of the Sun's Orb on one Side of the Centre of the Earth than there is on the other for which Reason though the Sun moves equally each Day in the Circle of his yearly Course yet to us he seems to move faster in some Parts thereof than he does in others and that makes the Right Ascensions greater near one Tropick than they are near the other And accordingly by the Tables of the Sun's Motion 't is found that he takes up but about 179 Days in passing that part of the Ecliptick between Libra and Aries whereas between the Two Points of Aries and Libra he spends above 186 so that he is almost 7 Days more in passing the Summer half of the Ecliptick than he is in passing that of the Winter and this seemingly swift and slow Motion of the Sun is the Cause that the Right Ascensions of 10 Days Motion near the Winter Tropick are 60 Minutes or a whole Degree more than those of the same Number of Days near that of the Summer one The Right Ascensions of 10 Days Time near the 2 Equinoctial Points do also differ somewhat for those of 10 Days Time near Aries are less by 30 Minutes than those near Libra the Reason of which is from hence in that the Suns greatest and nearest Distance to the Earth happens now in our Times to be about 8 Degrees and something more from the Tropick Points whereas had it fallen out exactly in the 2 Tropicks then the Right Ascensions near the Two Equinoctials would have been both alike Now by what has been said I hope the true Reason of the unequal Lengths of Natural Days will plainly appear and by consequence Men will not hereafter be so unreasonably nice and curious as some have heretofore been to expect always an exact Agreement between their Clocks and the Sun for if there be from the Nature of the Fabrick of the World and the Celestial Orbs above us a necessity for those Differences as are found in the Sun 's Right Ascensions and there being for that Reason a Necessity also that the Days bounded thereby should be unequal in proportion to those Differences T is then plainly impossible that a Royal Pendulum whose diurnal Revolutions are always equal and if well adjusted gives you the true Time of 24 Hours should agree with the Sun which makes the length of Days almost continually to differ and to be sometimes more than 24 Hours and sometimes less For in the first Place this makes it impossible to adjust a Clock well barely by the Sun For suppose one should attempt to adjust a Clock when the Natural Days are not fully 24 Hours long as about the middle of March where as appears by the first annexed Table the Day wants 20″ of 24 Hours long this Clock brought to go correspondent to the Days in March shall in June finish his Pendulum Day or his two 12 Hours Revolutions before the Sun shall compleatly pass between one Meridian and another that is before the Sun shall pass from the Hour of 12 one Day to that of the Hour of 12 on the next because now the Natural Day is longer than 24 Hours by 13″ whereas the Day to which it was before adjusted was 20″ shorter than 24 Hours and by consequence the Pendulum Day of the Clock must be finished sooner in June by 33″ than the Natural Day and gain each Day 33 Seconds On the contrary if a Clock could be adjusted to the Sun in the Month of December at which Time the Natural Day is longest being then 31″ or half a Minute above 24 Hours in length this Clock when Natural Days are shortest as in March where they want 20″ of 24 Hours this Clock I say shall not then finish his diurnal Revolutions in so little a Time as those Days shall be accomplished and by consequence shall go each Day 50″ too slow because those Days in March are shorter by 50″ than those in December to which your Clock is supposed to be adjusted Supposed to be adjusted I say for to do it exactly by the Sun we affirm to be impossible for the Length of Days continually altering he that would adjust a Clock to the Sun must be always altering of it accordingly and if he should accidentally bring it to go slow enough as he thinks for some Days such as those long ones in December are the length of the Day soon altering and becoming shorter he must again alter the Length of his Pendulum to make it go equal to Days that are now shorter and so not understanding the Nature of Time truly nor of what Length a mean or middle Day is he will in Hopes of making it go always true be continually altering of it as he sees it vary and that without ever being so happy as to make it keep the Time desired for 't is impossible a Motion that keeps always the same Time that its particular Length or pitch of Pendulum does admit of can be so adjusted by the bare Sun as to accord therewith in all those various lengths of Days which are made by its either slow or swift Motion Since then things are thus it remains that we shew How by Art that may be done which by meer Natural Observation can never be effected that is by what means a Clock regulated by a Royal Pendulum may be adjusted to such a middle Pitch of Motion as to make in a compleat Year just 365 equal Revolutions or so that each of its 24 Hours may be the same for Length as the 365th part of a Year is which is indeed the true Time of a 24 Hour Day and that 's the nearest and the most exact pitch to which 't is possible to adjust the best of Pendulums Now this is only to be done by the help of an exact Table of Equations which shall as nearly as 't is possible give you the true Length of every Day so that knowing by this means not only which Days are truly 24 Hours long but also which are shorter and which are longer 't will be easy then to know what must be taken from some or added unto others to make them equal to them that are truly 24 Hours which in short is the true Business of the Equation of Time And though this cannot be done in the Natural Day it self yet knowing how much all Days do differ from 24 Hours the Motion of a Clock may yet be adjusted thereby to a true Pendulum or 24 Hour Day by making it either lose or gain so much as the Days do exceed or fall short of 24 Hours And this may well enough be performed by the Tables of Signs and Tangents for by these you may readily frame a Table of the Sun 's natural right Ascensions and this shall shew you what Degrees of the Equinoctial are each Day upon the true Meridian when the Sun comes to it Now these being in their measure of Degrees and Minutes sometimes more and sometimes less you must
