practice , by 
 fliewing how to proceed, in Calculating 
 a piece of Watch-work. 
 
 The firft thing you are to do, is to 
 pitch upon your Train, or beats of the 
 Ballance in an hour: as, whither a fwift 
 Train, about 20000 beats (which is the 
 nfual Train of a common 30 hour Pocket- 
 Watch) or a flower Train of about 16000 
 (the Train of the new Pendulum Pocket- 
 Watches; ) or any other Train. 
 
 Having thus pitched upon your Train, 
 you muft next refolve upon the number 
 of turns you intend your Fufy lliall have; 
 and alfo upon the nufpber of Hours, you 
 .would have your Piece to go : As fuppofe 
 12 turns; and to go 30 hours, or 192 
 hours (which is 8 days) or Sfc. 
 
 Thefe things being all foon deternu* 1 
 ned ; you next proceed to find out the ‘ 
 beats of the Ballance, or Pendulum, in ( 
 one turn of the Fufy, by the laft § 6. j 
 part 3. viz. As the turns of the Fufy, | 
 To the hours of the Watch’s going : : So ! 
 is the Train, To the number of beats in 
 pne turn of the Fufy< In numbers thus, 
 I2 .ji 6:: 20000. 26666. Which laft 
 
 num- 1 
 
Scd:. 2. the Watch’ fart. 
 
 number are the beats in one turn of the 
 Fuly, or Great*Wheel ; and ( by Se(S. f. 
 ^ 5'. of this Chap.) are equal to the Quo 
 tientsof all the Wheels unto the ballance, 
 multiplied together. This number there- 
 fore is to be broken into a convenient 
 parcel of Quotients : which y ou are to do 
 after this manner. FirH, half your num- 
 ber of beats. Tyiz. 2666 i 5, for the rcafons 
 in Sed:. I. § 6 . of this Chap, the half 
 whereof is 13333. you are to pitch 
 
 upon the number of your Crown-wheel, 
 as fuppofe 17. :^Oivide 13333 by 17, the 
 Quotient will be 784 (or to fpeak in the 
 language of one that underftands not 
 Arithmetick, divide 15333 into 17 parts, 
 and ‘784 will be one of them ) This 784 
 is the number left for the Quotients (or 
 turns) of the reft of the Wheels and Pini- 
 ons : which being too big for one or two 
 Quotients, may be beft broken into three. 
 Chuie therefore 3 numbers, which when 
 multiplied ail together continually will 
 come neareft 784. As fuppofe you take 
 iOj-pjand9. Now lo rimes 9 is 90 5 and 
 9 times 90 is 810, which is fomewhat 
 too much. You may therefore try again 
 other numbers, as fuppofe ity 9, and 8. 
 '■ Thefe 
 
 23 
 
24 Calculation of Ch, II, 
 
 Tfeefe multiplied as thelaft, produce79x, 
 which is as near as can be, and conveni- 
 ent Quotients. 
 
 Thus you have contrived your Piece, 
 froni the Great -Wheel to the Ballance. 
 But the numbers not falling out exacSbly, 
 according as you at fit ft propofed , you 
 muft corre< 9 : your work thus. Firft to 
 find out the true number of beats, in one 
 turn of theFufy, you muft multiply 791 
 aforefaid, which is the true produtft of all 
 the Q,uotieots, by 17, the notches of the 
 Crown-wheel; the proJutS of this is 
 i j4<S4, which is half the number of true 
 beats in one turn of the Fufy, by Setft. 
 
 % y. of this Chap. Then to find the true 
 number of beats in an hour, fay by § 6. 
 part 4. of this Se<ftion, as the hours of 
 the Watch’s going, v/z. 16, to the ix 
 turns of the Fufy : : So is 1 3 464 the half 
 beats in one turn of the Fufy, to 10098' 
 the half beats in an hour : the numbers 
 will ftandthusid. iz :: 13464. 10098. 
 
 Then to know what Quotient is to be 
 laid upon the Pinion of Report, - fay by §, 
 6. part y. of this Se£t : As the hours of 
 the Watch’s going, viz, 1 6, to the turns 
 of the Fufy, vie. ix;; So are the hours 
 
Se( 5 t. 2 the Watch-part- 2 5 
 
 of the Dial-plate, vk. ii, To the Quo- 
 tient of the Pinion of Report. In num- 
 bers thus, 16. 12. : : ii. 9. 
 
 Having thus found out all 
 
 4 ) 5 ^C 9 your Quotients, his ea fie to 
 
 I determine what numbers your 
 
 5')ssC-r. Wheels fhall have : lor chufe 
 5 ') 45’(9 "'hat numbers your Pinions 
 
 5) 40(8 lhall have, and multiply the 
 
 ■ Pinions by their Quotients , 
 
 17 and that produceth the num- ' 
 bers for your Wheels, as you 
 ' fee in the Margin. Thus 4 is the num- 
 ! ber of your Pinion of Report, and 9 its 
 i^btient; therefore 4 times 9, which 
 ■makes 36, is the number for the Dial* 
 
 I wheel. So tlie next Pinion being 5, and 
 dts quotient II, this multiplied produces 
 55 for the Great-wheel. And the like of 
 the reft of the following numbers. 
 
 Thus, as plain as words can exprefs it, 
 il have Ihewed how to Calculate the num- 
 bers ofa t (5 hour Watch. 
 
 S 8- This Watch may be made to go a - .. 
 [longer time, by leflening the Train, arrd sfft. 
 ■altering the Pinion of Report, Suppofe 
 you could conveniently flacken the Train 
 to X'':. the half of which is 8000. 
 
 ■ ' E Then 
 
26 Calculation of Ch, II. 
 
 Then fay (by %. 6. part 2. of this Sedf.) 
 M the halfed Train, or Beats in an hour., 
 ■viz. 8ooo, To the halfed beats in one 
 turn of the Fufy, ■viz^ • • So are 
 
 the turns of the Fufy, ■viz, iz, To the 
 hours of the Watch’s going; in numbers 
 thus, 8000.13464;; IX. 20 So that this 
 Watch will go 20 hours. 
 
 Then for the Pinion of Report, fay, by 
 the fame §, part y, As 20 the Continu- 
 ance ; To 12 the turns of the Fufy ;: 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 fame asbe^ 
 4^28(7 fore, as to the numbers ; only 
 
 the Dial- wheel is but 28, be-? 
 
 5)y5-(ii caufe its quotient is altered 
 5)45(9 to 7 ; as appears in the Mar- 
 .5)40(8 gin, by the Scheme of the 
 — ^ work. 
 
 17 ^9. f fhall give the Reader 
 
 one example more , for the 
 fake of fhewing him the ufe of fome. of 
 the foregoing Rules, not yet taken notice 
 of in the former operations. Suppofeyou^ 
 Id. ib, would give numbers to a Watch of aboin! 
 I (2.; 1 0000 beats in an hour, to have i a 
 
Sc(5b* the Watch fart. 
 
 I of the Fufy, to go 170 iiours, and 17 
 
 I notches in the Crown-wheel. 
 
 This work is the fame as in the lad Ex- 
 ample ^ 7. In Ihort therefore thus, As 
 the turns I2: are To the Continuance 
 170 So is the Train 10000, To 141666, 
 which are the beats in one turn of the 
 Fufy. The numbers wdl (land thus, 
 12. 170 :: iGooo 14I666. Half this 
 laft is 7o?'3 3. Divide this half iHto 17 
 parts, and 4167 will be for the quotients. 
 And becaule this number is too big for 5 
 quotients, therefore chufe4: as fuppoie 
 10, 8, 8, and 6 | (/. ei 6 and 3 fifths ) 
 Thefe multiplied together as before^ and 
 with 17, maketh 71808, w^hich are half 
 the true beats in one turn of the Fufy* By 
 this you are to find out your true Train 
 firfi, faying as in the former example, As 
 170 to 12 :: So 7 1808, to 5069 5 which 
 laft is the half of the true Train of your 
 Watch. Then for the Pinion of RepcuT, 
 fay, as 170, to xt So ii, to 
 Which Fracftion arifeth thus: If you mul- 
 tiply II by Ui. it makes 144 5 ariddivicie 
 144 by 170, you cannot; but fectlng the 
 144 (the dividend) over 170 (the Divi> 
 tor) and thcr6 arifeth this fradion FI ' , 
 
2 8 Calculation of Chap. II. 
 
 which is a Wheel and Pinion ; the lower 
 is the Pinion of Report, and the upper is 
 the Dial-wheehaccorcJing to Sed.!. ^ 3. of 
 this Chapter. Or ( which perhaps will 
 be more plain to the unlearned Reader) 
 you may leave thofe two numbers j in 
 tlieir Divifional pofture thus, 170)144, 
 which does exprefs the Pinion and Wheel, 
 in the way I have hitherto made ufe of. 
 
 But to proceed. Thefe numbers being 
 too big to be cut in fmall 
 Wheels, may be varied, as 
 
 — you fee a like Example is 
 
 6^6o(jo S' of this Secffion: vh, 
 6)48(8 6'ay, as 144. is To 170:: 
 
 5)40(8 So is 360, To 425. Or, as, 
 *70, to 144 So is 360, 
 
 — . Xo 305. In number thus, 
 
 17 144. 170 :: 360. 425. Or 
 
 170. 144 :: 360. 305. Dl- 
 l' vide 360, and either of thefe two fourth 
 and laft numbers by 4, 5, 6, 8, (as is 
 diredled in the Rule laft cited.) If you 
 divide by 8, you will have for your 
 numbers 7^4 ^ or * 4 . If you divide by - 
 1 5 (which will not bring it fo near an 
 integer) you will have •’ which 
 
 laft are the numbers fet down in the Mar- 
 
 gin,- 
 
iScdl* 2* the Watch-part 2p 
 
 gin ; where the numbers of th® whole 
 iMovement are fet down. 
 
 § ro. Having faid enough, I think, 
 concerning the Calculation of ordinary 
 Watches, to Ihew the hour of the day j, 
 
 I lhall next proceed to fuch as flieW 
 minutes and feconds. The proceis 
 whereof is thus; Firft, having refolved 
 upon your beats in an hour, you are next 
 to find how many beats there will be in 
 a minute, by dividing your defigned 
 Train into 6o parts. And accordingly 
 you are to find out fuch proper numbers 
 for your Crown-wheel, and quotients, as 
 that the Minute-wheel lhall go round once 
 in tin hour, and the Second- wheel once 
 in a minute. 
 
 An Example will make all plain, tet 
 m chufe a Pendulum of 6 inches to go 8 
 days, with i6 turns of the Fufy. By 
 Mr Smith's Tables , a Pendulum of 6 
 inches vibrates 9^68 in an hour. This 
 divided by 60 gives 156 beats for a mi- 
 nute. Half thefe fumms are 4684 and5^£j 
 78. Now the firft work is to break this § 6,' 
 78 into good proportions ; v/hith will 
 fall into one quotient, and the Crowm- 
 W'heel. Firft, for the Crown- W'he^l; let 
 
30 Calculation of Ch, 11, 
 
 it have ly notches. Divide 78 aforcfaid 
 by this I the quotient will be And 
 fo this firft work is done : for a Crown- 
 wheel of I f , and a VV'heel and 
 8)40(5 Pinion, whofe quotient is 5- (as 
 
 in the Margin ) will go round 
 
 15 in a minute, to carry a Hand 
 to Ihew Seconds. 
 
 Next for a Hand to go round in an 
 hour, to Ihew Minutes. Now becaufe 
 there are 60 minutes in an hour, ’tis but 
 breaking 60 into two good 
 8)54(8 quotients ( which may be lo 
 8)60(7^ and 6, or 8 and 7 i, or &c . ) 
 8)40(5 and the work is done. 
 
 Thus your number 4684, is 
 
 I f broken, as near as can be, into 
 proper numbers. 
 
 But becaufe it does not fall out exadly 
 into the above* mentioned numbers, you 
 muft Corred: ( as you were direded -be- 
 fore ) and find out the true number of 
 beats in an hour, by multiplying 15 by 
 5, w'hich makes 75; and this by 60 
 makes 4500, which is the half of the true 
 Train. Then to find out the beats is one 
 turn of thy Fufy, operate as before, '&iz. 
 and § ^ number of turns, 16, To the con- 
 
 tinuance 
 
le(St. 2 . the Watch-fart. 31 
 
 ^inuance 191 So is 4500 to 5'4ooo, 
 vhich are half the beats in one turn of 
 Jk Fufy. In numbers thus, i 6 . ipx : : 
 
 4500. 5'4000. This 5-4000 muft be di- 
 vided by 4^00 , which are the true 
 jiumbers already pitched upon, or beats 
 in an hour. The quotient of this divifion 
 is iz, which being not too big for one 
 lingle quotient , needs not 
 9')ro8Ci2. be divided into more. The 
 g) 64(8 work will Hand, as you fee 
 3 } 60(7; in the Margin. 
 
 3 ) 40(5 As to the Hour-hand, the 
 
 ■ Great- Wheel, which performs 
 
 15-^ only one revolution in la 
 turns of the Minute-wheel, 
 iwill Ihew the hour. Or rather you may 
 order it to be done by the Minute-wheel* 
 ias lhall be Ihevv’d hereafter. 
 
 ^ II. I fliall add but one Exampje 
 ■ more, and fo conclude this Setfiion ; and 
 that is. To calculate the numbers of a 
 Piece whofe Pendulum fwings Seconds, 
 
 .to Ihew the hour, minutes, and feconds, 
 
 .and to go 8 days ; which istheufual per- 
 ( formance of thofe Movements called ^ ^ . 
 [Royal Pendulum.s at this day. Firft, caft 1^3.^ 
 iup the number of feconds in iz hours p.u«. 
 
 I (which 
 
32 Calculation of Ch. II» 
 
 (wh ich are the beats in one turn of the 
 Great-wheel) Thefe are ix times 6o 
 minutes, and times that, gives 43x00, 
 which are the feconds in ix hours. Half 
 this number (for the reafons before) is 
 v.^Sea.1.2^ jgQQ_ “j-ijg Swing-wheel muft needs 
 ^ * be 30, to fwing 60 feconds in one of its 
 revolutions. Divide xi6oo by it, and 
 7x0 is the quotient, or number left to be 
 broken into quotients. Of thefe quoti- 
 ents, the firft muft needs be 12 for the 
 Great-wheel, which moves round once 
 in IX hours. Divide 7x0 by ix, the 
 quotient is 60 ; which may be conveni- 
 ently broken into two quotients, as i o 
 and 6, or y and ix, or 8 and 7 I, which 
 laft is moft convenient. And 
 3)96(12. if you take all the Pinions 8, 
 8)64(8 the work will ftand as in the 
 8)6o(;t Margin. 
 
 According to this computa- 
 
 30 tion, the Great-wheel will go 
 about once in ix hours , to 
 Ihew the hour, if you pleafe : the Seconds 
 wheel once in an hour, to fhew the mi- 
 nutes ; and the Swing-wheel once in a mi- 
 note, to Ihew the feconds. 
 
Se( 5 t. 2* the Watch-part. 3 .3 
 
 Thus I have endeavour’d with ail |K>f- 
 iible plainnefs, to unravel this mofl my- 
 ifterious, as well as ufeful part of Watch-* 
 work. In which, if I have cfFvnded the 
 more learned Reader , by unarrificial 
 terms, or multitude of word-, i dcfire 
 the fault may be laid upon my earncil; 
 intent to condefcend to the mcandt ca- 
 pacity. 
 
 SECT. Ilf. 
 
 To Calculate the Striking part of a Clock. 
 
 ^ I. A Liho this part confiffs of manv 
 L \ VV heels and Pinions, yet refpedt 
 needs to be had only to the Count -voheel.^ 
 Striking-wheel, and Detent-wheel: which, 
 'move round in tliis proportion ; Tlie 
 Count-wheel moveth round commonly 
 ;Dnce in li, or 24 hours. The Detent- 
 wheel moves round every ftroke the 
 Clock Rriketh, fometimes bur once in 
 two ftrokes. From whence it follows, 
 
 _ I. That as many Pms as are in tiie 
 Pin-wheel, fo many turns hatii the Dc- 
 tent^wheel, in one turn of the Pin-wheel. 
 
 'Or ( which is tile fame ) the Pms of tiie 
 E P.n- 
 
 I 
 
34 Calculation of Ch. II? 
 
 Pin-wbeel are the Qiiotient of that 
 Wheel, divided by the Pinion of the De- 
 tenNwheel. But if the Detent- vi^heel 
 moveth but once round in two ftrokes of 
 the Clock, then the faid (Quotient is but 
 half the number of Pins. 
 
 a, As m^ny turns of the Pin-wheel as? 
 are required to perform the ftrokes of iz 
 . hours ( which are 78 ) So many turns 
 muft 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 fliall be 
 the Quotient of the Pinion ofReporr* All 
 this is, in cafe the Pinion of Repor;t be 
 fixed to the arbor of the Pimwheel, as is 
 very commonly done. 
 
 All this I take to be very plain : or if 
 it be not, the example in the Margin wilf 
 clear all difficulties. Here 
 8‘;)48(6 the Locking-wheel is 4?, 
 
 , the Pinion of Report is 8, 
 
 the Pin-wheel is 78, the 
 6)6c/ 10 Striking-pins are 13. And 
 
 6;48, 8 fo of the reft, I need only 
 to remark hero, that 78 
 being divided by the 1 5 pins, gives 6 
 which is the Qiiotient of the Pinion 
 
 of 
 
Sed:. g; the Clcckpari. 
 
 of Report : as was before hinted. 
 
 As for the Warnin^wkeel, and Fljin^- 
 Piniox, it matters Jittle what numbers 
 they have, their ufe being bniy to bridle 
 the rapidity cf the motion of the other 
 Wheels. 
 
 Befides the lad cbfervatibn, there are 
 other ways to find out the Pinion of Re* 
 port, which will fall under the next 
 § Thefe following Rules will be of 
 great ufe in this part Of Calculation, viz. 
 
 Rule i; As the number of turns of the 
 Great-wheel, or Fufy ; 
 
 . To the days of the Clock scontinuaucc: 
 . So is the number of ftrokes in 24 
 hoursj viz. if6, 
 
 . To the ftrokes in one turn of the Fufyj 
 Or Great-wheel. 
 