shew how many Seconds those Days are shorter than 24 Hours And here you are to note That in those parts of the Year where days are above 24 Hours long there a well adjusted Clock will gain because the pendulum-Pendulum-Day which is the 24 Hours of its own Motion will be finish'd before the natural-Natural-Day is ended On the contrary Where the Days are less in length than 24 Hours there the Clock will lose or go too slow because the pendulum-Pendulum-Day will not be ended so soon as the Natural one London Printed for R. Cumberland at the Angel in S. Paul's Church-Yard A Second Table of Equations Shewing how to order a well-adjusted Clock so as that the whole Year round it shall not differ above the Sixteenth Part of an Hour from the Sun or 3′ 45″ By JOHN SMITH C. M.  Jan. Feb. Mar. Apr. May June July Aug. Sept. Octo. Nov. Dec.  ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ 1 7 ♠8 2 49 1 40 3 28 1 48  59 1 34 1 28  20 2 5  34 2 43 2 3 21 2 49 1 57 3 11 1 51 1 00 1 41 1 19  00 2 19  43 3 12 3 2 58 2 47 2 14 2 55 1 54 1 11 1 48 1 10  20 2 33  53 7 ♠28 4 2 35 2 45 2 32 2 39 1 55 5 ♠8 1 55 1 1  41 2 46 1 3 3 15 5 2 13 2 41 2 50 2 24 1 55 3 33 2 1  50 1 2 2 59 1 13 2 45 6 1 52 2 37 3 8 2 9 1 55 3 11 2 7  38 1 23 3 12 1 24 2 15 7 1 32 2 33 3 26 1 55 1 54 2 58 2 13  25 1 44 3 25 1 36 1 45 8 1 13 2 28 7 ♠29 1 41 1 52 2 45 2 19  12 2 6 5 ♠10 1 48 1 15 9  55 2 23 3 27 1 27 1 50 2 32 2 24  2 2 28 1 11 2 1  45 10  38 2 17 3 9 1 13 1 47 2 19 2 28  16 2 50 1 1 2 16  15 11  22 2 9 2 51 1 0 1 44 2 6 2 32  31 3 11  52 2 33  15 12  6 2 1 2 33  47 1 41 1 53 2 35  46 7 ♠17  44 2 50  45 13  10 1 52 2 15  35 1 37 1 40 2 37 1 1 3 25  37 3 8 1 15 14  26 1 43 1 56  28 1 33 1 27 2 39 1 17 3 5  30 3 26 1 45 15  42 1 33 1 37  12 1 28 1 14 ◠40 1 33 2 45  24 7 ♠20 2 16 16  57 1 23 1 1 17  1 1 23 1 1 2 40 1 50 2 25  18 3 25 2 47 17 1 1 1 12  57  9 1 17  49 2 40 2 7 2 5  13 3 4 7 ♠3 18 1 24 1 00  37  19 1 11  37 2 39 2 24 1 45  9 2 42 3 14 19 1 36  47  17  29 1 5  26 2 37 2 42 1 25  6 2 19 2 44 20 1 47  34  3  39  59  15 2 34 3 00 1 9  3 1 56 2 14 21 1 58  21  22  49  52  4 2 30 3 19  47  1 1 32 1 44 22 2 8  7  41  58  44  7 2 26 7 ♠23  28  1 1 8 1 14 23 2 17  7 1 00 1 5  36  18 2 22 3 26  9  1  44  44 24 2 25  22 1 19 1 12  27  28 2 18 3 7  10  1  19  14 25 2 31  37 1 38 1 19  17  38 2 13 2 48  28    6  16 26 2 36  52 1 57 1 25  7  48 2 8 2 29  45  4  31  41 27 2 40 1 7 2 16 1 30  4  38 2 3 2 9 1 2  6  56 1 12 28 2 43 1 23 2 35 1 35  16 1 8 1 58 1 44 1 18  9 1 22 1 40 29 2 46   2 54 1 40  26 1 17 1 52 1 29 1 34  13 1 48 2 7 30 2 48   3 13 1 44  37 1 26 1 45 1 00 1 50  19 2 15 2 34 31 2 49   7 ♠16    48   1 37  40    26   2 59 Note the Day on which this Mark ♠is plac'd are Rectifying Days on any Day then that is not a Rectifying-Day let the Clock be Set so much too Slow as the Black or so much too Fast as the Red Figures express and so let him go on till a rectifying-Rectifying-Day on which let Him be Set backward if the Figures on the rectifying-Rectifying-Day are Black or forward if the Figures are Red just so many Minutes and Seconds as the sum of Figures are on the Rectifying-Day and continue so to do each Rectifying-Day following and then the Clock in the Intermediate Spaces between will agree with the Sun as the Figures in the Table express that is will be either so must too Fast or so much too slow London Printed for Richard Cumberland at the Angel in S. Paul ' s Church-Yard 1694. of use no longer than the Sun shines The next to this of any value and Esteem was that of the Hour-Glass an excellent Contrivance if its Usefulness at all Times be considered but the Care required to keep it in continual Motion did still excite the Ingenious to endeavour the Discovery of something else that might not only be yet more exact but free too from the continual Toil as I may call it and Trouble of Attendance In process of Time this came to be performed in part by the way of Clock-Work a Device first of all started among the Germans from whom the Art of making Clocks dispersed it self over other Parts of Europe but as yet Defective as to its exact and steady keeping of Time At length in Holland an Ingenious and Learned Gentleman Mr. Christian Hugens by Name found out the Way to regulate the uncertainty of its Motion by the Vibration of a Pendulum From Holland the fame of this Invention soon past over into England where several eminent and ingenious Workmen applyed themselves to rectify some Defects which as yet was found therein among which that eminent and well-known Artist Mr. William Clement had at last the good Fortune to give it the finishing Stroke he being indeed the real Contriver of that curious kind of long Pendulum which is at this Day so universally in use among us An Invention that exceeds all others yet
known as to the Exactness and Steadiness of its Motion which proceeds from Two Properties peculiar to this Pendulum The one is the weightiness of its Bob and the other the little Compass in which it plays The first of these makes it less apt to be commanded by those accidental differences of Strength that may sometimes happen in the Draught of the Wheels and the other renders the Vibrations more equal and exact as not being capable of altering so much in the distance of its Swinge as those other kind of Pendulums are who fetch a larger and by consequence a less constant Compass For Pendulums that swing or vibrate very far out as all Crown-Wheel Pendulums do are apt by reason of many Accidents that happen to vary much in the Distance they swing and that 's the reason they do not always go or move the same Pace a larger Vibration taking up more Time to be performed in than lesser ones do But the Vibrations of this Pendulum of Mr. Clement's contrivance is so very exact and steady that when 't is well in Order and the Air of the same Consistence it shall in Five hundred or a Thousand Revolutions of its Index keep so equal a Time that no Human Art can discover the least considerable Difference in any of its Revolutions an excellence to which no other known Motion can as yet pretend and for which I think it will not be improper now at last to call it the Royal Pendulum But although the Motion thereof be so very curiously exact and equal yet 't will not for all that regulate the Motion of a Clock in such a manner as that the Index or Hand shall continually agree with that Time which the Sun gives for by constant Experience we find that the best of Clocks when exactly adjusted will yet be found in some considerable Time of going to be either too fast or too flow for the Sun although it was at the first set right therewith Now this Disagreement cannot be occasioned by any Defect proper to the Motion of the Pendulum each Twenty Four Hours of which when well rectified being the same for length of Time but it does proceed from an irregularity in the Sun 's apparent Motion which does occasion great diversity in the Lengths of Natural Days 'T is generally believed indeed that the natural Day or the Time between 12. and 12. a Clock is always in length just 24. Hours But this is a great Mistake for it will appear by the following Accounts of it that it is but in some Parts of the Year that the Days are so in all the other Parts between these they are found continually to differ being sometimes above 24. Hours long and sometimes less than 24. Hours and though the Differences may seem but a small matter to some the greatest excess being not above half a Minute yet if these seemingly but little Differences be added together for the space of a Month or Two together they will amount to a very considerable Sum of Time Now to make the reason of this irregular Length of Days as plain as I can be pleased to take notice That as Natural Days are that space of Time in which the Sun or as others think the Earth by the Motion of those Orbs that divide Time into Days is moved round just one whole diurnal Revolution or passes from the Meridian or Twelve a Clock Point of one Day to that of the next so it must follow that all such natural Days cannot be of a true and equal Length unlese the Sun in that space of Time does also move in such a manner in his annual Orb as that the Equinoctial may be always divided into equal Parts by those Meridians on which the Sun is upon each particular Day But that this is not done is plain to all that are verst in Astronomy and rightly understands the Use of the Globe This an exact Table of the Sun 's Right Ascensions does demonstrate for by that 't will be found that the Meridian Sun of each Day doth not divide the Equinoctial into equal parts their Differences not being equal but more on some Days than they are on others and these their Differences will appear yet more plain and visible if you will be but at the Pains to compute what the Right Ascensions amount to in to or 20 Days Time in some parts of the Year and compare that with those of the like Number of Days in some other part So also if on the Globe you mark out on the Ecliptick 10 or 20 Days Motion of the Sun as 't is found set down in an exact Ephemeris or Almanack that shews the Sun 's true Place and passing this under the brazen Meridian note what number of Degrees on the Equinoctial are included in that Space the which compare with those of the like number of Days Motion in some other part of the Ecliptick and the Degrees so compared will be found to differ or be more in Number in some Places than they are in others which plainly demonstrates the Thing asserted Now the Reason of these Differences in the Right Ascensions and by consequence in the different Lengths of Days proceeds in the First Place from the cross Position of the Zodiack and the Equinoctial which on Globes do represent the Circles of the Sun 's yearly and dayly Motion for the Course of the Sun 's daily Motion being directly from East to West and the Circle of his yearly Motion being in position Cross-ways thereunto from the almost South West to the North East as by the Globe is apparent it follows that the Right Ascension will be still unequal for 't is impossible that the Sun in his Motion near Aries and Libra where the Zodiack lyes cross the Equinoctial should in any certain number of Days make the same Number of Degrees in Right Ascension as he will do near the two Tropicks of Cancer and Capricorn where the Ecliptick runs in a manner parallel to the Equinoctial Circle And accordingly 't is sound by the best Tables of Right Ascension that the Right Ascensions belonging to 10 Days Motion of the Sun near the Tropick of Capricorn amounts to about 11 Degrees 30 Minutes whereas that of the same Number of Days near the Equinoctial Points of Aries or Libra will be found to be hardly 9 Degrees And as the Right Ascensions of the Tropicks differ from those of the Equinoctial Parts of the Ecliptick so the Right Ascensions of one Tropick differs from that of the other Now the Cause of this differs from the Cause of the former unequalities for this proceeds from the excentricity of the Centre of the Earth and the Centre of the Sun 's yearly Orb for the Centre of the Earth on which we live not being the same with the Centre of the Ecliptick in which the Sun moves but distant from it as some Astronomers affirm about 316000 Miles it follows that there must be a greater part