 Rule 2.. As the number of ftrokes in 
 14 hours, which are iy6, 
 
 . To the firokes in one turn of the Fufy, 
 or Great-wheel, 
 
 : : So are the turns of the Fufy, or Great- 
 wheel, 
 
 . To the days of the Clock s continuarcfc^ 
 or going. 
 
 Rule 9 . As the ftroites in one turn of 
 the Fuly, 
 
6 
 
 Calculation of Chap. 11. 
 
 ^To the ftrokes of 24 hours, *viz. i 
 : : So is the Clock’s continuance, 
 
 . To the number of turns of the Fufy, 
 or Great-wheel. 
 
 Thefe two laft Rules are of no great ufe 
 (as the firft is ) but may ferve to corredl 
 your Vv/ork, if need be, when in breaking 
 your Strokes into Qjaotients ( of which 
 prefently) you cannot come near the true 
 number, but a good many ftrokes are left 
 remaining. In this cafe, by Rule 2. you 
 may find whether the continuance of 
 your Clock be to your mind. And by 
 Rule 3, you may enlarge or diminilh 
 the number of turns for thispurpofe. The 
 praxis hereof wdll follow by and by. 
 
 The z following Rules are to find fit 
 numbers for the Pinion of Report, and 
 the Locking-wheel, befides whatisfaid 
 before § I. Inference z. 
 
 Rule 4. As the number of Strokes in 
 the Clocks continuance, or in all its 
 turns of the Fufy, 
 
 . To the turns of the Fufy, 
 
 : : Soaje the Strokes in 12 hours, which 
 are 78, ^ 
 
 . To the Quotient of the Pinion of Re- 
 port, fixed upon the arbor of the Great- 
 wheck But 
 
Sed. 9 . the Clochfati 37 
 
 But if you would fix it to any other 
 Wheel, you may do it thus, as is before § f. 
 hinted, viz. • 
 
 Rule 5. Firft, find out the number of 
 Strokes, in one turn of the Wheel you in- 
 itcnd to fix your Pinion of Report upon 
 (which I lhall Ihew you how to do in 
 I the following Divide 78 by this 
 number, and the number arifing in the 
 [Quotient, is the Quotient of the Pinion 
 fof Report. 
 
 Or thus. Take the number of Strokes 
 in one turn of the Wheel, for the num- 
 ber of the Pinion of Report, and 78 for 
 the Count (or Locking) wheel, and vary 
 them to lefler numbers, by Sedf. x. ^ y . 
 of this Chapter. 
 
 Rule 6 . The foregoing Rules are of 
 greateft ufe, in Clocks of a larger conti- 
 nuance 5 altho, where they can be ap- 
 plied, they will indifferently ferve alb ' 
 iBut this Rule ( which will ferve larger 
 Clocks too) I add chiefly for the ufe of 
 leffer Pieces, W'hofe continuance is ac- 
 counted by hours. 
 
 The Rule is to find the Strokes in the 
 Clocks continuance, wz;As ix, is 1078 : t 
 So are the hours of the Clocks continu- 
 ance, 
 
Calculation of Gh. II; 
 
 ance, To the number of Strokes in that 
 time. 
 
 This Rule (I faid) may bfe made ufe of 
 for the largeft Clock j but then you 
 muft be at the trouble of reducing the 
 Days intoHours Whereas the fliorteft way 
 is to Multiply the ftrokes in one turn of 
 the Great' heel, by the number of Turns. 
 Thus in an 8 day piece the Strokes in 
 one turn are 78. Thefe multiplied by iiJ, 
 the turns, produce 1x48 ; which are the 
 Strokes iti the Clocks continuance. If 
 you work by the foregorng Rule, the 
 hours of 8 days are ipx. Then fay, 
 iz 78 : : igii 1x48. 
 
 § 3 In thisParagraph^ I lhall (hew the 
 Ufeot the preceding Rules, and by exam 
 pies make all plain that might feem oh 
 fcure in them. 
 
 I begin with fmall Pieces : of whicl 
 but briefly. And firft, having pitcher 
 upon the number of turns, and the conti i 
 nuance, you muft find, by the laft Rule 
 how many Strokes are in its continu 
 ance. Then divide thefe Strokes by th 
 number of turns, and you have the num 
 ber of Striking'pinsi Or divide by th) 
 number of Pins, and you have the num ; 
 ber of Turns. 1 Thu i 
 
3 . the Cloc^-f art. 
 
 Thus a Clock of 30 hours, with ly 
 turns cf the Great-wheel , hath- 195' 
 Ilrokcs. For by the laft Rule, I2. 78 :: 
 ^0. 195. Divide 19J by ly, it gives 13 
 I for the Striking-pins, Or 
 
 ^5)i 95’(I3 if you chufe 13 for yotar 
 *3)195(15 number of Pins, and divide 
 ■ 195 by it, it gives 15, for 
 
 |the number of turns, as you fee in the 
 Margin. 
 
 ! As for the Pinion of Report, and the 
 
 [reft of the Wheels, enough is fiid in the 
 
 ■ 
 
 \ But fuppofe you would calculate the 
 inumbers of a Clock of much longer con- 
 kinuance, which will neceffitatte you to 
 [make your Pinrwheel further diftant froth 
 ithe Great-wheel, you are to proceed thus : 
 Having refolved upon your turns, you 
 imuft find out the number of ftrokes in 
 (one turn of the Great-wheel, or Fofy, by 
 f 2 - R.ule I. Thus in an 8 day piece, of 
 16 turns, 1(5.8 ; : 156. 78. So ina piece 
 of 32 days, and 16 turns, 16 32:: 156. 
 312. Thefe ftrokes fo found out, are 
 the number which is to be broken into a 
 bonvenient parcel of Quotients, thus j 
 j’ Firft refolve upon ypur number of Stri-i 
 
)4Q Calculation of Ch. II. 
 
 king-pins: divide the laft named number 
 by it : The quotient arifing hence, is to 
 be one, or more quotients, for the Wheels 
 and Pinions. As in the ,]aft examples. 
 Divide 78 by '8 (the ufoal pins in an 8 day 
 piece) and the quotient is 9 J 5 which is 
 a quotient little enough. S.® in the 
 Month-piece : if you take your Pins 8, 
 divide jix by it, the quotient is 59. 
 Which being too big for one, muft be 
 broken into two quoti- 
 «ntSj for Wheels and 
 8)48(6 Pinions, or as near a? 
 
 6)48(8 pins can be : which may be 
 7 and5’,or 6 and 61 . The 
 latter is exadly ^ 9, and may therefore 
 ftand : as you fee is done in the Margin. 
 
 The quotients being thus determined, 
 and accordingly the Wheels and Pinions, 
 as you fee ; the next work is to find a 
 quotient for the Pinion of Report, to car- 
 ry round the Count (or Locking) wheel 
 once in ix hours, or as you pleafe. If 
 you fix your Pinion of Report on the 
 Great-wheel arbor, you muft operate by 
 the Rule 4. of the laft paragraph. As in ; 
 the laft example in the Month-piece : by 
 Rule 6. before, the ftrokes in the continu- 
 ance 
 
Sedb. 5- the ClGckftvri. 41 
 
 ance are 4992. Then by Rule 4 fay, 
 
 499Z. 5 or 1505,4991)1248. 
 
 I The firfl: of which two numbers is the 
 I Pinion, the next is the Wheel. Which ' 
 
 I being too large, may be varied to or v. Sedr 
 1 56)9 ; or to or 24)6, by Se(3:.2 § 5 * 
 
 ! before. 
 
 Thefe numbej*s being not the ufual 
 (numbers of a Month-{>icce, but only made 
 jufeof by me, as better illuflrating the 
 Toregoing Rules : I lhall therefore, for the 
 ! fuller explication of what has been faid, 
 
 ^briefly touch upon the calculation of the 
 :more ufual numbers. They commonly 
 iencreafc the number of Striking-^pins, and 
 :fo make the Second-wheel the Striking-" 
 iwheeh Suppofc you take 24 Pins; Di- 
 ivide ^i2 by it, and the Q^iotient is i]. 
 
 Which iS Ur tie enough 
 6)104(13 for one Qiiotienc ; 
 
 6) 72(12.24 pins and may therefore 
 hand ns you lee is 
 3 one in the Margin : ^diere thcQiiotienc 
 Df the firft Wheel is 13. lathe fecond 
 Wheel of 72 teeth, are the pins, nltho 
 'ts quotient is but 12, becaufc the Hoop- 
 '^dieel is double, and goes round bur once 
 m two ftrokes of the Pin- wheel, 
 
 Q Ths 
 
Calculation of Chap. 11. ' 
 
 The Pinion of Report here, is the fame 
 with the laft, if fixed upon the arbor of 
 the Great- wheel. But if you fix it on the 
 arbor of the Second, or Pin-wheel, its 
 quotient then is found by § i. Infer, z, 
 or by §z. Rule y. viz. Divide 78 by 24, 
 and the number arifing in the quotient, is 
 the quotient of the Pinion of 
 12)39(34 Report, w hich is 3 i The 
 Pinion of Report then being 
 12, the Count-W'heel will be 39, as in 
 the Margin. 
 
 To per fed: the Reader in this part of 
 Calculation, I will finifli this Sed:ion with 
 the calculation of a Year-piece of Clock- 
 work. The Procefs w^hereof is the fame : 
 with the laft, and therefore 1 may be - 
 more brief with this, except w^here I have 
 not touched upon the foregoing Rules. 
 
 ‘ VVe will chufe a piece to go 39^ days 
 with 16 turns, and 26 Striking-pins. By 
 § 2. Rule i. there are 3851 ftrokes in one 
 turn of the Great- wheel.* For 16. 395' :: 
 156. 3851. This laft number divided by 
 the 16 Pins, Reaves iq8 in the quotient, 
 to be broken into two or more quotients, 
 for Wheels and Pinions. Thefe quotients 
 may be 12 and 12 ; which multiplied 
 
 make.* 
 
SwA. 3. the Clockrpart. 4 3 
 
 i makes 144, which is 
 
 f io)i2o(ix as near as can well be, 
 
 } 8) 96(ix to i48.The work thus 
 I - 78116 pins far contrived , will 
 
 (land as you fee in the 
 
 Margin. 
 
 Before you go any further, you may 
 correct: your work, and fee how near 
 your numbers come to what you propo- 
 fed at firft, becaufc they did not fall out 
 exad. And firft, for the true continuance 
 cf your Clock ;; If you multiply n, 11, 
 
 : and f\, e. the Qjiotients un 0 the Stri- 
 ktng*pm^ and thofe Pins) you have the true 
 number of Strokes^ in one turn of the Great- 
 \ wheel: Which, in this example, make 
 • 3744* For II times ii, is 144; and i6 
 ^ times that, is 3744- (This Diredtion I 
 would have noted, and remembered, as 
 a Rule ufeful at any time to difeover the 
 nature of any piece of Clock-work.) Ha- 
 ls ving thus the true number of Strokes de- 
 1 fired, by % i. Rule 2. you may find the 
 true Continuance , to be only 384 days. 
 
 For 156. J744 16. 384, IfthisConti- 
 nuance doth not pleafe you, you may 
 come nearer to your firft propofed num- 
 ber^ ol 395 days, by a fmali encreafe of 
 i G 1 the 
 
44 Calculation of Ch. II 
 
 the number ol Turns,* according to x. 
 Rule 3. viz, by making your turns al- 
 moft 16 For 3744. 156 ; : 16 1 
 
 almon:. 
 
 Lafliy, For the Pinion of Report, if 
 you fix it upon the Great-wheel, it will 
 require an exceffive number : if you fix it 
 upon t'le Pin-whee! (which is ulual) then 
 by % X. Rule 5, the quotient 
 13)39(3 3 > tho-^ Pinion of Re? 
 
 port being i % , the Count- 
 wheel will be 39 ; as you lee in the Mar- 
 gin. 
 
 But for the better exercifingthq Reader, 
 let us fix it upon the Spindle oNhe Se- 
 pond'whee! 96. Its quotient is iz; 
 which mulriphed by x6 (the pins) pro- 
 duceth 3 1 2 ; which r re the Strokes in one 
 turn of that Second-wheel. Then by §x. 
 Rule 5, Divide 78 by 3 ix, /. e. Set them 
 as a Wheel and Pinion thus, 3i x)78, and 
 vary them to kiTer numbers ^by Sed. x. 
 § y.) VIZ. 36)9, or to 24)6, or the 
 like. 
 
 I think it needlefs to fay any thing of 
 Pocket-clocks, whofe calculation is the 
 yery lame, with what goes before. 
 
 Thaj 
 
 ■’a," 
 
Se<9:. 3 . the Clock-part. 
 
 That the unlearned Reader may not 
 think any thing going before difficult, I 
 need only to advife him, to look over the 
 vvorking of the Rule of Proportion, in 
 Sed. 2 .-^ 4 . Fori think all will be plain, 
 if that be well underftood. 
 
 SECT. 4. 
 
 Of Oerters and Chimes. 
 
 T Hc Reader will expe<3: that I mould 
 fay fomewhat concerning Quarters 
 and Chimes : but becaufe there is little, 
 but what is purely mechanical in it, I 
 [lhall fay the lets, and leave the Reader to 
 his own invention. 
 
 § I. The Qmrters are generally a di- 
 ftin^ part from the Clock-part, which 
 iftriketh the Hour. 
 
 The Striking-wheel may be the FirR, 
 Second, or Wheel, according to your 
 Clocks continuance. Unto which Wheel 
 you may fix the Pinion of Report. 
 
 ThtLocking-vcheelm\i^^ be divided(aso- 
 therLocking- wheels) into 4,8.nr more un* 
 (equal parts, lo asto ftrike the Quarter, and 
 j lock at the firft Notch j the haii-hour, and 
 
 lock 
 
 45 
 
4^ 'taking of Cb II. 
 
 lock at the fecoad Notch, ^c. And in 
 doing this, you may make it to chime the 
 Quarters, or ftrike them upon two Bells, 
 or more. 
 
 *Tis ufua! for the Pin-wheel, or the 
 Locking-wheel, to unlock the Hour-part i 
 , in thefe Clocks ; which is eafily done by. i 
 fome jogg or Latch, at the end of the i 
 laft Quarter, to lift up the Detents of the i 
 Hour- part. , 
 
 If you would have your Clock ftrike ; 
 the Hour, at the Half-hour, as well as 
 whole Hour, you muft make the Locking- i 
 wheel of the Hour- part double : i. e. it i 
 muft have two Notches of a fort, to ftrike > 
 I, z, 5, 4 , ©"c. twice apiece. i 
 
 J X. As for Chimes^ I need fay nothing | 
 I of the Lifting-pieces and Detents, to lock 1 
 and unlock j nor of the Wheels to bridle i 
 the motion of the Barrel. Only you are ■ 
 to obferve, that the Barsel muft be as long 
 in turning round, as you are in Singing |i 
 s, the Tune it is to play. As for the Chime- 1 
 Barrel^it may be made up of certain Barrs, t 
 that run athwart it, with a convenient n 
 number of holes punched in them, to put n 
 in the Pins, that are to draw each Ham- 
 mer. By this means, you may change i 
 
 the 
 
Se<5t. 4. Quarters and Chimes. 47 
 
 the Tune, without changing the Barrel. 
 
 Fhis is the way of the Royal Exchange 
 Clock in London, znd of others.In this cafe, 
 the Pins or Nuts, which draw the Ham- 
 mers, muft hang down from the Barr, 
 fomemore, fomelefs, and fome Band up- 
 fight in the Barr ; the reafon whereof is, 
 fo play the Time of the Tune rightly, 
 for the diflance of each of thefe Barrs, 
 may be a Semi-brief, or &c. of which here- 
 after,' 
 
 But the moft ufual way is, to have the 
 Pins that draw the Hamm.ers, fixed on 
 the Barrel. For the placing of which Pins, 
 you may make ufe of the Mufical Notes, 
 or proceed by the way of Changes on 
 Bells, viz. i,x, 4, &c. The firfi be- 
 jng far the better way, I fhall fpeak of 
 that chiefly, efpecially becaufe the latter 
 will fall in to be explained with it. 
 
 ■ And firfl, you are to obferve what is 
 the Compafs of your Tune, or how many 
 Notes or Bells there are from the higheft 
 to the loweft: and accordingly you muft 
 divide your Barrel from end toend. Thus 
 in the examples following, each of thofe 
 Tunes are 8 notes in compafs ; and ac- 
 cordingly the Barrel is divided into 8 
 
 parts. 
 
a 
 
 Making of Ch. II- 
 
 parts. Thefe Diviuons are ftruck round | 
 the Barrel, oppofite to which are the 
 Hammer-tails. . 
 
 I Ipeak here, asif there Was only onei j 
 Hammer to each Bell, that the Reader 1 
 may more clearly apprehend what I am J 
 explaining. But when two Notes of the | 
 fame found come together in a Tune,* i 
 there miift be two Hammers to that Bell, \ 
 
 , CO ftrike it. So that if in all the Tunei 
 you intend to Chime, of 8 notes compafs, ; i 
 there fhould happen to be fuch double i 
 Notes on every Bell, inftead of 8, you i 
 muft have i6 Hammers and according- 
 ly you muft divide your Barrel, and ftrike |l 
 l6 ftrokes round it oppofite to each Ham- ;1 
 mer-tail. Thus much for dividing yont 
 Barrel from end to end. .II 
 
 In the next place, you are to divide it d 
 (round about) into as many divifions, a^ 
 there are Miifical Barrs, Semibriefs,* 
 Minums, in your Tune. Thus the-' 
 looth Pfalm-iune hath 20 Semibriefs; jc 
 the Song“tune following, hath ^4 Barrs^ jj^ 
 of triple time: and accordingly their Bar* ^2 
 rels are divided. Each divifion therefore 
 of the looth Pfalm Barrel is a Semibrie^ 
 and of the Song»tune kis three crotchets I 
 
 And j 
 
ISed:- 4- Quarters afici Chimes. 4^ 
 
 I And .therefore the intermediate Spaces 
 ilervcfor the fliorter notes : as, one third 
 of a divifjon, is a Crotchet, in the Song- 
 jtune. One half a divifion, is a Minum ; 
 land onequarter a Crotchet, in thePfalni" 
 jtune. Thus the firft note in the looth 
 i'Pfalm, is a Semibrief, and accordingly on 
 the Barrel, ’tis a whole divifion from, 5 
 ito 5*. The fecond is a Minum, and there* 
 ifore 6 is but half a divifion from 5 ,• and 
 ifo of the reft. And fo alfo for the Song* 
 tune, which is fliorter time : The two 
 jfirft notes being Quavers, are diftant from 
 one another, and from the third pin, but 
 half a third 'part of one of the divifioos. 
 
 3ut the two next pins ( of the bell 3, 
 being Crotchets, are diftant fo many third 
 parts of a divifion. And the next pin (of 
 Ihe bell 1 ) being a Minum, is diftant 
 from the following pin (4) two thirds of 
 Mivifion. 
 
 ! From what hath been fald, . you may 
 :onceive the furfece of a Chime-barrel, 
 ro be reprefcnted iri the Tables following, . 
 as frretched out at length: or ( to fpeak 
 plainer) that if you wrap either of thefe 
 Tables round a Barrel, the Dotts in the 
 fahie, vvdll fhew the places of the 
 i H Vim, 
 
Making of Ch 
 
 A Table oF Chimes to 
 the 100 Pfalm. 
 
 8 725' 4g2i^ 8 75^4321 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ar" 
 
 ( 
 
 ) 
 
 
 
 
 
 
 
 " "i 
 
 
 
 1 . 
 
 
 
 
 — ... Jg 
 
 , if 
 
 f 
 
 
 1 
 
 
 
 
 
 r 
 
 
 
 
 1 
 
 ^ - 
 
 
 — i 
 
 
 
 
 
 
 
 i 
 
 
 
 r.. -i 
 
 ! , 1 
 
 u 
 
 
 
 ! 
 
 
 1 
 
 H 
 
 □ 
 
 
 
 
 
 
 
 f \ 
 
 ' 
 
 i 
 
 
 
 
 < 
 
 > 1 
 
 L 
 
 
 
 
 p 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ -- 
 
 
 
 < 
 
 & 
 
 i i 
 
 f 
 
 
 
 
 :: 
 
 
 f 
 
 1 
 
 1 ^ 
 
 > 
 
 
 
 
 
 
 
 
 
 LLL 
 
 
 
 The Mulical Notes of Pfalm 100. 
 
Sed. 4, Quarters and Chimes. 
 
 Pins, to be fet on the Barrel, 
 
 _ You may obferve in the Tables, that 
 hrom the end of each Table to the begin- 
 ning is the diftance of two. or near two 
 dmfions: which is for a Paufe, between 
 the end of the Tune, and its beginnine 
 to Chime again. ^ 
 
 I need not fay, that the Dotts running 
 about the Tables^ are the places of the 
 Pins that play the Tune. 
 
 ■* , would have your Chimes com- 
 pleat indeed, you ought to have a fet of 
 cells, to the Gamut notes ; fo as that 
 each Bell having the true found of Sol, 
 
 •V • 5'™ may play any Tune!' 
 
 With Its Flats and Sharps. Nay, youmav 
 
 by thefe means, play both the Bafs and 
 Ireble, with one Barrel. 
 
 ffany thing going before appears gib- 
 benfli, r can t help it, unlefs I fliould here 
 teach the skill of Mufick too. 
 
 As to fetting a Tune upon the Chime- 
 barrel from the number of Bells, viz. 
 
 I) 4 , f fliall here give you a fpeci- 
 men tnereof. 
 
 Such Command o're my Fate, in num- 
 bers, 
 
 H 
 
 77ir. 
 
52 
 
 Making of, &c. Ch. II. 
 
 775^’ 5’ 3» ^*4’ 6, 4» 4’ 
 
 4, 3, 2.,,3>4, 6, 5,5. 7, 7» 7-11 
 
 5, 6, 8, 8, 4. 4^ 4; 5, 5,4. 
 
 <^.5^ 7, 3;4T. ^ 
 
 3» 3’ I5 3» 5* 55'4) 4» 
 
 4 . 3 ; 2.3, 3; 55, j, 7, 7, 7. 
 
 In thefe numbers, a Comma 
 fignifies the note before it, to be a Crotchet. 
 A prick’d Comma, or Semi-colon Q;3 de- 
 noteth a prick’d Crotchet. And a Period 
 is a Minum. Where no pundtation 
 is, thofe Notes are Quavers. 
 
 I fhall only add further, that by fet- 
 tiog the Names ofyour Bells at the head 
 pf any Tune (as is done in the Tables be- 
 fore) you may eafily transfer that Tune, 
 to your Chime-barrel, without any great 
 .skill in Mufick. But obferve, that each 
 line in the Mufick, is three notes diflant; 
 
 e. there is a Note between each line, as 
 well as upon it : as is manifeft by infped- 
 ing the Tables. 
 
 SECT. 
 
Sedt. 4^ Calculation of^ &c, 
 SECT. 
 
 T'o Calculate any of the Celejlial 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 pleafe) the flow motion of the Suns 
 Apogieum^ of the Fixed Stars, the motion 
 oi the Planets, &c, 
 
 ^ I. For the effecting thefe Motions, 
 you may make them to depend upon the 
 Work already in the Movement 5 or elfe 
 meafure them by the beats of a Ballance, 
 or Pendulum. 
 
 If the latter way, you muft however 
 contrive a .Piece (as before in Watch- 
 work) to go a certain time, with a cer- 
 tain number of turns. 
 
 But then to Specificate, or determine 
 the Motion intended, you muft proceed 
 one of thefe two ways : either, 
 
 I. Find how many beats are in the Re- 
 volution. Divide thefe beats by the beats 
 in one turn of the Wheel, or Pinion, 
 w^hich you intend fliail drive the intended 
 Revolution ; and the Quotient Ihall be 
 
 the 
 
 53 
 
54 Cekftial Motions. ^ Cb. Jf.' 
 
 the number to perform the fame. Which, 
 if too big for one, may be broken into 
 more Quotients. Thus, if you would 
 reprefent the Synodical Revolution of the 
 Moon, which is 19 days, iz | hours) 
 with a Pendulum that fwings Seconds, 
 the Movement to go 8 days, with 16 j 
 turns of the Fufy, and the Great-wheel to ' 
 drive the Revolution. Divide zjfi y 00 
 ( the Beats in 2,9 days 12, 4 hours ) by 
 43100 (the Beats in one turn of the Greats 
 wheel) and you will have 5^9 in the Quo- 
 tient : which being too big for one, may 
 be put into two (Quotients. Or 
 2. You may proceed as is direcS'ed be- 
 fore, in the Sedlion of Calculating Watch- 
 '§ work, W2. Chufe your Train, turns of 
 the Fufy, Continuance, &c. And then 
 inftead of finding a Quotient for the Pini- 
 on 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 Quoti- 
 ent of the Revolution 
 
 Thus to perform the Revolution of Sa- \ 
 turn (which is 29 years, 183 days) with a 1 
 
 16 i 
 
Sc<5t. 4 . Calculation of the 
 
 16 hour Watch, of 16918 Beats in one 
 turn of the Fufy, and 20196, theTrain: 
 the quotient of the Revolution, will be 
 19^814 For, As 16918, To 10196:: 
 So i5843i(the Hours in 197. and 18 j d.) 
 To 19^814. 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 DiaF wheel, and the 
 Work already in the Movement ( which 
 in great Revolutions, is for the moft part, 
 as nice as the laft way, and in which I in- 
 tend to treat of the particular Motions) 
 in this cafe, 1 fay, you muft firft know 
 the Days of the Revolution. And becaufe 
 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 j 
 as fhall be Ihewed in the following exam- 
 ples. 
 
 S 2. A Motion to fhew the Day of the 
 Month. 
 
 55 
 
5^ Cekjiid yionoHs. Cli. II. 
 
 Oughmi, xhe days in the largeft Month are 3 1. 
 
 ^ Thefe doubled are 6x, which are the turns 
 of the Dial-wheel, which may be broken 
 into thefe two quotients 1 5 J 4 ; which 
 multiplied together make 61. 1 herefore 
 chufing your Wheels and Pinions, as hath 
 been diredied in the former Sections, your 
 work is done. The Wheels 
 
 4) 62(152 and Pinions mav be, as you 
 
 5) 20^4 fee done in the Margin. 
 
 Or if a larger Pinion than 
 one of 5 be neceflary, by reafoft it is con- 
 centrick to a Wheel, you 
 4)62(15? maytake iofor the Pinion, 
 10(40(4 and 40 for the Wheel, as in 
 the Margin. 
 
 The work will lye thus in the Move- 
 ment, VIZ, Fix your Pinion 10, concen- 
 trical to the Dial- wheel (or to turn round 
 with it upon the fame Spindle.) This Pi- 
 nion 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 fide into 31 days. 
 
 Or, you may, without the trouble of 
 many Wheels, effedi this motion ; 
 
 By a Ring divided iqto 30 or 31 days, and 
 as many fangs or Teeth, like a Crown- 
 wheel 
 
 
.Sedl. 5. Celeftial Motions. 
 
 wheel teeth, which are caught and pu/li- 
 I ed forward orice in 24 hours, by a pin m 
 I a Wheel, that goeth round in that tinle. 
 
 I This is the ufual way in the Royal Pendii- 
 I lums, and many other Clocks ; and there- 
 fore being common, I ffiall lay no more 
 of it. 
 
 § l» A Motion to fhei)} tjje of the 
 Moon, 
 
 The Moon finilheth her courfe^ fo as 
 to overtake the Sun, in 29 days, and 3 
 little above an half. This 29 I days (no4 
 regarding the fmall excefs } makes 59 
 twelve hours, or turns of the Dial-wheel, 
 which is to be broken into convenient 
 
 quotients:which 
 4)59(14.^ may bey.pand 
 4)40(10 10)40(4 io,as inthe firft 
 
 example,* or 144 
 ind 4, as in the fecond Example in the 
 Vlargin. So that if you fix a Pinion of 
 :o concentrical with your Dial-%vheel, to 
 Irive a Wheel of 40 (according to the 
 ift example) which Wheel 40 drives a 
 finion 4, which carries about a Ring, or 
 V'heel of 59 teeth, divided on the upper 
 dc iato 29 i, ’twill Ihew the Moons 
 
 
 
 I 
 
Calculation of the Chap. II. 
 
 § 4. ^ Motion to Jhevo the day of the 
 Tear, the Sun's place in the Ecliptick, Suns 
 Rtfing or Setting, or any other annual motion 
 of days. 
 
 The double of 365' is 730, the turns'of 
 the Dial- wheel in an year : which may 
 
 be broken into 
 4)7 ;(i 84 4)73(18^ thcfe quotients, 
 
 4)40(10 4)?^(8 T/z. i8|,andio, 
 
 y)zo(4 4)20(5" and 4, according 
 
 to the firft exam- 
 ple; ori8i, 8, and 5, according to the 
 iecond. So that a Pinion of y is to lead 
 a Wheel of 20; which again by a Pinion 
 of 4, leadeth a Wheel of 40 ; which third- 
 ly, by a Pinion of 4, carrieth about a 
 Wheel, or Ring of 73, divided into the 
 12 months, and their days ; or into the 
 j a figns, and their degrees ; or into the 
 Sun's Riling and Setting, &c. For the 
 fetting on of which laft, you have a Ta- 
 ble in Mr. OughtredH Opufcula. 
 
 J 5. Te fhew the Tides at any Port. 
 
 This is done without any other trou- 
 ble, than the Moon’s Ring (before menti- 
 oned § 3.) to move 'round a fixed circle 
 divided into twice 12 hours, and num- 
 bered the contrary way to the age of the 
 Moofi, To 
 
 
Se(5t. 5 , Celejiial Motions* 
 
 I To fet this to go right, you mull: find 
 lout at what Point of the Gompafs 
 the Moon makes full Sea , at the 
 place you would have your Watch ferve 
 to. Convert that point into hours, al- 
 lowing for every point North or S. loft 
 4j' of an hour. Thus at Lon^on^lridge 
 ’tis 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 theMoon’sSouthing, ’tis High* 
 water.Or thusjfind at what hour it is High* 
 water, at the Full or Change of the Moon t 
 as at London-hridge^ the full Tide is com- 
 monly reckoned to be 3 hours from the 
 Moon’s Southing ; or at 5 of clock at the 
 Full and Change, The day of Conjunefti- 
 on, or New-Moon, with a little ftad to 
 point, being fet to the hour fo found, Will 
 afterwards point to the hour of full Tide. 
 
 This is the ufual way; but it being al- 
 ways in motion, as the Tides are hot, a 
 better way may be found out, viz. By 
 icaufinga Wheel, or Ring to be moved 
 forward, only twice a day, and to keep 
 * time (as near as can be) with Mr. Flmi- 
 fteed " s moft corred; Tables. But this I 
 I X Iball 
 
do. 
 
 Calcuhtim of the Ch* II. 
 
 Hiall commit to the iReaders contrivance, 
 it being eafie, and more of curiofity than 
 ufc. 
 
 § 6. to Calculate Itumhers, to Jhew the 
 Motion of the Vianet s, the Slow Motion pf \ 
 the Fixed Stars, and of the Sun's Apo-‘ ‘ 
 geum, &c. 
 
 Having faid enough before that may 
 be applied here, and they being only cu« 
 liofuies, feldom put in pradice, I fliall ! 
 not therefore trouble the Reader, or fw ell ' 
 my Book with fo many words, as would ' 
 be required to treat of thefe Motions di- ' 
 ftindly, andcompleatly. ' 
 
 Only thus much in general. Know'ing ’ 
 the years of any of thele Revolutions, you ' 
 may break this number into quotients j 
 if you will make the Revolution to de- 
 pend upon the year’s Motion ; which is, 
 already in the Movement, and defcribed 
 % 4. before. Or if you would have it de- 
 pend upon the Dial-wheel, or upon the 
 Beats of a Pendulum, .enough is faid be- 
 fore to dired in this matter. i 
 
 In all thefe Slow motions, you may 
 fomewhat Ihorten your labour, by end- 
 lefs Screws to ferve for Pinions, which 
 are but as a Pinion of one tooth. 
 
 $ir 
 
Sc(5t. 5* Celejlial Motio^si 
 
 Sir fe»ai Moors account of his large Mat.eom: 
 Sphere going by Clock-work, will fuffi-P- " 7 - 
 riently illuftrate this paragraph. In this 
 Sphere, is a Motion of 17100 years, for 
 he Sun’s Apogeum, performed by iix 
 iV heels, thus, as Sir Jottat relates it j 
 ■For the Great- wheel fixed is pd, aSpin- 
 ‘dle-wheel of ix bars turns round it 8 
 ■ times in 24 hours, that is, in 3 hours ; 
 
 • after thefe, there are four Wheels, zo, ^ 
 
 ‘73, a4> and 7y, wrought by endlef} 
 
 ' Screws that are in valuebut one : there- 
 \fore 3, xo, 73, X4, and 75 multiplied to- 
 gether continually, produceth 7884000 V ^ a 1 
 •hours, which divided ? by 24 gives §4, y. 
 3x85-000 days, equal to 900 years. 
 
 Now on the laft wheel 75 is a pinion of 
 ‘ 6,turning agreatWbeel,that carrieth the 
 Apogeum number 1 14 : and 1 14 divided 
 by (5, gives 19 the quotient: and 900 
 times X 9 is 17 loo years. 
 
 Thus I have, with all the perfplcuity I 
 ould, led my Reader through the whole 
 irt of Calculation, fo much of it at leaft, 
 lat I hope-he will bemafter of it all ;not 
 nly of thofe motbns, which I have par- 
 cularly treated about, but of any other 
 ^t mentioned : Such as the Revolution 
 
 of 
 
62 Calculation of^ &c. Ch. II 
 
 of the Dragons Head and Tail, whercbj 
 the Eclipfes of the Sun and Moon are 
 found, the Revolution of the feveral Orbs 
 according to the Ptolemaick Syftem, or o: 
 the celeftial bodies thetnfelVes, according 
 to better Syftems, with many other fuel 
 curious performances, which have made 
 the Sphere of Archimedes of old famous 
 and fince him, that of William of Zeland 
 De Subtil, and another of Janellus Turrianm of Cre- 
 mona, mentioned by Cardan : and of late 
 that elaborate piece of Mr. Watfon, late 
 of Coventry, now ol London, iti her late 
 Majefties Clofet. 
 
 CHAP. III. 
 
 To alter CUck:trork_, or convert om 
 Movement into another. 
 
 T His Chapter I delign for the ufe c 
 fuch, as would convert old Bal 
 lance Clocks into Pendulums, orwoul 
 make any old work ferve for the tryal e 
 new motions, or would apply it to an 
 ether fuch like ufe. ^ i 
 
Ch. III. To alter ClocksVPor^. 
 
 S I. To do this, you may draw a 
 Scheme of your old work: and fo you 
 will lee what Quotients you have, and 
 what you will want. To do all which, 
 there are fufficient iaftruiStions in the pre- 
 ceding Chapter. A few inftances will 
 make all plain. 
 
 § z. Let us chufe for inftance an old 
 Ballance clock to be turned into a Pendu- 
 lum of 6 inches. The old work is, The 
 Gtreat-wheel 56, the Pinion 7; the next- 
 Wheel 54, the Pinion 6 ; the Crown- 
 wheel 19, &c. The Scheme 
 4')48(rz of this work is in the Margin. 
 7_)56(^8 The Quotients and Crown' 
 6)f4(9 wheel and z Pallets multiplied 
 — together continually, produce 
 ip which are the Strokes 
 
 of the Ballance, in one turn 
 of the Great-wheel, by Se< 9 :. I. ^4, y.^if 
 the laft Chapter. And by the Quotient 
 of the Dial-wheel (which is iz) it appears, 
 that the Great-wheel ^eth round once in 
 an hour-Or you may nnd the Beats in an 
 hour, by § j.laft cited. Having thus found 
 the Beats in an hour, of the old work, you 
 mull next find the Beats in an hour, of a 6 
 inches Pendulum ; which you may do by 
 
 Chap 
 
^4 ClockcVDOfk; Ch. Ill- i 
 
 Hmivif. Chap 5.^4. following ; or by Mr. Smith's' 
 T ables, according to whom the number is- 
 936S. Divide this by %736, and you 
 have the C^uotient, which 
 2,756)9368(3? is to be added to the 
 Scheme of the old work. 
 This Quotient is 3 and near I, as you fee 
 in the Margin. j 
 
 The work thus altered, will 
 4)48^ 1 2 (land as you fee in the Mar- 
 gift- "viz. a Pinion 6, and a j 
 6)j4C9 Contrate-wheel 2I, muft be I 
 6(21(31 added. 
 