next find out what a mean or equal right Ascension will amount to by dividing the 360 Degrees of the Equinoctial into 365 Parts agreeable to the number of Days contained in a Year then compare each natural right Ascension with the mean ones and by substracting the lesser from the greater you will by turning the differences between them into Time come to know their true Equation that is how much each Day is longer or shorter than 24 Hours for so much as the natural right Ascension is more than the Mean in Time so much is that Day longer than 24 Hours and so much as the Natural is less than the Mean so much is that Day wanting of 24 Hours long But Men may now well spare themselves the trouble of doing this in regard that Tables of this nature are already published by divers excellent and learned Men As first by Mr. Hugens Printed Novem. 29. Of the Philosophical Transactions Secondly by Mr. Flamsteed commonly made use of by Mr. Tompion Printed also in Parker's Almanack Thirdly by Mr. Molyneux in his Sciothericum Telescopicum or ingenious Tract of the Telescope Dial. Fourthly by the learned Dr. William Salmon in his Almanack for this Year 1694. And fifthly by Mr. Samuel Watson the curious Contriver of that rare Celestial Orbitery now in the present Queen Mary's possession in each of which the Equations are nearly enough the same for substance as you will soon find by substracting any of their Numbers from the greater next it and 't is not material which you choose provided you understand them rightly but for my part I believe from good Experience there are not many that truly do this and therefore having for some Reasons which I shall not now mention made choice of Mr. Hugens's Equations for the Uses intended in this Work I have thought fit to cast them into such peculiar Forms of my own as I judge more plain and natural than they are in the Form in which I find them published in the Philosophical Transactions and I believe will by the generality of them that are possest of Royal Pendulums be better understood too Now in order to understand rightly the first Equation Table for length of Days take notice that the first Colume contains the Days common to every Month the other 12 Columes belong to the Months whose Names are set over them in the which D 24. denotes which Days in the Year are just 24 Hours long and where you find red Figures there the Days are so many Seconds of Time above 24 Hours long as the Figures express and where-ever the Figures are black there the Days want so much of being 24 Hours as those Figures in Seconds of Time do amount to so that by the Colour of the Figures you may discern at what times the Clock will naturally gain or lose and by the sum thereof you will know the time so lost or got each Day The Table being thus briefly explained I shall now shew how thereby to adjust a Royal Pendulum so exactly as that its Diurnal or Daily Revolutions which is that of its twice 12 Hours going may be equal to the true 24 hour-Hour-Day To do this let the Clock be set right to the Sun and note the Day on which 't is so set then let it continue going till you find the Time given by the Sun and that which the Clock shews visibly to disagree observe then how much the difference is that is how much 't is either too fast or too slow then count how much the whole number of Seconds amounts to included between the two Days of your first setting and last observing save one by allowing 60 Seconds to one Minute of Time and if the difference between the Clock and the Sun be equal to what the sum of Equations so cast up amounts to then is the Pendulum very well and truly ajusted But in doing this that is in summing up the Equations contain'd in the Table you must be sure to observe as I said to take in the Equation of the Day on which you set it and leave out that which belongs to the Day of your last observing for should the last be taken in they would make the sum of Seconds lost or got to be so much more than the truth and if it hath both got or lost during the time it has gone as it sometimes may happen when the Sun appears not of a long time to make an Observation then you must substract the lesser sum of Equations from the greater and the Remainder shall shew the true time lost or got as if the gaining Numbers be 20 and the losing 15 then the true time it should have got is just 5 Minutes But if the Clock have gone more too fast or too slow than the sum of the Equations in the Table amounts to then must the Motion of it be altered accordingly by screwing up the Bob or making the Pendulum shorter in case it has gone too slow or by letting the Bob down longer in case it has gone 100 fast and then having set it true to the Sun a second time try it again as you were before directed and if its disagreement with the Sun be not yet answerable to the sum of the Equations belonging to the time it has gone in let the Bob be rectified a second time and let the Clock be set a new and thus continue to do till you find its difference with the Sun to be nearly equal to the sum of Equations contain'd in the Table Now when the Clock is by this means adjusted right its Daily Revolutions or each 24 Hours time of its going will be equal to the true 24 hour-Hour-day or the just 365th part of a Year for if a Year be exactly divided into 365 parts each of these parts will be equal in length to the 24 Hours motion of a welladjusted Pendulum and the Motion of a Pendulum so exactly regulated will be such that if it be at any time set right and so let go the whole Year about it will the same Day Twelve-month agree nearly with the Dial to which it was set a Year before But yet in its Course of thus going a whole Year round 't will sometimes be found to differ very much from the same Dial 't was at first set to and these various Differences which its Motion will be subject to will still be agreeable to what the nature of the time was 't was set in For set at one time of the Year t' will be always more or less too slow till the time of its coming right the same Day Twelve month Set at another time 't will go always too fast till just the same Day Twelve month Set at some other time 't will go sometimes too fast and sometimes too slow the Reason of which is plain and evident by the Table of Equations that gives the length of natural Days For it appears by that that in all that Space where black Figures are