 - — According to this way, the 
 
 19 old work will (land as before, 
 only the. Crown-wheel njuft 
 be inverted. 
 
 § 3 . But becaufe the Crown-wheel is j 
 too big for the Contrate-wheel (which is ‘ 
 unfeemly) therefore it will be beft, rto ' 
 make both the Contrate, and Crown- J 
 wheels new ; aad encreafe the number of ‘ 
 the Contrate-whe^, butdiminilh that of * 
 the Crown-wheel. To do which, pitch 
 upon fome convenient number for the 
 Crown-wheel. Multiply all the Quoti- | 
 ents, and this new Crown-wheel number', 
 as before 5 and divide 9368 by it. As, ‘ 
 
 produd^ 
 
Chap. III. To alter ClockrVPdrk: 0% 
 
 Suppofe you pitch upon 1 1 for the Crown- 
 wheel ; if you multiply 8, 9 and 1 1, the 
 Produd: is 792, ; which multiplied by 
 the X Pallets, makes 15^84, which are the 
 Beats in one turn of the Great-whCel, ory.Sea.i 
 in an hour. Divide 9568 by it, and you § 
 have near 6 for the Quotient 
 4)4812 of your Contrate-wheel. The 
 7)5 6f 8 work thus ordered, willftand 
 6)74(9 as in the Margin. 
 
 6)j 6((5 If ycti would corred your 
 work, to find the true num- 
 n ber of Beats in an hour, (Sc. 
 you mu ft proceed, as is flieWn 
 Sed. 2. ^ d, and latter end of § 7. of the 
 laft Chapter. - ^ 
 
 § 4. But fuppcfe’you have a mind to 
 change the former old Watch, into 330 
 hour piece, and to retain the old Baliance- 
 wheel ( which may be often done : ) in 
 this cafe, you muft add a Contratc-w'heej, 
 and alter the Pinion of report. For tire 
 Contrate-wheel, chufe fuch a 'Quotient, 
 is will beft. fuit with the reft of vour 
 work 3 and then multiply ail your Quo- 
 tients, Crown-wheel and 2 Pallets toge- 
 ther, and fo find the number ef turns in 
 the Great- wheel, as before. Then fay by 
 K bed. 
 
66 To alter Clockcvorl^. Chap. IIL 
 
 $£( 51 :. a. ^ part f. before, As the Beats /' 
 in one turn of the Great-wheel, To the 
 Beats in an hour : : So are the hours of ' 
 the Dial,v To the quotient of the Pinion < 
 of Report. , '< 
 
 Thus in the old work before; to the f 
 old quotients 8 and 9, you may add ano- 
 ther of 8, for the Contrate-wheel. Thofe H 
 multiplied, as was now diredfed, make !' 
 
 - 2.1888, for the Beats in one turn of the ( 
 Great-wheel. And then for the quotient t 
 of the Pinion of Report, fay in numbers 
 thus, 2:1888. 9 j 68 .:: 12. y. 1 
 6 )^of5' The quotient for the Pinion of | 
 y)y6(_8 Report is fomcwhat more than i 
 6)5' 4'; 9 S', which overplus may be neg- 
 
 6 j48(8 leded, as'you fee by the Scheme t 
 -i- of the whole work in the Mar- 1 
 19 gin. I' 
 
 ^ If you defire to know what f 
 number of turns, the Fufy mufl; have in t 
 this work 3 Say by the laft quoted ' 
 part 1 , in numbers thus , 21888.9568 ' 
 :: 50.1] almofl. So that near ij turns d 
 will do. 
 
 If you would correct: your work, to ‘li 
 fnow the exa<S Beats &c, you are refer- Hi 
 red to diredions in the end of the laft pa- !i 
 
 ragrsph. § y. Hi 
 

 7)56,8 pins 
 ^)5-fC9 
 
 Chap. III. To alter Clockcmrk.^ 
 
 ^ § s- r ftall add but one thine more 
 
 S^hiV M iJ? the Striding part 
 ofthis old Movement, into a jo h^„r 
 
 A Scheme of the old 
 Work is in the Margin. 
 
 And to alter it, the bed 
 way is , to double the 
 number of Striking pins, 
 
 that ^ K " Detent- wheel double, 
 
 ttet the _Pm-wheel may ftrike two ftrokes 
 in Its going round once. ’ 
 
 inconvenience here, will 
 ^cauK ‘he rapidity of the Strokes 5 
 becaufe a quotient of (2 only, added to 
 the old work, will be fulljcieiit for this 
 numb^^'* inconvenient 
 
 Wheels^nH more 
 
 th^ulr , ^ ^r!"f ‘han may be 
 
 ^nought worth the while. ' 
 
 turns number of 
 
 S t. require; you ma‘i 
 
 find how many Strokes are. n h^ars 
 
 by Sed. 5. S 1. R. 6. before. fire"e a- 
 rpyj which divided by thet^tui^ 
 Kz 
 
 
7)j6(i.t6 pins gin. 
 
 6 )54 9 
 
 6)48^8 
 
 CHAP. IV. 
 
 To fixs Wheels and TinicTis^ or; 
 proportion them to each other ^ 
 both Arithmetically and Mechani- 
 cally. 
 
 To Siz$ the Ch. IV.^ 
 
 gives fomewhat more than i% turns of| 
 the Fufy. 
 
 Laftly, for the Pinion of Report, you 
 muft purfue the direeStions in the laft quo- 
 ted place, R. y. 
 
 The work thus altered, | 
 yV4rif will ftand as in the Mar 
 
 i i< 
 
 f( 
 
 I. moving 
 
 of the Wheels and Pinions to- 
 gether, it is neceflary that they Ihould 
 fit each other, by having their teeth and 
 leaves of the fame widenefs, or near of 
 the fame widenefs. For many do make 
 
 ... jjjg 
 
Iliiap IV, Pinions and Wheels. iSp 
 
 :he Leaves of the Pinion narrower than 
 he' Teeth of its Wheel, by reafon of 
 heir running deep in each other ; which 
 s as if the Diameters of the Wheel and 
 ’inion were lefs. But this I leave to thofe, 
 vhofe pratSice and obfervations are great- 
 T than mine in thefe matters. 
 
 ^ 2. 'To make the-Teeth of a Wheel 
 ,nd Pinion alike, the way Arithmetically 
 s thus, Firft you muft find the Gircumfe- 
 ence of your Wheel and Pinion ; which 
 /ou may beft do by the Rule of Three 
 To often made ufe cf before) the Rule is 
 thus, as 7 is to zz :2 fo is the Diameter to 
 :he Circumference. Or more exadJIy 
 thus, as I, is to 3,1416:: So Diam, to 
 iTircum. ^ 
 
 Suppofe you have a Wheel of z inches 
 diameter, and 60 Teeth, and would fit to 
 it a Pinion of 6 Leaves. Firft 7 iz::z.6,^. 
 
 The circumference of the Wheel, is then 
 6 inches, and 3 tenths of an inch. Then 
 fay, as the Teeth of the Wheel, to theoir- „ 
 tumference of it:: So are the Leaves oflijfcom! 
 the Pinion, to the circumference thereof, r, 5. 
 
 In numbers thus 60. 6,3 :: 6 ..63. The 
 Pinion then is 63 hundredth parts of an 
 inch round. 
 
 Now 
 
/o To 5%. See. Chap, IV.i 
 
 Now to find the Diameter, 'tis but the 
 reverfe of the former Rule, viz. As zz. to ; 
 7:: So the Circumference to the Diame- 
 ter. In numbers thus, for the foregoing 
 Pinion, 2Z.7 :: The Diameter then 
 
 of the Pinion muft be two tenths of an 
 inch, to fit the aforefaid Wheel of a inches 
 diameter. 
 
 § 3. But becaufe this way may bedifE - 1 
 cult to perfons unacquainted with Deci- 
 mal Ariihmetick, which isvery neceflary. ! 
 here j therefore l lhall fet down a way to 1 
 do it mechaHkallj/Maving drawn a Circle, , 
 divide it into as many parts, as you in- > 
 tend leaves in the Pinion you would fize. 
 From two of thefe points in the Circle, 
 draw two lines to the Center : to which 
 apply two of the Teeth of your Wheel, , 
 guiding them up and down until they 
 touch at the fame width on thefe Radit ; 
 Mark where this agreement is, and a fmall , 
 circle drawn there, will reprefent the 
 circumference of the Pinion fought af- f 
 ‘ ^ ter. • ■ , 
 
 CH AP.i 
 
chap. V. Of Vendulumu 
 
 71 
 
 I CHAP. V. 
 
 Of Tendulums. 
 
 ^ I. A Mong all knowa Motions ; 
 
 .r\ none meafureth Time fo regu- 
 larly, as that of a Pendulum. But yet 
 Watches governed hereby are not fo per- 
 Fed, but that they arefubjed to the vari- 
 ations of weather, foulnefs, ©c. And the 
 Ihorter, and lefler the Pendulum is, fo 
 much the more fubjecSt fuch Watches are 
 lothefe annoyances. 
 
 There are two ways to obviate thefe in- 
 conveniences in fome meafure. One way 
 s, to make the Pendulum long, the Bob 
 fieavy, and to vibrate but a little way 
 From its fettleinent. Which is now the 
 moft uliial way in En^and. The other is 
 the contrivance of the ingenious Mr. Hu - 
 lens, wtiich is, to make the upper part of 
 ;:herod,^ play between two cheek parts of 
 t Cycloid* Sir Jonas Moor {a.ys, that af- 
 :er fome time, and charge of Experiments, 
 
7 * Of Pen^uiunis, Chap. VJ 
 
 W. ib. he believes this latter to be the betteii 
 
 ^ way. And Mr Hugens calls it admiralk: 
 
 If any defire to know how to mak(’ 
 thofe Cycloidal Cheeks, fit to all Pendu- 
 lums, 1 refer him to the aforefaid Mr. 
 
 Vt Horoh Book, becaufe I cant Ihew how 
 
 o/«7.p.io, to do it, without the trouble of Figures : 
 and this way is much ceafed, fince the 
 Crown-wheel method ( to which it is 
 chiefly proper) is fwallowed up by the 
 Royal Pendulums. _ 
 
 . § X. Another thing tp- be remark’d in 
 Pendulums is, That thelpnger the Vibra- 
 tion is, the flower it is. For if two ifo- 
 chrooe Pendulums do rhove, one the qua-, 
 drant of a circle, the other not above j, 
 ' or 4 degrees, this latter fliall move fome-| 
 what quicker than the former. Which is 
 the true reafoiiv vvhy fmall Grown-wheelj 
 Pendulums go fafter in cold w^eather, or 
 w'hen foul, than at other times. Yea,, in. 
 the beft Iloyal Pendulum,* if you put a, 
 divided plate behind the Ball, and ob- 
 ferye its fwings, you may perceive the^ 
 Vibraticns to be fometimes Ihorter ; and* 
 that then the Watch doth gain too much.i 
 Somewhat aifo may perhaps be attributed; 
 to the rarity or denfity of the air; which* 
 
Chap.V. 
 
 Of Pendulums. 
 
 I have not yet had an opportunity of ob- 
 ferving, by comparing with a good Baro- 
 fcope, the various vibrations of a good 
 Royal Pendulum. But Mr. Boyl fays , 
 that a Pendulum moveth as long, zndzs Machine 
 faft in a thick medium, as a thin one iPnmmat. 
 contrary to the opinion of feme Natura- 
 lifts, whothink the contrary. Hisopini- 
 on is grounded upon the experiment of a 
 Pendulum vibrating in his air-pump, the 
 air fucked out, and in 'the open air; 
 wherein was no a]< . n ' 
 
 
 § ]. F ir the calcuktu a o; 
 
 Ium5, 'ns nee (T > to fix upon (omc one, 
 o be as a Stan;u-tQ to tiie reit. f pitch 
 jpon a Pend, to vibrate Seconds each 
 Iroke. 
 
 Mr. Hugens lays down the length of a 
 ^end. to fwing oeconds to be ^ feet, j 
 tiches, and 2 tenths of an inch (according 
 o Sir 7. Mcors tcdu£tion of it to Eftghjh 
 aeafure. ) 
 
 The Honourable Lord Ermcker (Lith 
 ir jFo»^)“and found the length 
 
 to be jpexy inches, which a little exceeds 
 rfie other: and may be, wasjufteaedby 
 Mr. Hugem'% Rule for the Center of Of- 
 cillation. For Mount gu^s Pendulum, that 
 L “ fhaii 
 
Of Pendulums* Chap.V, 
 
 “ %’ibrate i times in a minute, it will be 
 “ found likewife 8 .i inches, agreeing to 
 “ 39.1 inches Therefore for cert 
 
 “ tain 39<i inches may be called the^ai- 
 “ and relied on, to be the, 
 
 “ near length of a Pend, that fliall fwing 
 Seconds each vibration. 
 
 But forafmuch as the different fize of j 
 the Ball, will make fome difference in the 
 length of this Standard Pend., therefore 
 to make this Pend, an Vniverfal meafurey 
 • to fit all Places and Ages, you muft mea? 
 
 - fure from the Point of Su^penfion, to the 
 Center of Ofcillation. Which Center is{ 
 found by this Rule, As the length of the* 
 ^ugnim String from the point of Sufpcnlion to the 
 center of a round Ball : is to the Semi?. 
 Sir diameter of that Ball : : So is that Semi- 
 diameter, to a fourth number. Add two* 
 fifths of that fourth number, to the for- 
 mer length, and you have the center of: 
 Ofcillation | and thereby the true length 
 of this Standard Tenduhm, I 
 
 If it be defired to fit a Ball of a triangu- j 
 }ar, quadrangular, or any other form to 
 this Pend , the center of Ofcillation in any 
 pfthefe bodies, may be found in the laft ' 
 filed book of Mr Zulkhem 
 
Chap. V- Of TenJuliims. 75 
 
 If it be asked. What is the meaning of 
 the Center of Ofdllation ? iThe moft in- 
 telligible anfwcr(althonot|)erfe<iWy true) 
 is. That it is that point of the Ball, at 
 which if yon imagine it divided into two 
 parts, by a circle, whoffe center is in the 
 point of Sufpenfion,. the lower part of the 
 Ball lhall be of the fame weight (or near 
 lb) with the uppers 
 
 J 4. Having thus fixed a Standard, I 
 lhall next fltew how from thence to find 
 the Vibrations, or Lengths of all other 
 Pendulums. Which is done by this Hulc, „ 
 The fquares of theTihrations, hear the fame 
 proportion to each other ^ at their lengths 
 do. And fo contrary wife. Wherefore^ . 
 find the length of a Pend, fay, As the 
 'Square of the Vibrations given : To the 
 Square of do (the Standard) : : So is the 
 length of the Standard (w2. j9^z)Tothe 
 ' length of the Pend, fought. 
 
 if by the length, you w'ould find the 
 Vibrations, ’tis the revet fe of the lad Rw!#j 
 yiz. As the length propofed : To the 
 "Standard (iJ9,i) : : So is the Square of 6,o 
 (the vibrations of the Standard ) : To thu 
 Vibrations fought. 
 
 Sup- 
 
 L 
 
Of Pendulums. Ch» V. 
 
 Suppofe for example, you Would know 
 what length a Pend, is, that vibrates lyj ' 
 ftrokesin a minute. The Square of ijj 
 (i. e. 153 times 1J3) 15x5409. Say, 
 13409. 3600 :: 39,x. < 5 . A Pend, then 
 that vibrates 153 in a minute, is about 6 
 incites long. 
 
 On the other hand, if you would know 
 how many ftrokes a Pend, of 6 inches 
 hath m a minute; Say, <^, 39,1 -. : 3600. 
 135x0. The fquare root whereof is 153, 
 and fomewhat more. 
 
 l^ete, Becaufe 141110 is always the 
 Produd of the two middle terhia, multi- 
 plied together, therefore you need only 
 to dhdde this number by the Square of the 
 Vibrations, it gives the length fought : 
 by the length, it gives the fquare of the 
 Vibrations. 
 
 If you operate by the Logarithms, you 
 will much cpntra(ff 3mur labour. For if 
 you feek the length,, tis but Subftradirig 
 the Logarithm of the Square of the Vibra- 
 tions, out of the Logarithm of 141110, 
 which is 5.149588, and the Remainder is 
 the Logarithm of the length fought. 
 
 If you fCek the Vibrations, it is but 
 SHbftra(aing put of the aforefaid Loga- 
 % rithra> 
 
 rii 
 
 k 
 
 II 
 
 £21 
 
 I 
 
 I 
 
 ( 
 
 ii 
 
chap. V. Of Fendttlums. 77 
 
 xithm f. 149588, the Logarithm of the 
 length given, and half the Refidue is the 
 Logarithm of the Vibrations required 
 The' following examples will illuftrate 
 each particular. 
 
 I To find the Length. 
 
 1 
 
 Logarithms. 
 
 i4iiao — ; ^ / 5. 149588 
 
 155 Squared is zj 409 4- 36938Z 
 
 iLerigth is more than 6 , o. 780x01? 
 
 To find the Vibrations; 
 
 Logarithms.’ 
 
 1411x0——— 5. 149588 
 
 6 inches long — — o. 778151 
 
 Square of the Vibr. — : — -4. 371437 
 
 Square-rootjornumb.of Vibr. x. 185718 
 is 153, and fome what more. 
 
 According to the foregoing birecliions, 
 
 I have calculated the following Table, to 
 Pendulums of various lengths : and have 
 therein (hewed the Vibrations in a minute, 
 
 and' 
 
yS Of Pendulums. Chafi *' 
 
 and an hour, from i to too inches. 
 any defire a more minute account, I rew: j, 
 him to Mr Smiih’sTahks in his late Boofi ; „ 
 PifquiJ. reafon why his calculation and mine : ^ 
 
 ' differ, is becaufe he meafureth the length ? | 
 of the Pend, from the point of Sufpenfion,i , 
 to the lower part of the Bob i and I only ,] 
 to the center of the Bob. His Standards | 
 are 6 i inches, and 41 inches j and mine : 
 is 3 for the reafons aforegoing. 
 