found there the Clock will still go too slow because the Pendulum Day is longer than the Natural Day On the contrary where the red Figures are found there a well adjusted Clock will go always too fast because there the Pendulum Day is shorter than the Natural Day and by consequence is finish'd before it Now 't is plain that if a Clock be set right to the Sun the First of February it must go all the Year after too slow because the losing between that and the Fourth of May is so much that it never gains it up till the very last part of its Years going On the contrary if it be set right the Twenty third of October it will gain so much by the last of January as no Loss shall afterwards countervail but that in the very last part of its Years going between the Sixteenth of July and the Twenty first of October 'T is likewise as plain that if a Clock be set right the Fourth of May 't will then in the time of a Years going be both too fast and too slow for the gaining at first being less than the next losing it will be too slow by the Twenty first of October though 't was too fast the Fifteenth of July and the like will happen if it be set right the Seventeenth of July for the losing that follows being less than the next gaining between October 24 and January 31. it must by consequence be sometimes too fast and sometimes too slow So that as a Clock may happen to be set it may in some considerable time of going be almost half an Hour too fast or half an Hour too slow though as to its own Motion it go exact and true as it should do and for this there is no help unless you understand well the nature of Time and know when and in what manner to set the Clock so as that for some good length of time after he may so humour the Sun's motion as never to be very far distant from it but sometimes too fast a little and in a little time fall back again as it were and so come to be right therewith and then in a little time after be a little too slow Now therefore in order to the reducing of the Motion of a well adjusted Clock much nearer the time given by the Sun than as yet any known Rule will direct us I have with great Care and Pains Composed a Second Table of Equations that shews how a good and well adjusted Pendulum may be kept all the Year round within a great deal less for the most part than 3′ 45″ of the time given by the Sun or the 4th part of a quarter of an Hour which is so small a matter as not to be perceived in common business Now in the explanation of the Second Table note That the First Colume contains the Days of every Month the other Twelve Columes belong to the Twelve Months of the Year whose Names are plac'd over them the Black Figures in any part of the Columes shew where and how much a Clock in the Natural Course of its Motion according to the design of the Table will lose or go too slow the Red Figures shew in what parts of the Year and how much in Minutes and Seconds of Time the Clock will go too fast As for the Days on which you find this Character ☉ those Days I call Rectifying Days because on them the Clock is still to be new set in order to keep it the better within the Limits design'd by the Table The Table thus explain'd I shall come now to shew you the Uses that may be made thereof And first I will shew you how by the Table also as well as by the first a Clock maybe adjusted now to do this Let this Clock be set to the Sun on any Day that is not a Rectifying Day observing this always to set it so much too fast as the Red or too slow as the Black Figures do express and then let it go for any considerable time provided it be not beyond a Rectifying Day and note whether its gain or loss be at any time equal to what the Table allows if it is then the Clock is truly adjusted but if it have lost or got more or less than it should do then rectifie the Bob by making it shorter if it have gone too slow or screwing it down longer in case it has gone too fast then set it anew and observe it a second time continuing your altering of the Bob and new setting till you have brought it to rights For example Suppose you set it the Sixth of January you must upon this Day set it too slow by one Minute fifty two Seconds because the time is there set down in black Figures let it go till the 11th of February on which Day if it be well adjusted it must be 2′ 9″ too fast because that sum of time is there set down in red Figures but if it should happen to be too slow or too fast for that time as suppose 10 Minutes too fast instead of 2′ 9″ you must then adjust it nearer by screwing the Nut of the Bob down lower or making it longer by what means soever the same is to be effected then set it anew just so much too fast as the Table for that Day does allow and so let it go till the 4th or 5th of March on which Day observe it again and correct what you find to be amiss in the Motion Note hear that in adjusting by this Table you save your self the labour of casting up the sum of those Equations that belong to the time the Clock has gone in and by consequence the work of adjusting will be easier done by this than by the former Table When the Clock is well adjusted it may then be kept the whole Year about as near the true time as the design of the Table allows of by the following method about 12 a Clock on any Day which is not a Rectifying Day set it so much too fast or too slow for the Sun as the Equation in the Table for that Day comes to that is too slow if the Figures are black or too fast if the Figures are red then let it go on till a Rectifying Day comes which is known in the Table by this mark ☉ upon which Day about Noon set it backward from the place where the Hand then stood if the Figures on that Day are black or forward if they be red so much in time as the Figures express and observe to do the same upon every other Rectifying Day and then if the Clock be well adjusted it will go in all the intermediate parts according to the time given by the Table Take one Example to make this plain Suppose you have not an Opportunity to set it till the 18th of January the Equation for that Day is one Minute 24 Seconds too fast because the Figures are Red let it therefore be set