 A Table of Swings in a Minnie ^ and in an ; 
 
 _ hour, toFendulamsoffeveral lengths. 
 
 Pend. 
 
 length 
 
 1 in 1 
 nches 
 
 VibJrat 
 ' in a 
 Minute. 
 
 Vibrat. 
 
 in an 
 Hour. 
 
 Pend, 
 length 
 ’ in 
 inches 
 
 Vibrat. r 
 in a i 
 Minute. 
 
 vibrat. 
 in an 
 Hour. 
 
 I 
 
 ; 7 rc 7 
 
 22542 
 
 30 
 
 
 4116 
 
 2 
 
 
 iy9;6 
 
 — — 
 
 
 
 
 216,9 
 
 13014 
 
 os 
 
 60.0 
 
 ;6oo 
 
 4 
 
 i 87 c 8 
 
 11268 
 
 
 
 
 s 
 
 168,0 
 
 10080 
 
 40 
 
 S 9 A 
 
 3264 
 
 6 
 
 
 .9204 
 
 *50 
 
 
 3186 ' 
 
 7 
 
 142,0 
 
 85*20 
 
 60 
 
 48 .S‘ 
 
 2910 
 
 8 
 
 1^2,8 
 
 7968 
 
 70 
 
 44<9 
 
 2694 
 
 9 
 
 12^,2 
 
 7^12 
 
 80 
 
 •42.0 
 
 2^20 
 
 la 
 
 118,8 
 
 7128 
 
 90 
 
 
 2376 
 
 20 
 
 84^0 
 
 J 5:040 
 
 100 
 
 Um 
 
 225-0 
 
 
(3iap. V. Of Fendulumsi 7 ^ 
 
 Theufeof this Table is manifeft, and 
 leeds noexplicarion. As to the Decimals 
 n the column of Minute-Swings, I have 
 idded them for the fake of calculating the 
 column of Hour-Swings; which would 
 have been judged falfe without them, and 
 [would not have been exatftly true without 
 them. 
 
 ■ § I have but one thing more to add 
 to this Chap, of Pendulums, and that is, 
 to Correll their Motion. 
 
 The ufual way isj to fcrew up, or let 
 'down the Ball. In doing of which, a 
 fmall alteration will make a confiderable 
 ivariat;ion of Time: as you will find by 
 calculation , according to the lall para- 
 graph* ' To prevent the inconvenience of 
 ifcrewine the Ball too high, or low, Mr 
 
 hSh contriv’d a very pretty Table IbW. 
 fordividingithe Nut of a Pendulum Screw, 
 fo as to alter your Clock but a Second in 
 a day, Butbyreafon no Screw and Nut 
 j can be fo made, as to be moft exadly ftrait 
 I and true, thcrefqre it may happen, that 
 inftead of altering your Watch to your" 
 mind, you may do quite contrary ; as ■ 
 inftead of letting the Ball down, you 
 may raife it higher , by the falfe run- 
 
So Of Pendulums. Chap. V.| 
 
 ning of the Nut upon the Screw. 
 
 Confidering this irremediable inconve- i 
 nience, I am of opinion, that Mr Hu - , 
 genis way would do very well, added to 
 Ibid, k this. His way is. To have a fmallWeight, 
 Prop! 237 Of Bob, to Aide up and down the Pend, 
 rod, atove the Ball (which is immovea- 
 ble. ) But I would rather advife, that the 
 Ball be made to fcrew up and down, to 
 bring the Pend, pretty ncer its gauge : 
 and that this little Boblhould ferve only 
 for more nice corrciSions ; as the altera- 
 tion of a Second, or &c. Which it will 
 do, better than the Great Ball. For a 
 whole turn of this little Bob, will not af- 
 fe< 3 : the motion of the Pend, near fo much 
 as a fmall alteration of the Great Bail. 
 
 The Dirediions Mt Hagens gives, about 
 this little CorretSor, is, That it fhould 
 be equal to the weight of the Wire, or 
 Rod of the Pend., or about a yoth part 
 of the weight of the Great Ball, which 
 he appoints to be three pounds. 
 
 Perhaps this Bob may do its ofl 5 ce, if 
 it be made to fcrew only up and down 
 the lower part of the Rod, below the Ball. 
 If not, you mull: mate it Aide above the 
 Ball, or be fcrewed up and down there. 
 
 See- 
 
jChap.V* Of Pendulums. 8i 
 
 Seeing this little Bob is not the only 
 Corre<^or ( as in Mr Zulichems way ) 
 therefore it is notneceflary to infert here^ 
 that ingenious perfon’s Table, lliewing 
 [ what alterations of Time will be made by 
 t Aiding the Bob up and down the rod, 
 
 I Only thus much may be obferved in that 
 Table of his, viz. That a fmall alteration 
 of the Corredior towards the'lower end 
 of the Pend., doth make as great an alte- 
 ration of Time, as a greater railing or fal- 
 tling of it, doth make higher. Thus the 
 little Bob raifed 7 divifionsof the Rod, 
 Ifrom the Center of Ofcillation, will alter 
 |the Watch ij feconds j raifed ’twill 
 liter it 30"; But whereas, if it be raifed 
 to If 4,3 parts of the Rod, it will make 
 fte Watch gofafter 3 minutes, 15 feconds, 
 l:he Watch lhall be but 3'. 30" fafter, if 
 rhe Bob be raifed to 192(6. So that here 
 
 I rOu have but 15" variation, by railing the 
 Job above 38 parts j whereas lower, you 
 lad the fame variation, when railed not 
 tbove 7 or 8 parts. 
 
 From what hath been faid, it appears, 
 hhat about half a turn of this little juflen- 
 ng Bob, will at no time alter the Watch, 
 tbove a fecond in 24 hours ; and that 
 M above 
 
8 9 The Antiquity Chap.VLl 
 
 above a whole turn, will not alter it fo 
 much, higher on the Rod ; fuppofing that 
 the Bob at every turn afcended or defcend- 
 ed a whole degree of the Rod; whichper- 
 haps it will not do in xo turns: and con- 
 fequently, it will require many turns, to 
 alter the Watch but one lecond. 
 
 C H A E VI. 
 
 The Antiquity, and general Hiftor) 
 of Watch, or Clockc^POrka 
 
 J r.TT is probable, that in all Ages 
 Jl^ fome Inftruments or other havi 
 beenufed, for the Meafuring of Time 
 But the earlieft we read of, is the Did o 
 • Jhaz, Concerning which, little of cer 
 . tainty can be faid. The ffehrew won 
 JHaValoth doth properly fignifie Degree 
 t,%.38.8.Steps, or Stairs, by which we afeend t 
 anyplace. And fo this word MaVdot 
 is rendered Ez.ek. 40, And according 
 ly the LXXII tranflate the Ma^doth c 
 Ahaz, by the words 
 
 ■ ’ ■ - t.i 
 
chap. VL of Clock^trkr 
 
 i. e. Steps or Afcents, The like doth the 
 Syriack, Arahick, and other Verfions. 
 
 Some pretend to give a defcription of 
 :his Dial of Ahaz : but it being meer 
 jueffing, and little to ray purpofe, I fball 
 aot trouble the Reader with the various 
 opinions about it. 
 
 Among the Greeks and Romans, there 
 .vcre two ways chiefly ufe’d to meafure 
 heir Hours. One was by Clspfydra^ oj- 
 Hour glafTes. The other by the Solaria, 
 
 3r Sun-dials. The kas4'"J's«, fays Suidas . 
 ind PhaVOrintlS, WZS’'OfytiVi>r atg^royDciy h ^ ink. !« 
 hSiat niT!«i>]ir. i. e.An Aflronomical Inflru-''‘''^t , 
 ment, h which the Bows were meafwedd'^'''^^^^^ 
 Alfo, That it was a F'effel, having a little 
 hole in the hot tom, which was fet in the 
 Zowts ofjudicatwe, full of water-, hy which 
 'he Lawyers pleaded. This was, fays ?ha- 
 'jorintu, to prevent babbling, that fitch as 
 pake, ought to brief iri their Speeches. 
 
 As to the Invention of thofe Water- 
 vatches (which were, no doubt, of more 
 .'omraon ufe, than only in the Law-Of*fWi- 
 'ourts)the Invention, I fay, of them, 
 
 Rtributed, .by, CenforinuSf ' to P. Cornelius 
 ^afica, ths -Cenfot (Scipio' Plafca, Pliky 
 ;alls him.) ■' 
 
 M 2, The ■ 
 
84 The Antiquity Ch*VI 
 
 The other way of tneafuring the Hours 
 Ibid. Sun-dials , feems, from Pliny ant 
 
 Cenforinus, to have been an earlier inven 
 Na. Hiff. T//»y fays, that Anaxl 
 
 ].s. ct je.tnenes Milefius, the Scholar of Anaximan 
 der> invented Dialling, and was the firll 
 that (hewed a Sun*dial at Lacedamon. Pi 
 De Arehit-truvius Calls him Milefm Anaximandet 
 1. f. c. 48. Yhis Anaximander or Anaximenes was^co' 
 temporary with Pythagoras, fays Laerti- 
 us and flourilhed about the time of the 
 Prophet Daniel, 
 
 But enough of thefe ancient Time- 
 engines, which are not very much to my 
 purpofe , being not pieces of Watch- 
 Work. 
 
 I (hall in the next place take notice 
 of a few Horological Machines , that 1 
 have met with j which, whether pieces 
 of Clock-work, or not, I leave to the 
 Readers judgment. 
 
 intheLife Dionyfius, which 
 
 of vhm Plutarch commends for a very magnifi- 
 cent , and iliuftrious Piece. But this 
 might be only a well delineated Sun-dial. , 
 
 Another Piece, is that of King ol 
 Perfia. Whether that Sapor, who W'as 
 Kufeb. I’it. cotemporary with Cenftantine the Great, 1 , 
 cw.#.]. 3 . know: 
 
chap. VI, of Clockzvpork. 85 
 
 know not. Cardan faith it was made 
 Glafs } that the King could fit in the mid**' 
 dJc of it, and fee its Stars rife and fet. 
 
 But not finding whether this Sphere was ‘ 
 moved by Clock-work , or whether it 
 had any regular motion, I lhall fay no 
 more concerning it. 
 
 The laft Machine I lhall mention in 
 this Paragraph, is one I find defcribed by 
 Fitruvius^ Which to me feems to be 
 piece of Watch-work, moved by an equal . ’ " 
 influx of Water. 
 
 If the Reader will confult ths French 
 Edition of Fitruvius, he will find there 3 
 fair Cut of it. 
 
 Among divers feats which this Ma- 
 chine performed (as founding Trumpets, 
 throwing Stones, &c . } one ufe of it was, 
 to Ihew the Hours (which were unequal 
 in that age) through every month of the 
 year. The words of Fitruvius are, Mq^ua- 
 liter influens aqua fuhlevatScaphum inverfum 
 (jqued ah artificihus Phellos jive Tympanum 
 dicitur') in quo coUecata regula, verfatilia 
 tympana denticulis tequalihus funt perfe£la. 
 
 Qjti denticuU alius alium impellentts, ver- 
 fationes modicas faciunt^ ac motiones. Item 
 alia Regulgy aliaque Tympana ad eundem 
 
 modum 
 
85^ the Antiquity Chap. VI. 
 
 modum dentata^ q^uce una motione coafla , 
 'verfando faciunt varzetatefque mo^ 
 
 tionum : in qutlus movent ur Sigilla, ver^ 
 tuntur Met^y calculi aut T^ona projiciuntur^ 
 Buccince canunt^ &c. In his etiam, aut in 
 columnar ant paraflatiqa Horce dejcrilun* 
 tur 3 quas Sigillum egrediens ah imo virgu- 
 Ice^ fgnificat^ in ^ietn totum : quarum hre^ j 
 vitates ant crefcentias , cmeorum adjelius ' 
 aut exemptus^ in Jingulis diehus^ menfihus^ \ 
 perficere cogtt. 
 
 The Inventer of this famous Machine, 
 Vitruvius fays, was one Ctefihius^ a Bar- 
 bers Son of Alexandria. Which Ctefihius 
 flouriflied under Ptolemy Euergetes, fays 
 Via.pi^/- Athenzeus, I.4. And if fo, he lived about 
 knd.mt.in%^o years before our Saviours days ; and 
 Vtmv. jnight be\COtemporary with Archimedes. 
 
 § 5 , Thus having given a fmall account 
 of the ancient ways of Meafuring Time, 
 it is time to come clofer to our bufinefs, 
 and fay fomething more particularly of 
 Clock-work. 
 
 Which is thought to be a much young- 
 er invention, than the fore-mentioned 
 Pieces : and to have had its beginning in 
 Germany^ within lefs than thefexoo years. 
 
 It is very probable, that our Ballancc 
 
 Clocks, 
 
chap. VI. of Chck^work: 87 
 
 Clocks, and fome other Automata, might 
 have their beginning there ; or that Clock- 
 work ( which had long been buried in 
 oblivion) might be revived there. But 
 that Clock work was the Invention of 
 that age purely, I utterly deny ; having 
 (befides what goes before) two inftances 
 to the contrary, of much earlier date, 
 
 § 4. The firft example is the Sphere of 
 Archimedes ; who lived about %qo years 
 before our Saviours days. There is no 
 mention of this Sphere in Archimedes his 
 extant works: but we have an account 
 of it in others. Cicero fpeaks of it more 
 than once. In his xd Book De Nature 
 Deorumy are thefe words ; “ Archimedem 
 “ ar hit rant ur plus valuijje in imitandisSpha:- ^ 
 rre converfionihuSy quam Maturam in effi<» 
 ciendis^ 6cc. And in his tufculane Que- 
 ftions, the Collocutor, proving the Soul 
 to be of a Divine Nature, argues from this 
 -Contrivance of Archimedes y and fays, 
 Nam cum Archimedes Lun^e^ Solis , quinque 
 Errantium mot us in Spbatram illigavity ef- 
 fecit y The Senfe is, That Archimedes 
 
 contrived a Sphere, which Ihewed , the 
 motion of the Moon, Sun, and five Pla- 
 nets, - 
 
 But 
 
S3 
 
 Bptgr*in 
 Spbxr* Ar- 
 chimed^ 
 Vid. card, 
 de Subtil. 
 !• 17 *^.. 
 
 The Antiquity Chap. VI. 
 But the moft accurate defcription is 
 that oiClaudian^ in thefe words. 
 
 fupiter in parvo cum cement athera vitro^ 
 Kifit^ & ad Superos talia diila dedit : 
 Huccine mortalis progreffa potentia cur a ? 
 
 Jam meus in fragili luditur orle labor. 
 Jura polij rerumque fidem^ Deorum^ 
 
 Ecce Syracufius tranjlulit arte Senex. 
 Jnclufus variis famulatur Spirit us aflris^ 
 
 Et vivum certis motibus urget opus. 
 Tercurrit proprium mentitus Signifer annum. 
 
 Et fimulata novo Cynthia menfe redit. 
 famque fuum volvens audax induflria mundum 
 Gaudet^ & humana Sidera mente regit. 
 Quid falfo infintem tonitru Salmonea miror i 
 Mmula ffatura parva reperta manus. 
 
 In Englijh thus : 
 
 When ]ovt efpyd in Glafs his Heavens made^ 
 He fmil*d^ and to the other Gods thus [aid : 
 Strange feats ! when human art fo far proceeds^ 
 To ape in brittle Orbs my greateji deeds. 
 
 The heavily motions^ Natures conflant courfe^ 
 Lo ! here dd Archimede to art transfers. 
 TU inclofed Spirit here each Star doth drive 5 
 And to the living work fure motions give. 
 
 The 
 
Chap. VI. of Cloc^-work: 8p 
 
 The Sun in counterfeit his year doth run^ 
 
 And Cynthia too her monthly circle turn. 
 
 S ince now hold man hasWcrlds of s own defer yd 
 He joys ^ and td Stars ly human art can guide. 
 
 Why fhould we fo admire proudSd\mous cheat s 
 When one poor handjTatures chief work repeats. 
 
 From this defeription itappeareth, that 
 in this Sphere, the Sim, Moon, and other 
 heavenly bodies, had their proper motion : 
 and that this motion was etle(9:ed by 
 fome enclofed Spirit, What this encUfed 
 Spirit was, I cannot tell, . but fuppofe it 
 to be Springs, Wheels or Pullies, or fome 
 fuch means of Clock-work : Which be- 
 ing hidden from vulgar eyes, might be 
 taken for fome Angel, Spirit, or Divine 
 [power ; unlefs by Spirit here, you un- 
 lerftand fome aerious, fubtiliz’d liquor, 
 
 )r vapours. But how this, or indeed any 
 hing, but Clock-work, could give fuch 
 rue, and regular motions, I am not able 
 0 guefs. 
 
 ^ y. The next inftance I have met with 
 f ancient Clock-work, is that famous 
 ne in Cicero^ which, among other irre- 
 'agable arguments, is brought in Lib. 
 
 rove, ‘‘That there is fome intelligent,^* 
 
 N dv' 
 
1 
 
 7he Antiquity Chap. VI. | 
 
 “ divine, and wife Being, that inhabiteth, j 
 “ ruleth in, and is as an Architect of fo i 
 “ great a work, as the World is, as the 
 Collocutor exprefleth himfelf. His words 
 (fo far as they relate to my prefent pur- 
 pofe) are thefe : “ Cum Solarium vel de^ 
 fcriptum, aut ex dilua contemplere, inteU \ 
 “ ligere declarari horas arte, non cafu, &c. 
 And a little after, Qmdfi in Scythiam, aut \ 
 in Britanniam, Sphreram aliquis tulerit hanc, | 
 qatm nuper familiarh m(ler effecit Fofidoni- j 
 us, cujus jingulee Converjiones idem efficiunt j 
 in Sole, in Luna, & in quinque Stellis \ 
 ertantihus, quod effieitur in ccelo Jingulis die^ \ 
 lus, & noBilus 5 quit in ilia harharie du- { 
 litet, quin ea Sphtsra fit perfelta ratione ? 
 The llim of the Authors meaning is , « 
 “ That there were Sun-dials defcribed, or j 
 “ drawn [ with Lines, after the manner | 
 ns our Sun-dials are : 3 “ and Ibme made i 
 “ with Water ( which were the Clepfy-' 
 drre, or Hour-glailes, before-mentionei ) 
 
 “ That Pofidonius had lately contrived a 
 ■ ‘ Sphere, whofe Motions were the fame 
 “ in the Sun, Moon, and y Planets, as 
 “were performed in the heavens each 
 t day ^nd ni^ht. 
 