so much too fast for the Sun and let it go till the 8th of March on which Day about 12 a Clock set it forward from the Place the Hand is at 7′ 29″ because the Figures are red and then instead of being too slow as it before was it will be made to be 3′ 45″ too fast let it go till the 31st of that Month and then set it again forward 7′ 16″ after which on the 4th of June set it back 5′ 8″ because there you find Black Figures On the 22d of August set it also forward 7′ 23″ and on the 12th of September 7′ 17″ set it forward likewise on the 8th of October 5′ 20″ and also on the 15th of November 7′ 20″ likewise on the 3d of December let it be set back 7′ 28″ and on the 18th 7′ 3″ and on the first Day of the next Year 7′ 8″ And thus with a very little Pains and Trouble you may keep a Clock near the true Time of the Day by a more easy Way and Method than has at any Time been practised heretofore But in case you should miss rectifying your Clock on a rectifying Day then you must the next or any other Day following set him by the Sun so much too fast or too slow as the Nature of the Table requires and then he will again go on in that Order which the Design of the Table makes necessary that is he will then be capable of humoring the Suns Motion so far as that between being sometimes a little too slow and othertimes a little too fast 't will with a little Rectification be always within less than a fourth Part of a quarter of an Hour of the true Time In such Clocks as shew not Minutes the Time of setting must be guest at as well as you can Now the Reason of thus setting a Clock sometimes backward and sometimes forwards upon the rectifying Days is this If a Clock at the beginning of the Year be set to the Sun according to the former Directions it will be too slow by the 8th of March at Noon 3′ 44″ Now the Design of the Table being to keep the Clock so as that it shall at no Time disagree with the Sun above 3′ 45′ or the fourth part of a quarter of an Hour I then to prevent its being more too slow as it will if let go longer am necessitated to set it forward 7′ 24″ and then 't will be too fast for the Sun 3′ 45″ Now the Clock naturally losing at this Time of the Year it will again by the 31st Day be too slow 3′ 31″ Now the Clock being still naturally inclined to lose I therefore to prevent his being above 3′ 45″ too slow set him again 7′ 16″ forward from the Place where the Hand then stands and so he is again too fast for the Sun 3′ 45′ which is the most that I suffer him to differ from the apparent Time Now after this he going on for about 9 Weeks will the 4th of June be too fast 1′ 23″ at which Time I set him back 5′ 8″ that so he may be now 3′ 45″ too slow for by thus doing he will continue going the longer before he will require to be again new set which next happens to be August 22d which is above 11 Weeks Time Now the like Reason is the Cause of his requiring to be set anew in any other Place or Part of the Year And here I think fit to add one Caution to those that desire to adjust their Clocks very nicely and that is that among Dials they make use only of the horizontal or brass Dials which are fixt on Posts for no other can possibly give the Time so near the Truth neither on that should they make use of above one certain Hour and the nearer Noon that is the better for 't is a difficult thing even for the best Masters in this Art to draw a Dial so true as to contain an equal Time between all its Hours which though in other Cases it be not very material yet in this of adjusting a Clock it may cause a considerable Error Besides few Dials are fitted truly to the Latitudes in which they stand and if we could be certain that all were right as to these Particulars yet no Human Art can prevent the Sun's Refractions which as they make his Body appear much bigger when near the Horizon so they make him for a good part of the Day to shew to us higher than really he is and that must cause him to give a false Shadow on the truest Dial so that these particulars considered together 't is plain that there can be no true account taken of the Time till near Noon or 12 a Clock and he that watches for that Moment need not matter the falsness of the Dial wrong Latitudes nor Refractions neither because upon the Meridian let the Sun be higher or lower yet it still gives you the true 12 a Clock But in regard 't is so very hard to distinguish to a Minute by the Shadow of the best Dial small ones not admitting of minute Divisions and in large ones the Haziness or Faintness of the Shadow renders a minute difficult to be discerned exactly 't will therefore be better if instead of a Dial you make use of the following Device which I call a Meridian Cranny Take then Two plain and flat Plates or Boards about six or eight Inches square joyn them so close as that an old Groat or a Six Pence at the most may but pass between them let them be then fixed so as that the Chink or Cranny between them may respect as near as may be the Meridian or true South Point this will plainly give you the Time to half a Minute and less if you are careful to watch for the very first Beam that by the Sun 's coming to the South shall be darted through it which may be perceived in a Moment by the help of a smooth Board or Plate of Brass made black and placed near it on the North Side to receive the Light by this means the true Time of the Sun 's coming to the very same Point on the Meridian may be more exactly obtained than it can be by the best and truest Dial except such a one as is described by Mr. Molyneux in his Sciothericum Telescopicum But now although the true Time of the Sun 's coming to the South may by this means be more nearly obtained yet you will for all that find the Work of truly adjusting a Clock to be exceeding difficult especially to do it precisely when you have already brought to go prety nearly tru and this has made some to censure the Equation Tables as false because they could never adjust a Clock so as to acord therewith exactly or come Right the same Day twelve Month with that Dial to which it was set a Year before Now that I may do right to Truth I affirm that this proceeds not from any material