Chap. VI- of Clockwork. 91 
 
 The age wherein this Sphere was in- 
 vented, was Ciceros time, which was a- 
 l>out 80 years before our Saviours birth. 
 
 And that It was a piece of Clock-work, 
 is nor (I think) to be doubted, if ic be 
 confidered, that it kept time with thofe 
 celeftial bodies, imitating both their an° 
 nual, and diurnal motions, as from the 
 defcriprion we may garher it did/ 
 
 It may be queftibiied, whether thofe 
 Machines were common or not : I believe ' 
 they were rarities then, as well as Mr 
 f§ns and others are accounted now. But 
 . merhinks it is hard to imagine, that fo ’ 
 ufefal an Invention lliould not be reduced 
 into common ufe * it being natural, and 
 oafie to apply it to the meafuring of 
 hours (tho unequal ) ef^ecially in two 
 fuch Ages^ as thofe of Archimedes and 
 Tulh were, in which the Liberal Arts fb 
 greatly flourifliedo ; . 
 
 § 6. After the times kft mentioned, I 
 find little worth remark/ till the laft Age 5 
 in which Clock-work was revived, qv 
 wholly invented anew in Germa^^y^ as is 
 generally thought, becaufe the ancient 
 Pieces are German work. But who 
 : the In venter, or in what time, I cannot 
 N % Jilco- 
 
p2 
 
 MdyTfienux, 
 Scioth. Te- 
 kfcop. Ep, 
 Vedic. 
 
 C(>fmog.l2> 
 
 The Antiquity CbVL 
 
 difcover. Some think Severn Boethius in- 
 vented it about the year j I o. Perhaps 
 it was in Regiomontanus his time ( if not 
 fo early as Boethius') which was above zoo 
 years ago. ^ It is very manifeft, it was be- 
 fore CW<?»’s time, becaufehe fpeaketh of 
 it, as a thing common then. And he 
 lived about i yo years fince. 
 
 ^7. As to thofe curious contrivances 
 in Clock-work, which perform ftrange, 
 furprizlng feats, I fhall fay little. Dt.Hey- 
 Jin tells US of a famous Clock and Dial in 
 the Cathedral .Church of Lmden in De«- 
 rnark, In the Dial (faith he) are to be 
 ‘‘ feen diftindiy the Year, Month, Week- 
 ‘‘day, and Hour of every day throughout 
 the Year 5 with the Feafts, both move- 
 “ able and fixed ; together with the Moti- 
 ‘‘ on of the Sun and Moon, and their paf- 
 fagr thro each degree of the Zodiack. 
 Then for the Clock, it is fo framed by 
 artificial Engines, : that whenfoever it is 
 ** to flrike, two Horfe-men encounter one 
 ‘‘ another, giving *as many blows apiece, 
 as the Bell founds hours : And on the 
 opening o f a door, there appeareth a 
 Theatrd, the Virgin Mary on a Throne, 
 ^'■with Chrift in her arms, and the three 
 
 Kings 
 
chap. VII, of Clockzveork. '^4 
 
 ‘‘ Kings or Magi (with their feveral trains'^ " 
 marching in order, doing humble reve^ 
 rence, and prefenting feveraljy their 
 Gifts ; two Trumpeters founding all 
 the wble, to adorn the Pomp of that 
 Prcceffion. , 
 
 To this I might add many more fuch 
 curious performances 5 but I rather 
 to refer the Reader to Schottus^ where 
 may find a great variety, to pleafe him. 
 
 ;c 
 
 u 
 
 CHAP. VIL 
 
 ' Of the Invention of Vendulwn 
 Watches. 
 
 i.'T^He firft that invented the way 
 of applying Pendulums to 
 Vatch-work, was Ux Chrijliaa Huiens o<i 
 lulichem-, as he afiirmeth of himfelF 
 /ith very cogent realons. ’ 
 
 This excellent invention, he fays, he 
 
 y'" “i;?- and oa. 
 a the following year ig^S, he printed P;? Edit- 
 delineation and defcription of it. 
 
 Others 
 
Invention of Chap. VII: 
 
 Others have claimed the honour of this 
 Invention; among which, the great Gali- 
 leo hath the moft to be faid on his fide. 
 Dr. John Joachim Becher (who printed a 
 Book when he was in England, entituled 
 De Idova Temporis dimetienM ratione Theo- 
 rta, ©r. which he dedicated to the EngUfi. 
 Royal Society, Anno 1680.) he, Ifay, tell; 
 us, ‘ That the Counf Magalotti (the Great 
 ‘ Duke of tufcanys ReGdent at the Empe- 
 ‘ rors Court) told turn the whole HiGorj 
 ‘of thefe Pendulum Clocks, and deniec 
 ‘ Mr 'Zulichem to be the A.uthor of them 
 Alfo, ‘That one (Clock-maker t( 
 
 * the Father of the theiiG-Dukeof tufcanj j 
 ‘ related to him the like Hiftory : and fail ] 
 ‘ moreover, That he had made the Grf j 
 
 * Pend. Clock, at Florence, by the com 
 
 * mand of the Great Duke, and by the di 
 
 * redtion of his Mathematician Galilaus , 
 
 ‘ Galtlmo ; a pattern of which was brough 
 
 * into Holland, And further he faith 
 ‘ That one Cafpar Dorns, a Fleming, an 
 ‘ Mathematician to John Philip 4 Schm 
 ‘ born, the late Elector of Mentz) told hin 
 ‘ that he had leen at Prague, in the tin 
 ‘ of Rudolphus the Emperor, aPend-Cloci 
 ‘made by the hxami JtJtus Bergen, M 
 
 ‘chani' 
 
Ghap. VII. Tendulum Watches. 
 
 chanick and Clock- maker to the Empe- 
 ' tor: which Clock the great Tycho-Brahe 
 ' ufed in his Aftronomical obfervations. 
 
 Thus far Becher. To which 1 maj add, 
 what is faidby the Academie del 
 viz. ‘ It was thought good to apply thej^e Arad. 
 
 ‘ Pendulum to the Movement of the Clocked eimm 
 ■ a thing which Galilceo invented, and 
 * his Son yincemio Galilei put in pra^icep._i2. ’ 
 ‘in the year 1649. 
 
 As to thefe matters thus related byhear- 
 fay by Becher, and fo exprefsly affirmed 
 by the Academy, I have little to reply, 
 but that Mr Hugens does exprefsly fay. He 
 was the Inventer, and that if Galileso everH«^« ibj 
 thought of any fuch thing , he never 
 brought it 'to any perfedion. k is cer- 
 tain, that this Invention never flouriihed 
 till Mr Hugens fet it abroad, 
 
 ^ 2. After Mr Hugens had thus invent- 
 ed thefe Pendulum Watches, and caufed 
 fevcraltobemade in Holland, Mr Froman‘ 
 til, a Dutch Clock-maker, came over into 
 England, and made the firft that ever were 
 made here : which was about the year 
 J66i. One of the firft Pieces that WaS 
 made in England, is now in GreJham-CoU 
 Udg, given to that Honorable Society by 
 
Invention of Ch3Lp. Yll. J' 
 the late eminent Seth, Lord Bifliop of Salifi \ '' 
 lury : which is made exa(Stly according to ' 
 Mr Zulkhem's directions. r 
 
 § For feveral years this way of Mr 1 
 ^ulkhem was the only method , 'viz. ‘ 
 Crown-wheel Pendulunis, to play between ' 
 two cycloidal cheeks, &c. But afterward* ' ^ 
 Mr W. Clement, a London Clock-maker, 
 contrived them (as Mr Smith faith) to go 
 with left weight, an heavier Ball (if you 
 p. 3. ’ pleafe) ancT to vibrate but a fmall compafs. 
 Which is now the univerfal method of the \ 
 Royal Pendulums. But Dr Hook denies 
 Mr Clement to have invented this; and 
 fays that it was his Invention, and that he i 
 caufed a piece of this nature to be made, i 
 which he,fhewed before the R. Society, 
 foon after the Fire of London, 
 
 § 4 . The Ufe of thefe Pendulum 
 Watches Mr. Hagens fetteth forth in feve- 
 ral inflances. Particularly, he giveth two 
 examples of their great ufe at Sea, in dif- 
 covering the. Difference of Meridians , 
 more exadly than any other way : which 
 he deduceth from the Obfcrvations of an 
 Englijh, and French S]\v^. 
 
 On Land, they were found very fer- 
 viceable, among other ufes, particularly 
 
 to 
 
Chai^. V=If. pf 
 
 »o thefe two. r* To mdafure the time 
 mote exadly, and equally thari the Sun. 
 
 TO'be ^as Sir Chrifidp^b* Wren firft pro* 
 i pofed) a perpetual, and liniVerfal Meafure, 
 
 I or Standard, to which all Lerigths may be 
 reduced j and by which they may be 
 judged, in all ages, arid countries, for 
 (as our Royal Society, Mr Huygens, and 
 f have projjofed after Sir Chrlfi'a. 
 
 \pher Wren) this fforary foot, or Tripedal 
 I Length, which vibrateth Seconds, Will fit' 
 i all ages and places. Biif theft relpe<S(: muft 
 i be had to the Cehtet of Ofcillation, which 
 I you have an account of in Mr Huy^pns his 
 I aforefaid book, de Horologio Ofiillatorio, 
 
 \ as hath before been faid. * 
 
 ; ^ y. There is oneJeontrivanCe more of 
 
 \ Pendulums, ftilJ behind, vk. the Circular 
 Pendulum : which is rnenriofled by Mr 
 Hugest as his own, but js claimed by the 
 i ingenious Dr.- Jdook is teklly his. This 
 
 Pend, doth nor vibrate backward and for- 
 ward, as thole we have been fpealvine of 
 do ; but always round, round j the String; 
 
 being fufpended above,, at the triped^ 
 
 : length, and the Ball fixed below, as'fupl 
 pofe at rheentl of the fly. of a Gom.moh 
 Jack. 
 
 the 
 
 O 
 
pS Invention of the \ Ch* 
 
 Theraption of this Circular Pend. i$ as* 
 regular, and much^. the fame with what > 
 goeth before : and was thus far made, very 
 ufeful in Anronpmical .obfervations.,'by' 
 the faid Dr UoQk, ‘fiz.-To give warning at 
 any rnoment of itscir/cumgyratiop, eitherf 
 when it had turned but a quarter, halfypri 
 any leder, or greater part of its circle. 
 Sqthat hpre you ha'd mptice not only of 
 a Second, but of the ntoft mipute part of 
 
 ^ Sj^cond^pf Timpi .iVdh 
 
 fqnptijpil pfjthiSjPe^d^«»«, aod other mat- 
 ters iyiongipg.tP:jt^; ifl- Dx Hook' i teHi- 
 'on& Cutt'^r^ana- in HevelmMoch, 
 
 
 Vf ^tje,f^nven0ov of thofe Poc^t- 
 . WdtMiesimnmmlt ca lied PeTidxi- 
 , hrh-Waiches. ‘ 
 
 § ^t. ’ teafpn they are called Pen- 
 
 'fji;. ii' plulum-Watches ^ is.feom. the 
 
 fogulaVity' of their Strokes, and Motion, 
 
 Which 
 
jCKip. Vfll- Piicf^t^Wdtcheii 
 
 •Which exad;nefe is eft^i^ed bt the govern- 
 nwrit'bf a final! Sf^ral Spring, running 
 rotiaJ <he uppet’parp oifthe Verge of the 
 Baflancci' which* Sp^irfg is called' the Regu- 
 ■Idthry > ■ . • ■ ' • ; ■■■ • 
 
 ^ The firft Inventer hereof, Was 
 that ingenious and learned member of our 
 Rifdi-SmetyjYi^ Hook :’' who contrived va- 
 ' riOus ways of Regtflatidn. One way was 
 Mwirh 'ti Load-ftonO f another was with a 
 tefldft' ’ftfait Sprihgi one end Whereof 
 played backward, and forward, with the 
 b'aflSnce s So that the ballance Was to this 
 as the bob of a Pendulutn ^ and the 
 little Spring, as the Rod thereof. And fe- 
 Veral other contrivances he had befides of 
 thisriatwte< - ■ 
 
 j; ■ But the Invention which btft art- 
 fweredesi'pe^ation, was at firft, with two 
 bailances : of which T have feen two forts, 
 ■althO' there were ffeVeral Others. One 
 "Way Was without Spiral Springs , the 
 other with. They both agreed in this. 
 That the outward Rims of both thi lial- 
 lances, hadalfe number of Teeth ; which 
 running in each other, caufed each Bal- 
 lance to vibrate alike. 
 
 0 % 
 
 Out 
 
.f<so hventim of the Gbajp. VIU. 
 
 But as to the former of thde, which had 
 no Spiral Spring 5 the Verges of its Bal- 
 lances, had each but one Pallet apiece, 
 about the middle of the Verge, . The 
 Crown-wheel lay (contrary to others) re- 
 verfed, in the middle of the Watc^ in 
 the place, and after the manner of th& ' 
 Contrate-w heel. The teeth of this Crown- 
 wheel, were cut after the manner of Con- 
 trate-wheel teeth, viz, lying upwards, 
 but very wide apart, fo as that the Pal- 
 lets (which were about one tenth of an 
 inch long, and narrow) might’play in and | 
 out between each tooth. The Verges of 
 the two Ballances, were fet one on one 
 fide, the other on the other fide of the 
 Crown-wheel, fo that the Pallets might 
 play freely in its teeth. And when the , 
 Crown-wheel in moving round, had de- 
 livered its felf of one Pallet, the other 
 Pallet on the oppofite fide, was drawn 
 on to make its Beat, by means of the mo- 
 tion which the other ^llance had given 
 its Ballance, (the two Ballances moving 
 one another, as hath been faid in the be- 
 ginning of this Paragraph^ And fo the 
 fame back again. 
 
 It 
 
E hap. VIII* VdckgtMiUchesi acoj 
 
 It may be here noted) that for the 'iSBore 
 ear underftanding- of the laft cdntri* 
 
 1 vance, I have defcribed the two Ballancds, 
 i as having Teeth on the edges of their 
 RimS) running in one another. But the > 
 contrivance was really thus. There was a 
 /mall Wheel under each Ballance, propor- 
 1 tioned to the width of the Grown-wheel. 
 
 I But the Ballances were much larger. Arid 
 I fo the Teeth of thefe two little fore- 
 1 faid Wheels or Ballances, •junning ini-otje 
 another, moved thedargerBallanceS above 
 them, all one, as if thefe two gijeati Bat' 
 lances had been toothed andplayed imt^^ 
 other* - ■ ■ u \i. 
 
 § 4. The other way, with tWo Bah 
 lances alfo, moving ea^ other '(as 'was 
 I faid in the b^inniog of the lafl had a 
 ! Spiral Spring to each Ballance, for its Re- 
 ' gulator. In this Invention, only one Bat- 
 : lance had the Pallets , as the common 
 Ballances have: and the Crown-wheel 
 . operated upon it, according to the ufual 
 way. But then when this Ballance vi- 
 brateth, it giveth the fame motion back- 
 ward and forward, to the other ballance ; 
 gs hath been ftid. 
 
 The 
 
tBe GlMp. VIIl. 
 
 The firft of the|fe two waysp wiB;twver ! 
 profecuted fo i far, as perha^it>defefvdd. 
 ^And the excelleftcyiof the fattet is,-that ! 
 ho'jirk, or the moft confiifed fhake, cah : 
 in the leaft alter itsrVibrations. ■ ' -WhtGh-ft ' 
 will do in the teft' Pendalutn Watefo with 
 -one ballance noWi i comniorU^j ufffd. * i For i 
 if you lay one -df ,thefe: Wajlehei tip&n a 
 Table, and by the PendatJiu jlrg it 'back- 
 ward and forward^ you wUlpuf it into the 
 greateft hurry ■; whereas the laft moti- 
 oned Watch, with’ two ballances, will be 
 nothing afiedled with it. ''Butiinofwith- 
 ftanding this'ficcmVeniencej yet the Watch 
 with one ballance and one Spring (which 
 was alfo Dr. Inventiorf) prevailed, 
 and grew common, being? now the uni- 
 verfal Mode : but of the other very few 
 were ever made. The reafjSfl herOf, I 
 judge, was the great trouble add vaft nice- 
 nefs required in it, and perhaps a little 
 foulnefs in the-ballance-teeth may retard 
 the motion of the ballances. But the o- 
 ther is eafier made, and perfornKth well 
 enough, and in' a pocket is fcarce fubjetfl 
 to the aforefaid diforder, which iS caufcd 
 rather by a tprn, than a ibake. 
 