it went too slow then conclude that that Division has altered it in a Day six Minutes and by consequence if you turn it two thirds back it will make the Watch go right as it ought to do I shall only add one more Note concerning Spring Clocks or those that go with Crown-wheel Pendulums and that is that although as yet they have not been capable of keeping so exact a Time as the Royal Pendulum yet if the Pendulum of a Spring-Clock instead of playing upon an edge as they now generally do were hung upon a String about two Inches long and that Spring were so filled according to the Rules of Art as that in the Pendulums vibration it might bend proportionable to the Cycloid its Center of Motion would then still shorten as the way of its vibration grows longer and by consequence the farther the Pendulum swings out the quicker would its return be and so all its vibrations whether longer or shorter would be performed in the same equal time and then its Motion would be much more steady than it is and be nearly as exact as that of a Royal Pendulum The manner of Rightly fixing or Setting up Pendulums to go well THE Difficulty of setting up Pendulum Clocks rightly in such places where the help of the Clock maker cannot be had is the Reason that many Gentlemen who live far off from London are as yet unfurnished with them and it also too often happens that Clocks who at first have been set up well as to matter of going have by accident been misplac'd or jumbl'd awry and so are made to stand still and become useless meerly for want of Skill in the Owner to put them again to rights in order therefore to Enable all Persons not only to Set a Pendulum Clock up Rightly but also to Reduce him again to rights when by accident he is misplac'd I have here made publick the following Directions First Let the Workman by whose Hands the Clock is made set him upright at home in his own House and there having made a through tryal of his going let him then stop the Pendulum and when 't is perfectly at rest let him fix or drive into the back of the Case a strong Stud of Brass or Iron with the end turn'd a little up which he must place so as that the Beak that turns up may stand exactly under the lower end of the Pendulum Rod and this will sufficiently direct you how to Set him up in any other Place For when the Clock is to be Set up by him that buys him 't is but placing the Case so that the end of the Pendulum Rod may hang just over the Beak of the Stud and then he will stand upright as he did before in then Workman's Hands But in case this provision be not made then the Rule to do it by is this Set the Clock up in the place 't is to stand in let the Peâ—â—ulum and the Pulleys which usually are fix'd to the Case be unfastned hang on the Weights and set the Pendulum a going by making of it swing between the Sides of the Case now if when the Clock is thus set a going you find the Pendulum to beat equally that is if there be the same Distance of Time between all its Blows which an attentive Ear will soon discover then does the Clock stand well and you must make him fast to the Place he stands against But if you find one Blow Beat in less Time than the other then you must a little incline the Case to that Side which the Pendulum plays to when he strikes the shortest Blow and then you will find him to Beat more equal and when you have inclin'd the Case so much that you find exactly the same Distance of Time between the Blows or Vibrations then the Clock stands right for Going and you are to fix Him that He may stand firmly in that Posture Now the Rule before given is general to all Pendulums for they all must stand so that the Beats of the Pendulum may be equally distant as to length of Time for otherwise if they stand awry so that one Blow or Vibration of the Pendulum is struck in less time than the other that Pendulum upon the least accident that shall happen will be apt to stand still and therefore great Care ought to be taken that not only Royal Pendulums but also Spring Clocks be set up exactly upright in the Places that they are to stand in and they never stand upright as they should do unless the Blows of the Pendulum beat equally Note That as a long Swing-Clock ought to stand so as that the Pendulum beat equally so he must stand so as that the Pendulum play free from the back of the Case for if it stand right in this respect the Rod of the Pendulum will all the way up be parallel or equidistant from the back-part Moreover take Care that the Clock be fix'd fast and firm that no Violence may justle Him out of his Place but if by Accident it should so come to pass you must then set Him again to Rights by the Rule before given from the exact beating of the Pendulum A Table of Crown-Wheel'd Pendulums shewing the number of Beats made in an Hour by any length of Inches and Quarters from One Inch to Twelve the Bob about an Ounce in Weight Inches Beats 1 22946 1 20524 2 18735 3 17345 2 16225 1 15298 2 18735 3 13837 3 13248 1 12732 2 12265 3 11852 4 11473 1 11131 2 10817 3 10528 5 10262 1 10014 2 9781 3 9569 6 9368 1 9178 2 9000 3 8832 7 8672 1 8524 2 8381 3 8242 8 8107 1 7989 2 7870 3 7764 9 7653 1 7544 2 7448 3 7349 10 7256 1 7167 2 7081 3 6998 11 6919 1 6842 2 6767 3 6694 12 6623 1 6565 2 6497 3 6431 The first Row of Figures are Inches the second are Quarters of Inches the Figures against each of these are the Beats that a Pendulum of that length make in an Hour For example 2 Inches beats 16225 Blows in an Hour and 3 Inches and a half beats 12265 and 6 Inches 3 quarters beats 8832 Divide any of these Numbers by 60 and it shews you the Beats made in a Minute multiply any of these by 24 and it shews you the Beats made in a Day A Table of Royal Pendulums shewing what Beats any Length makes in an Hour from 12 to 60 Inches the Bob 2 Pound Weight or more Inches Beats 12 6651 13 6393 14 6161 15 5955 16 5765 17 5591 18 5433 19 5288 20 5154 21 5030 22 4915 23 4807 24 4706 25 4610 26 4522 27 4437 28 4356 29 4281 30 4209 31 4141 32 4075 33 4013 34 3953 35 3897 36 3843 37 3790 38 3793 39 3691 40 3645 41 3600 42 3557 43 3515 44 3475 45 3436 46 3399 47 3362 48 3327 49 3293 50 3260 51 3228 52 3196 53 3166 54 3137 55 3108 56 3080 57 3053