Poc^t-Watches} lirf 
 
 g: 5. The time of thefe Inventirtns 
 ibout-the year i6y8j.as appears (amohj^ 
 jther evidence) from this infcription^ tifidtf 
 )fleof the aforciaid douhteifiaUanee-\^«h- 
 ;s, prefentedito K. Chide ill, vkJ lUih'd 
 j^okittven. t6^2, Tomphit fecif $/ 
 
 i This Watch was wonderfully approved 
 lof by the. Ring ; and lb the =Inventiti|if 
 grew into reputation, , and m«cb tSiK^ 
 
 bd of at homCy and abroad.?' nPartibafe}^ 
 its faote flew ictto Fnwce,, 'Tronr Whetice 
 the: Dauphine feat for two 5 whioft 
 eminent Artift Mr. ’iTotnpm made 'fo^ 
 hkn. :'n ^ ‘“j'' ■ ; 
 
 § 6. Dr. Hook had long before this y 
 canfed feveral pieces of this nature, to be 
 made, ahho they did not take till after 
 idyy. - Hovilever. he had before fo far 
 proceeded; herein, as i to have a Patent 
 (drawn, tho not Icaled) for thefe, and fc>tn& 
 other-Gontfivances,: ^out Watches, irt 
 the year 1^60, But thfe reafon why that 
 Patent didm® further proceed, was Ibme 
 dda^edhientrabout fome Articles- in' it^ 
 t^dth.' fdme ;Nobl& -Perfons who Were 
 fioncejrned .fbrthe proctiring it. The lime 
 sng«iiottsdE)r;baAailbri Orant for a-Pa^ 
 
 •*«p.p fotitH^fi Way of Fa ring 'Watches 
 ■i: ■■ is 
 
[i o4 Jn&^ion of ih& Cbtp. VIlX 
 
 in the year 167-5' : but he omitted the 
 taking it out, as thinking it not worth 
 the while. i ■ ' 
 
 5 7* After thefe'IawentionsofDr. 
 and (no doubt) after the Publication of 
 4 Mr. s book de Horokgt Ofcil. at 
 
 Paris 1673 ( for there is not a word of 
 this, tho of feveral other Contrivances) 
 after this, I fay, Mr. Z 7 age»’s Watch with 
 a Spiral spring came abroad, and made a 
 great noife in England^ as if the Longitude 
 could be now found. One of thefe the 
 Lord fent for out of France^ 
 
 (where Mr Hugens had a Patent for them) 
 which I have feen. 
 
 L This Watch of Mr. Zulkhenis agreed 
 with Dr. Hook'sy in the application of the 
 Spring to the ballance •• only Mr. 2 a//* 
 chems had a longer Spiral Spring, and the 
 Pulfes and Beats were much flower. That 
 wherein it differs, is i. The Verge hatha 
 Pinion inftead of Pallets ; and a Gontrate- 
 wheel runs therein, and drives it round, 
 more than one turn. a. The Pallets are 
 on the Arbor of this Gontrate-wheel. gf. 
 Then followeth the Crown wheel, ^c. 
 4. The ballance, inftead of turning fcarce 
 quite round (as Dt.HooPs) doth turn feve* 
 ral rounds every vibration. § S. 
 
€#hap. Vlli. Pocket-Watches^ i 
 
 § 8. As to the great abilities of Mr 
 no man can doubt, that is 3^^ 
 quaiiited with his Books, and his /hare in 
 thePhilofophical Tranfadlions, &c. But 
 I have fomer6afon to doul)t, whether his 
 Fancy was not firft fet on work, byfome 
 Intelligence he might have of Dr I/oofs 
 Invention, from Mr Oldenhur^^^ or others 
 his correfpondents here in England. 
 
 But whether or no that ingenious per- 
 fon doth owe any thing herein to our in- 
 genious Dr Hdok^ it is however a very 
 pretty, and ingenious contrivance ; but 
 fubjecft to fome defetSs : viz^ When it 
 ftandeth dill, it will not vibrate, until it 
 is fet on vibrating : which, tlio it be no 
 defeS: in a Pendulum Clock, may be one 
 in a Pocket-Watch, which is expoled to 
 continual jogs. Alfo, it doth fomewhat 
 vary in its Vibrations, making fometimes 
 longer, fometimes Ihotter turns, and fo 
 fome flower fome quicker vibrationso 
 
 I have feen fome other contrivances of 
 this fort, which I mention not, bccaufe 
 they are of younger (landing. But thefe 
 twm (of Dr Hook and Mr Hugeni) I have 
 taken notice of, becaufe they were the 
 firft that ever appeared in the world, 
 
 ' P CHAPo 
 
10 ^ 
 
 Invention of Ch. 
 
 CHAP. IX. 
 
 The Invention of Repeating Clocks. 
 
 § I.' I '’He Clocks I now fhall fpeak of, 
 JL are fuch as by pulling of a 
 String, &c. do (trike the Hour, Qiaarter, 
 or Minute, at any time of the day and 
 night. 
 
 ^ a. Thefe Clocks are a late Invention 
 of one Mr Barlow, of no longer (landing 
 than the latter end of K. Charles II. about 
 the year i6j6. 
 
 This ingenious Contrivance ( fcarce fo 
 much as thought of before) foon took air, 
 and being talked of among the London 
 Artifts, (et their heads to Work ; who 
 prefently contrived feveral ways to effhd 
 iacb a performance. And hence arofe the 
 divers ways of Repeating work, which fo ■ 
 early might be obferved to be about the j 
 Town, every man almolt pradifing* ac* i 
 cording to his own Invention. 
 
Chap. IX. Repeating Clocks. i 
 
 S This Invention was pradlifed chief* 
 ly, if not only, in larger Movements, 
 
 I till K. James II/s Reign : at which time it 
 I was transferred into Pocket-Clocks. But 
 1 there being fome little conteft concern- 
 I ing the Author hereof, I lhall relate the 
 bare matter of fadi, leaving the Reader to 
 his own judgment. 
 
 About the latter end of K. James If s 
 f Reign, Mr Barlow (the ingenious In venter 
 beiore-mentioned ) contrived to put his 
 Invention into Pockcc-watches ; and en- 
 deavoured (with the Lord Chief JuHice 
 Allehone^ and fome others) to get a Patent 
 : for it. And in order to it, he fet MxTom^ 
 pion^ the famous Artift, to work upon it : 
 Who accordingly made a Piece according 
 to his directions. 
 
 Mr Qjiare (a very ingenious Watch*' 
 ‘maker in London) had fome years before 
 been thinking of the like Invention: but 
 mot bringing it to perfeddon^ he laid by 
 the thoughts of it, until the talk ofMr^^r * 
 How'^ Patent revived his former thoughts ; 
 ’which he then brought to effed- Tliis 
 being known among the Watch-makers, 
 they all prefled him to endeavour to hin- 
 der Mr Barlows Patent. And accorciins^- 
 
 P X ly 
 
loB Invention of , 6cc. Chap. IX. 
 
 ly applications were made at Court, and 
 a Watch of each Invention, produced be- 
 fore the King and Council. The King, 
 upon tryal of each of them, was pleafed 
 to give the preference to Mr Q.uares : of 
 which, notice was given foon after in the 
 Gazette. 
 
 The difference between thefe two In- 
 ventions was, Mr Barlom was made to 
 Repeat by pufhing in two pieces on each 
 fide the Watch-box: one of which Re- 
 peated the Hoijr, the other the Quarter. 
 Mr Quare's was made to Repeat, by a 
 Pin that ftuck out near the Pendant | 
 w hich being thruft in (as now ’tis doneby 
 thrufting in the Pendant) did Repeat both 
 the Hour, and Quarter, with the fame 
 thruft. 
 
 It would (I think) be very frivolous, to 
 fpeak of the various contrivances , and 
 methods of Repeating work, and the In- 
 venters of them j and therefore I fhall fay 
 nothing of them, - 
 
 G H A Po 
 
/^umbers, &c. 
 
 sop 
 
 CHAP. X. 
 
 ljumbers for fever al forts of Move* 
 ments. 
 
 I Think it may be very convenient to 
 fet down fome Numbers, fit for feve- 
 ral Movements ; partly, to be as Exam- 
 ples to exercife the young Reader, in the 
 foregoing Art of Calculation : and part- 
 ly, to ferye fnch, who want leifure or 
 underftahding to attain to this Art. 
 
 § I. But firft it may be requifite, to 
 Ihe'w the iifual way of Watch-makers wri- 
 ting down their Numbers, Kvhich is fome. 
 what different from that in the preceding 
 Book, ' ' 
 
 Their way reprcfenteth the Wheel and 
 Pinion, on the fame Spindle j hot as they 
 ' play in one another. Thus the numbers 
 1 of an old’ Houfe-Wateh, ' of hours, is 
 I written thus ; ' • 
 
10 
 
 My way 
 
 19 
 
 Numbeys for' Chap. X. 
 
 The Watch-makers way. 
 
 y6 — 4 
 
 54 — 7 
 JSS 
 
 According to my way, the Pin. of Re- 
 port Q43 drives the Dial-wheel {^48 ;] 
 the Pinion [73 plays in the Great-wheel 
 But according to the other v^^ay, 
 the Dial-wheel ftands alone ; the Greats 
 wheel ha th the Pinion of Report on the 
 fame arbor : the W heel [54] h uh the Pin : 
 [73 and the Crown-wheel II193 the Pin : 
 C 63 on the fame Spindles. 
 
 This latter way ( tho very ineonveni- 
 ent in Calculation) reprefenteth a piece 
 of work handfomely enough, and fome- 
 what naturally. 
 
 § t. Numbers of an 8 iay Piece, with 
 16 turns the Barrel, the Pend, vibrates Se- 
 conds, and fliews Minutes, Seconds, &c. 
 
 The Watch-part. 
 8)96 
 
 8)60— »4S)4^“"07^ 
 
 7)56 I 
 
 The Clock part. 
 8)78 
 
 6)48 8 pins. 
 6)48 
 
chap. X. ’Motjements. i i i 
 
 In the Watch-part, the Wheel 6o is 
 the Minute-wheel, which is fet in the 
 middle ©f the Clock, that its Spindle may 
 go thro the middle of the Dial- plate to 
 carry the Minute-hand. 
 
 .Alfo on this Spindle is a Wheel 48, 
 ■which driveth another Wheel of 48 , 
 
 I which laft hath a Pinion 6, which driveth 
 round the Wheel 71 in ix hours. Note 
 here two things : i. That the two Wheels 
 48, are of no other ufe, but to fet the Pi- 
 nion 6 at a convenient diftance 'rom the 
 I Minute-wheel , to drive the Wiitei yz, 
 
 , which is coiKentrical with the Minute- 
 wheel. For a Pinion 6 driving a Wheel 
 71, would be fufBcient, if the Minute- 
 il hand and Hour-hand had two different 
 : centers, a. Thefe numbers, 60-48)48-6)72, 
 
 I fet thus, ought (according to the laft §) 
 
 ! be thus read, viz. The Wheel 60, hath 
 i another Wheel 48 on the lame Spindle ; 
 
 which Wheel 48 divideth, playeth in, or 
 t turns round another Wheel 48 ; which 
 i hath a Pinion 6 concentrical with it: 
 
 I which Pinion driveth, or divideth a Wheel 
 of 72. For a Line parting two numbers 
 (as 60 — 48) denoteth thole two numbers 
 to be eencentrical, or to be placed upon 
 
 the 
 
tiz Numbers for Chap. Xi 
 
 the fame Spind/e. And when twonum- j 
 bers have a hook between them (as 48)48) 
 it fignifies 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 pnee in ix hours. 
 
 ^ j. A Piece of 32, days, with 16, or ! 
 12 turns both parts : the Watch Iheweth 
 Hours, Minutes, and Seconds ; and the i 
 Pend, vibrateth Seconds. 
 
 , The Watch- part. 
 
 With id turns. With 12 turns. I 
 
 16)96 
 
 
 9^72- . ^ ^ 
 
 9)7^ 
 
 8)6 o-“ 48)48“'6)7^ 
 
 8)6 o-' 4S)4^"'^)72' 
 
 7)5^ 
 
 7)f6 
 
 e— » 
 
 30 
 
 , 30 
 
 The Striking part. 
 
 With 16 turns. 
 
 With 12 turns. 
 
 10)130 
 
 8)128 
 
 
 
 6)72 Double hoop. 
 
 8)96 Double hoop. 
 
 6)60 
 
 8)80 
 
chap. X. Movements- i 
 
 The Pinion of Report is fixed on tBe 
 end of the arbor of the Pin wheel. This 
 , Pinion in the firfl is iz, the Count*wfieeI 
 39 5 thus, ix)j9. Or it may be 
 In the latter (with iz turns) it maybe 
 6)1.8, or 8 ^^4. 
 
 ^ 4. A two month Piece, of 64 days? 
 With 16 turns; Pend, vibrateth Seconds, 
 
 : and flieweth Minutes, Seconds, 
 
 Watch.part. 
 9)90 
 8)76 
 
 l8)6o"*48}48'»6)7a 
 
 ' 7)>-6 
 
 Clock-part. 
 10)80 
 to) 6 s 
 
 30 
 
 
 ■8)si 
 5'}6c-DoubleHoop’ 
 
 i u^f ^ is the Pio-wheel,' 
 
 [which alfo carneth the Pinion of Repore 
 8, driving the Count-wheel jz; 
 
 Of thus. 
 
 Watch-part; 
 
 8)80 
 
 :8)do■•48'i48-6)7^ 
 
 17)76 
 
 Clock-part. 
 6)144 
 
 •0J24 
 
 6 j 7 z-DoubieHoop' 
 
 6 j6o 
 
 je 
 
1 14 Ntcnibers for Gh. X. 
 
 § A piece of 1 3 weeks, with Pendu- 
 lum, Turns, and Motions, as before. 
 
 The Watch part. 
 
 8 Or thus. 
 8J8S 
 
 8)60—48)48—6)72 
 
 7)56 
 
 30 
 
 TheC 
 Sjljz Or thus. 
 8>4— 37J?o 
 8 J48 — iz pins 
 
 6) 48 Double Hoop 
 
 7) 40 
 
 6 ) 7 z 
 6 J66 
 
 6 ) 4 ^'" 4 ®) 4^*”^37 ^ 
 6)4^ 
 
 30 
 
 ock part, 
 
 I <5)9 o 5! 
 
 6)60 
 
 •30 pins 
 z4 )6 z 
 
 ■ S 6 . A Seven Month Piece, with Turnsi 
 Pendulum, and Motions, as before. 
 
 The Watch. 
 8)60 
 8)56 
 8;48 
 
 6 ) 45 '“ 48 ) 4 ^ 7 ?^ 
 
 sMo 
 
 30 
 
 The Clock. 
 
 8J96 
 
 8J88 — Z7J1Z 
 8)64' — 1 6 pins 
 6)48 Double Hoop 
 
 <5^48 
 
 7 ' 
 
Chap.X. Movements. * ^15 
 
 § 7- A Tear Piece, of’ 584 days, with 
 lurns, Pendulum, and Motions, as be- 
 fore. 
 
 The Watch. 
 ii-JioS 
 9J72. 
 
 8)64 
 
 8)6 o --48)48.6)7 z 
 
 7)5^ 
 
 The Clock. 
 io)izo 
 8)96 — 36) 9. 
 6)78 26 pins 
 6)72 Double Hoop 
 6)60 
 
 If -you had rather have the Pinion of 
 Report, on the Spindle of the Pin-wheel, 
 it muft be 13)39. 
 
 % 8. A Piece of 30 Hears, Pendpiurn 
 about 6 inches. 
 
 The Watch. The Clock. 
 
 12)48 8)48 
 
 6)78 
 
 6)60 
 
 6)42 
 
 6)78 13 pics 
 6 jdo 
 
 6)48 
 
 ^9. A Piece of 8 days, with turns, 
 Peed alum about 6 to fliew Minutes, 
 
 Seconds, ^c. 
 
 Q, i The 
 
lumbers for Chap. X. 
 The Watch. The Clock may 
 be the fame 
 o;64 48)^8r—6)y% ^virh the 8 day 
 
 0^*^°-,., r. before, 
 
 oj4o The Seconds Wheel. §i. 
 
 
 jy lo. A Month Piece 
 Pendulum, Turns, and 
 laft. 
 
 The Watch. 
 
 8)^4 
 
 8^48 
 
 6)48 48)48 
 
 ^ks 
 
 iSj^o Seconds Wheel. 
 
 of days, with 
 Motions, as the 
 
 The Clock may 
 have the fame 
 numbers , as 
 the Clock § 
 
 ^ II. A Tear Piece of 384 days, with 
 Pendulum, Turns, &c. as the laft. 
 
 The 
 
 T 
 
II7 
 
 Chap. X. Movements. 
 
 The Watch part. 
 
 10)90 Or thus^ with a Wheel lefs, and 
 8)64 not to Ihew Minutes and Se- 
 
 7^56 
 
 conds. 
 
 
 6)48 
 
 — »-48)48 — 6)71 
 
 8)9^ 
 
 6)4f- 
 
 <5)7*'— 36)9 
 
 <5)30 
 
 6)66 
 
 
 Seconds Wheel. 
 
 6)60 
 
 
 
 ^JS 4 
 
 
 
 — 
 
 19 
 
 In the latter of thefe two Numbers, 
 the Pinion of Report is 9 6, on the Second 
 Wheel. The Dial Wheel is 9. 
 
 The Clack-part may have the fame Num- 
 bers, as the Year-piece before § 7. 
 
 § iz. An 8 Day Piece, tolhewthe 
 Hour and Minute, Peitr/. about 3 inches 
 long. 
 
 6^96 The Clock may have the 
 
 8)64-6)7z fame numbers, as the 8 
 7)49 day piece before, § 2. 
 
 19 
 
 Automata 
 
1 1 8 Numbers for Chap. X* 
 
 Automata fiewhg the Motion of the Celeflid 
 Bodies. 
 
 ^ I. Numbers for the Motion of the 
 Sun and Moorh See before in. Chap, z. 
 Se&. s>S h 4 - 
 
 § 2. Numbers to fhew the Revolution 
 of the Planet Saturn, which confifts of 
 1075' 9 tlays. 
 
 ontheDial-whed. If you would make it de- 
 5)69 pend upon a Wheel go- 
 
 , 4752 ing round in a year, thus, 
 
 448 or thus, 4)118 
 
 4)40 6) JO 
 
 i Note, The lowermoft Pinion in thefe, 
 and the following numbers, is to be fixed 
 concentrtcal to the Wheel, which is to 
 drive the Motion, viz, the Dial-wheel, 
 Year-wheel, or &c. 
 
 § j. Numbers for the Planet Jupiter, 
 whofe Revolution is 4332 j’days. 
 
 Onthe Dial-wheel. 
 
 4)48 Or thus, on the Year-wheel. 
 4)40 6)71 
 
 4)56 
 
 4) 32, 
 
 Note here, That the two laft numbers 
 
 of 
 
chap. X. Movements. up 
 
 Of Saturn, may be the two firft of Jupiter 
 a]fo. 
 
 By the permiflion of my ingenious 
 friend Mr FlamfteeJ, I here infert a de- 
 fcription of Mr Olaus Romer, the French 
 King’s Mathematician’s Inftrument , to 
 reprefent the Motion of Jupiter s Satel-^ 
 liter j a copy of which he fent to Mr 
 FlamfteeJ in 1^79. 
 
 Upon an axis f which turns round once 
 in 7 days 7 are four Wheels fixed : one of 
 87 teeth 5 a fecond of ^3 ; the third 41 3 
 and the laft of 28 teeth. On another axis 
 run 4 other Wheels (or Pinions you may 
 call them) which are driven by the afore- 
 faid Wheels. The firft is a Wheel, or Pi- 
 nion of 22 leaves, driven by the Wheel 
 87, which carrieth round the firft Satel- 
 lite. The fecond is 32, driven by the 
 Wheel 63, which carrieth round the fe- 
 cond Satellite. The third hath 43 leaves, 
 driven by the Wheel 42, which carrieth 
 the third Satellite. And laftly , is the 
 Pinion 67, driven by the Wheel 2 8, which 
 carrieth round the fourth Satellite. 
 
 On the firft axis is an Index, thatpoint- 
 ■eth to a circle divided into parts, 
 which are the hours in 7 days. 
 
 On 
 
20 
 
 Numbers for Chap. X. : 
 
 On the other axis all the Pinions run j 
 concentrically, by means of their being ^ 
 hollow in the middle. In the midft of 
 them all, the axis of Jupiter himfelf is fix- 
 ed, with a little Ball at the top, repre- 
 fenting Jupiter $ body. On the ends of 
 4 fmall Wires, fixed in the four feveral 
 Sockets of the aforefaid Pinions, may 4 
 lefier Globules be placed C at theit due di- 
 ftance from Jupiter’s Globule) to repre- 
 fent the 4 Satellites going round that Pla- 
 net. 
 
 ^4. Numbers iov Mars ^ whofe Revo- 
 lution is 1 year days. 
 
 On the Dial-wheel. 
 
 4)48 The two laft Numbers of Sa~ 
 
 4)40 turn may be the two firft of 
 
 4)45 Mars alfo, 
 
 S S' Numbers for re»us, whofe Revo- 
 lution is in 2x4 days. 
 
 On the Dial-wheel. 
 
 4)32 Nere, The laft number of 
 
 4)32 ter may be the firft of f^enus. 
 
 4)28 
 
 § 6 . Numbers for Mercury^ whofe Re- 
 volution is near 88 days. 
 
Chap. X*. Movenients, 
 
 On the Dial-wheel. 
 
 4)56 
 
 § 7. Numbers to reprefent the Motion 
 of the Dragons HeaA and 'tail, (near 19 
 years) to Ihew the Eclipfes of the Sun and 
 Moon. ; 
 
 On the Dial-wheel. On the Year-wheel. 
 
 4)4^ 4)7<> 
 
 4)40 Note, The two laft numbers 
 4')44 of Saturn be the twofirftof 
 4)4^ this on the Dial-wheel- 
 As to the placing thefe feveral Motions 
 6nthe Dial-plate, I ihall leave it wholly 
 to the Work-mans contrivance. He may 
 perhaps make thern to reprefent the Co- 
 pernican, or fonae other Syflent. 
 
 Numhers for Pocket- WdicheL 
 
 § I. A. Watch to.go 8 Days, with ix 
 turns, fo (hew Minutes arid' Seconds, the 
 Train 16006. 
 
 6)96 
 
 6)48 — ix) 48 — -ix)y6. . , 
 
 6)4^ On the wheel |_4x(l is tlfe Second’s 
 • ^)4x hand placed , and on the \Vhcel 
 (48} the Minute hand. 
 
 IK 
 
122 
 
 liumbers for Chap. X. 
 
 Ji. Another of the fame, without Mi- 
 nutes and Seconds, to go with only 8 
 turns. 
 
 2o)io 
 
 6)46 
 
 6)6o 
 
 5)^0 
 
 5)4S 
 
 19 
 
 J 3. A Pocket-Watch of 32 Hours, with 
 8 turns, to (hew Minutes and Seconds, 
 Train as the laH:. 
 
 12)48 
 
 6^48 — 12)48—12)36 
 6)46 
 
 6)41 — Seconds Hand. 
 
 19 r u 
 
 § 4. The ufual Numbers of 30 hours 
 Pendulum Watches, with 8 turns, to 
 ihew the Hour and Minute. 
 
 12)48 
 
 6)s4 — 
 
 6)48 
 
chap. X, Movements* 12 
 
 § 5. The ufua! Numbers of the old 30 
 hours Pocket-watches* 
 
 With 5- Wheels. With 4 Wheels. 
 10)30 6)3 x 
 
 7)65 6)66 
 
 6;4X ^ s)so ^ 
 
 ^ 6)36 5r)45' 
 
 15* . 
 
 If any of the Numbers of the preceding 
 Wheels and Pinions lliould not pleaie the 
 Reader, he may eafily correct them to his 
 mind, by the Inftruftions in the forego*' 
 ing Book. The way in Ihort is this : Di- 
 vide the Wheel by the Pinion, apd fofind 
 the number of turns, according to Chap. 
 
 Sed: I. S' 2, Multiply the Pinion you 
 like better, by this number of turns, and 
 theProdud is the Wheel. Thus in the 
 8 day Pocket-watch § i, if you think the 
 Great-wheel too large, you make it in- 
 ftead of 6)96(16 thus, 'vh. 5')8c^i6 r.e. 
 chufingthe Pinion only y, and multiply- 
 ing it by 16 (the turns) the Wheel will be 
 80. 
 
 R 2- CHAR 
 
1 24 
 
 Tables of Time. Cfa. XL 
 
 CHAP. XI 
 
 Tables of Time relating to Watch- 
 
 VPOrk: 
 
 Seconds. A Table of Time. 
 
 Minutes. 
 
 60 
 
 :j6go 
 
 86400 
 
 6048 
 
 00 
 
 2992000 
 
 956000 
 
 60 
 
 Hours. 
 
 1440 
 
 10080 
 
 45200 
 
 929600 
 
 24 Day 
 
 168 
 
 720 
 
 8760 
 
 7 
 
 50 
 
 Week. 
 
 -I 
 
 4 Month. 
 
 12 Year. 
 
 
 , The foregoing be of good 
 
 ufe in Calculation, for the ready finding 
 out the parts of Time: which is thus. 
 Find the parts of tirne you feek for, the 
 number in the concuirehce of Squares, is 
 the anfwer to your queftion. Thu^ fup 
 pofe you feek for the number off Sec0 
 
Ciiap. X L Talks of Time. 125 
 
 in a Year; in the Square under Seconds 
 in the fame line with Tear (which is the 
 lowermoft Square on the left hand) is the 
 number fought, 31 j, ^c. So Minutes 
 ina Month, are 4^200. 
 
 If ydu would know any number, where 
 thereis 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 
 2^59" ") and the Seconds in a Day (which 
 are 86‘r-f J and you have the humbef 
 fought, vk, 2678400. 
 
 J Table to fet a Watch ly the Fixed Stdh* 
 
 Night 
 
 Hour.Min.Seg. 
 
 Night 
 
 Hour.Min.Sec. 
 
 ; I 
 
 0 
 
 ; 
 
 S 7 
 
 s 6 
 
 I 
 
 3 
 
 20 
 
 2 
 
 0 
 
 7 
 
 J 4 , 
 
 17 
 
 I 
 
 7 
 
 17 
 
 V 5 
 
 0 
 
 II 
 
 
 18 
 
 I 
 
 11 
 
 H 
 
 
 0 
 
 
 47 
 
 T 9 
 
 I 
 
 hf 
 
 II 
 
 'T 
 
 0 
 
 19 
 
 44 
 
 2b ] 
 
 1 ^ 
 
 19 
 
 8 
 
 6 
 
 0 
 
 23 
 
 41 
 
 21 
 
 ! I 
 
 23 
 
 S’ 
 
 7 
 
 0 
 
 27 
 
 48 
 
 22 
 
 \ I 
 
 27 
 
 ij 
 
 : 8 
 
 0 
 
 31 
 
 
 23 1 
 
 j I 
 
 30 
 
 n 
 
 9 
 
 0 
 
 3 ^ 
 
 
 24 ! 
 
 1 I 
 
 34 
 
 Sil 
 
 . 10 
 
 0 
 
 39 
 
 29 
 
 25- 
 
 ! I ‘ 
 
 
 fi 
 
 11 
 
 0 
 
 43 
 
 z 6 
 
 26 
 
 [ I 
 
 -42 
 
 49 
 
 i,; 4 ? 
 
 0 
 
 47 
 
 2? 
 
 27 
 
 1 1 
 
 1 
 
 46 
 
 4 ^^ 
 
 
 0 
 
 5 ^ 
 
 29 
 
 28 
 
 I 
 
 50 
 
 43 
 
 
 0 
 
 
 26^ 
 
 29 
 
 I 
 
 14 
 
 4 ' 
 
 
 V 'O 
 
 
 2;! 
 
 30 
 
 I 
 
 yB 
 
 
1 
 
 12^ Tables of Time. Chap. XI. 
 
 Explanation of the f able. 
 
 This Table fliews how much the Sidc^ 
 real, goeth fafter than the Solar day, in 
 any number of nights for a month. So 
 that obferving by your Watch, the nice 
 time when any nxed Star cometh to the 
 Meridian, or any other point of the Hear 
 vens : if after one Revolution of that fame 
 Star to the fame point, your Watcn goeth 
 3'. 5*7" flower than the Star; or after two 
 nights 7'. 5'4"3 or nights, i h. zo'*, 
 then doth your Watch keep time 
 rightly with the Mean motion of the Sun. 
 
 If it vary from theTablejou muft alter the 
 length of yourPend.to make it fo keep time. 
 
 To obferve the time nicely, when the 
 , Star cometh again to the fame point of the 
 heavens, ’tis necellary to make the obfer- 
 vation with a Telefcope, that hath crofs‘ 
 
 . threads !n the focus of the objec9:-glafs 3 
 and fo leaving the Telefcope fixed in the 
 fame pofl:ure,till afecondObfervation.You 
 may do this with the telefcopular fights of i 
 a Quadrant, or Sextans, and fo leaving it | 
 ^ Handing until anoher night of Oblervation. I 
 Or for want of this more nice way, you | 
 may do it by looking along by the edge 
 of two Strings, fufpended with Plumbets,, 
 
 . in;,; 
 
chap. XL Tables of Time. i 
 
 in a room, at fome diftance from one ano- 
 ther. Or by looking at the edge of a 
 Chimney, as Mr PVai/m hath dired:- 
 ed, at the end of Mr Smith's Hord. Dif- 
 quif. But to make a tolerable obfervation 
 any of thefe laft way?, ’tis necefiary to 
 have a Candle Ihine upon the edge of the 
 ftrrthermoft String, or Chimney ; withi* 
 out which you cannot fee exadly when 
 the Star cometh thereto. 
 
 A Talk fheivhg the Variations mai^e in the 
 true Hour of the Day., by the Refrallion of 
 ' the Sun in the Equator, and loth the Soljiices. 
 
 . SunVSun’s 
 
 Variation 
 
 V ariation iV ariation 
 
 alti- 
 
 'Refra- 
 
 at doe N, 
 
 at the E- 
 
 at the S. 
 
 tude.'dlion. 
 
 Solftice. 
 
 quator. 
 
 / tf 
 
 Solftice. 
 
 Deg. 
 
 < 
 
 u 
 
 / 
 
 u 
 
 t 
 
 
 00 
 
 33 
 
 • 0 
 
 4 
 
 34 
 
 3 
 
 32 
 
 4 
 
 38 
 
 I 
 
 23 
 
 00 
 
 2 
 
 34 
 
 2 
 
 28 
 
 3 
 
 19 
 
 2 
 
 ^7 
 
 00 
 
 1 
 
 i 2 
 
 24 
 
 I 
 
 49 
 
 2 
 
 31 
 
 
 13 
 
 
 I 
 
 46 
 
 1 
 
 27 
 
 2 
 
 3 
 
 4 
 
 II 
 
 50 
 
 I 
 
 29 
 
 r 
 
 12 
 
 I 
 
 40 
 
 y 
 
 9 
 
 ;o 
 
 I 
 
 12 
 
 I 
 
 I 
 
 I 
 
 33 
 
 6 
 
 7 
 
 50 
 
 0 
 
 
 0 
 
 49 
 
 I 
 
 17. 
 
 7 
 
 7 
 
 00 
 
 0 
 
 
 0 
 
 44 
 
 I 
 
 16 
 
 8 
 
 6 
 
 00 
 
 0 
 
 43 
 
 0 
 
 39 
 
 I 
 
 8 
 
 9 
 
 5 * 
 
 00 
 
 0 
 
 3 ^ 
 
 0 
 
 34 
 
 *1 
 
 2 
 
 10 
 
 4 40 
 
 0 
 
 25 
 
 0 
 
 29 
 
 1 
 
 2 
 
 Remarks 
 
28 of Time. Chap, xt 
 
 Remarks upon the Table, 
 
 The Column of the Sun’s Refradions, 
 I owe to that accurate obferver of the ce- 
 leftial motions, Mr Flam^eed. Which Re- 
 fradions, altho in the Table the fame, yet 
 do differ at different feafons of the year, 
 nay perhaps^ according to the different 
 temperature of the air fometimes, in the 
 fame day. Thus Mr Flamjleed found the 
 Refradions in February very different 
 from thofe in April : and it is obferved , 
 that the Refradions are commonly great- 
 er, when the Mercury is higher in the Ba- 
 rometer; 
 
 The Table therefore doth not Ihew what 
 the Refradions always are, but only about 
 the middle quantity of them, at every de- 
 of the ic firft of the Sun\ altitude. 
 And accordingly I have calculated the 
 Variations thereby made in the hour of 
 the day. 
 
 Thefe Variations of the hour are greater 
 or lefler, according as the angle of the 
 Suns diurnal miotion is acuter with the 
 horizon. The reafon is plain 5 becaufe as 
 the Sun appears by fefradion higher than 
 
Chap. XI. Idles c/ 13we. itf 
 
 realty he is j fo this felfc beighi (doth af- i 
 feft the hours in Winter, marc (than the . 
 Summer half year. 
 
 There is no ray indeed of the SBin^ bo* 
 what Cometh refra&ed to a Siio^al: 
 and confequently, there is no Dial but 
 what goeth more or lefs falfe (except at 
 Noon in Dials that caft a Shade, where 
 the refradtion makes no variation.) But 
 the RefraAion dccreafeth apace, as the 
 Sun gets higher, and caufeth a variation 
 of Bot above half a minute, at to degrees 
 of the Sun’s altitude ; except when the 
 Sun is in, or near the Southern Tropicb. 
 Nearer than half a minute, few common 
 Sun-dials Ihew the time. And therefore, 
 partly for this reafon, and partly, becaufe 
 Mr. Flam^eed’s obfervations reach not 
 much farther, I have calculated my Table . 
 to only to degrees. 
 
 The Table needs little explication. For 
 having the Sun’s height, you have againft 
 it, in the next Column, the Refradion : 
 and in the 3 next the alterations of the 
 hour, at 3 times of the year. Taking 
 therelore by a Quadrant the Sun’s alti- 
 tude , and obferve at the fame time, the 
 hour of the day by a Sun-dial, by theTa- 
 
 S ble, 
 
If o TSles of Time. Chap- XI. 
 
 ble, you fee hov<r many minutes, and fe- 
 conds, the Dial is too fall. As at/the 
 Sun^rifing a Sun-dial is too fail 4'. ;4'', 
 about June ii, and about Mar. 
 
 10. and Sept. 12., and4' 38'' about D«c.ii. 
 
Addendot 
 
 131 
 
 Addenda. 
 
 T O the Fifth part of the Rule in ^ <J. 
 
 p. ii. If you haveoccafion to lay 
 the Pinion of Report upon any other 
 Wheel, and not the great-Wheel, you 
 may do it by this Rule, the Beats in 
 one turn of any Wheel j To the Beats in an 
 how : •. So are the hours of the Dial ; To 
 the Qjtotient rf the Hour-voheel JiviJed by 
 tie Pinion of Report, 
 
 To page Suppofe in altering an old 
 Watch, you would have it ftiew minutes, 
 as well as hours; you may do it thus: 
 Divide the Beats in one turn of the Qreat- 
 wheel, by the Beats in an hour ; thj^Quo- 
 tient will Ihew in how many hdurs the 
 Great-wheel goeth round once. If the 
 Beats in the Great- wheel exceed the Train, 
 you muft chufe your Minute-wheel firft, 
 and multiply it by the (Quotient j this 
 will give the Pin. of Report. But if the 
 Train exceeds the Beats of the Great- 
 wheel, you muft chufe the Pin, of Rep. 
 and multiply the Qpotieacbyit : the pro- 
 duift is the Minute-wheel 
 
 But 
 
1 3 ^ ' Ad^etdn, 
 
 But it often falls out, that the Traio 
 and Beats of the Great-wheel will not ex- 
 adlly meafure one another : if fo, the beft 
 way is to half the two numbers, as far as 
 they will equally admit of halfitig^ or 
 divide them by fome common divifor, and 
 fo having brought them to as fraall num- 
 bers as you can, you may fuppofe them to 
 be a Wheel and Pinion, and reduce them 
 to lefler numbers , by Chap. x. SedJ'. i. 
 % <). Thus fuppofe you would make the 
 old dull Movement there mentioned, d 
 Minute-watch ; you may reduce the num- 
 bers of the Great-wheel x 1888, and the 
 Train 9^68, to a Pinion and Wheel i8) IX. 
 Which Pin. 18 being let upon the Spin:lle 
 of the Gr.Wh. wiMdrivea Wheel IX round 
 once in an hour, to fliew Minutes. If 
 you make this Wh. 11 drive another of 
 48; concentrical to which, is a Pin. ix 
 driving a Wheel (which Wheel is cotl- 
 Centrical with the Minute-wheel^ thiswill 
 Garry a Hand I'ouod in IX hours. Butin 
 this cafe, you wuft place the Pin. 18 on 
 the Spindle -of the Gr. Wh. fo sts to Hide 
 found fliffly, when 3»ott earn the Minute- 
 ’hand to re^ifie the W-ateb* 
 
 Fjujs, ; 
 
 / 
 
fjrx 
 
 r 
 
 n e> 
 
 GEITV CENTER LIBRARY