Horological Disquisitions Concerning the NATURE of TIME AND THE Reasons why all Days from Noon to Noon are not alike Twenty Four Hours long In which appears the Impossibility of a Clock's being always kept exactly true to the Sun With TABLES of EQUATION and Newer and Better RULES than any yet extant how thereby precisely to adjust ROYAL PENDULUMS and keep them afterwards as near as possible to the apparent Time With a TABLE of PENDULUMS shewing the BEATS that any Length makes in an Hour A Work very necessay for all that would understand the true way of rightly managing Clocks and Watches By JOHN SMITH C. M. To which is added The best Rules for the Ordering and Use both of the Quick-Silver and Spirit Weather-Glasses And Mr. S. Watson's Rules for adjusting a Clock by the Fixed Stars LONDON Printed for Richard Cumberland at the Angel in S. Paul ' s Church-Yard 1694. Licensed January 17. 1693 4. D. Poplar TO THE READER THE Design of these Papers is not to cover the Clock-Makers Imperfections as some have suggested but plainly to demonstrate thetrue Reason of those unavoidable Variations between the Time given by the Sun and that of a good and well-adjusted Clock and to give such Directions as may yet reduce them to a nearer Agreement in Time In doing of which I have endeavoured to express my self in such Words as I thought most proper to inform the Reader 's Understanding What is here exposed to publick View is not the Result of mere Speculation but of Skill and Practice for as it has been my Profession so it has been my Care and Concern also to understand exactly not only the Nature of a Clock but that also of its Motion and the Result of my Discoveries As to the latter you have very briefly laid down in the following Discourse and I assure you that I have not spoken any thing of the Truth of which I was not first well satisfied The Style indeed is purely Mechanick but this is no Argument against its usefulness since in Books Men ought not so much to heed who 't is that speaks as what is spoken He always writes best that from his own Knowledge and Experience can inform the World of something that 's advantagious to Human Life which was not known to Mankind in the Times before Farewel A Table of Equations Shewing the true Length of every Natural-Day or the Seconds of Time that they are either Longer or shorter than XXIV Hours By JOHN SMITH C. M.  Jan. Feb. Mar. April May June July Aug. Sept. Octo. Nov. Dec.  ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ ′ ″ 1  22 D 24  17  17  3  11  7  9  20  14  9  20 2  23  2  17  16  3  11  7  9  20  14  10  30 3  23  2  18  16  1  12  7  9  21  13  10  30 4  24  4  18  15 D 24  12  6  11  21  13  10  30 5  2◠ 4  18  15 D 24  12  6  12  21  13  11  30 6  2◠ 4  18  14  1  13  6  13  21  13  12  30 7  19  5  18  14  2  13  6  13  22  13  12  30 8  18  5  18  14  2  13  5  14  22  11  13  30 9  17  6  18  14  3  13  4  14  22  10  15  30 10  16  8  18  13  3  13  4  15  21  9  17  30 11  16  8  18  13  3  13  3  15  21  8  17  33 12  16  9  18  12  4  13  2  15  20  7  18  30 13  16  9  19  12  4  13  2  16  20  7  18  30 14  16  10  19  11  5  13  1  16  20  6  19  31 15  15  10  20  11  5  13 D 24  17  20  6  20  31 16  1◠ 11  20  10  6  12 D 24  17  20  5  21  31 17  13  12  20  10  6  12  1  17  20  4  22  31 18  12  13  20  10  6  11  2  18  20  3  23  30 19  11  13  20  10  6  11  3  18  19  3  23  30 20  11  13  19  10  7  11  4  19  19  2  24  30 21  10  14  19  9  8  11  4  19  19  1  24  30 22  9  14  19  7  8  11  4  19  19 D 24  24  30 23  8  15  19  7  9  10  4  19  19 D 24  25  30 24  ◠ 15  19  7  10  10  5  19  18  1  25  30 25  5  15  19  6  10  10  5  19  17  2  25  28 26  4  15  19  5  11  10  5  20  17  2  25  23 29  ◠ 16  19  5  11  10  5  20  16  3  26  23 28  ◠ 17  19  5  11  9  6  20  16  4  26  27 29  ◠   18  4  11  9  7  20  16  6  27  27 30  1    17  4  11  8  8  20  15  7  28  25 31 D 24            9      8    24 The Character D 24 shews what Days are truly 24 Hours long the Red Figures shew the Seconds of Time that those Days on which they are plac'd are longer than 24 Hours and the Black Ones
Defect in the Tables but either from their not rightly understanding which way to perform the Work they took in hand or from some other unavoidable Accidents with which Nature too often sportsher self in the Disappointment of Men's Designs 'T is probable indeed that there may be some Error in the Tables as suppose a Minute at the most this signifies little as to the Business in hand and if it did yet we ought to value a Guide that will bring us in sight of the thing we aim at rather than follow an apparent Uncertainty as I have proved those do that would attempt to adjust a Clock by barely setting of it true to the Sun there must be grains of Allowance given for Human Infirmity for no Man that understands himself dares pretend to an infallible certainty in things so much above him as those are about which Astronomy is conversant there 's no measuring the divisions of the Celestial Spheres with Scale and Compasses all our Knowledge in things of this nature is derived from Observations made by Instruments which we know is so difficult to be done exactly that if ten Men should attempt at the same Time to find out the Sun's Declination the Ground work on which Equations are built perhaps they would all differ as to their Accounts thereof Now we know if the Premises are never so little out the Conclusions drawn therefrom can never be exactly and critically true Therefore granting the Possibility of some inconsiderable Error in the Tables of Equation yet still we are sure of this That they come so near the Truth that perhaps no Man can here after Mend 'em and the Work of adjusting a Clock is thereby made a hundred Times more easy than it would be to do it with out them Besides we see that the most learned in Astronomy agree all of them as to the mean thing namely That there is such a thing as Difference in the length of Natural Days and their Tables all agree as to the Parts of the Year in which these Differences happen they also accord very nearly so as to the Quantity of Time that any natural Day is longer or shorter than 24 Hours and therefore we may very well rest satisfied that there are no material Errors committed therein and perhaps could we demonstrate any Table of Equations to be really exact to a tittle yet this Work of adjusting a Clock truly would not be found more easy to do then than now it is for much of this depends not only upon the right understanding which way to perform best the Work we are about but on the Constant Temper of the Air as will hereafter appear But to the end that we may not be in the dark as to the true Nature of this Difficulty I affirm that it chiefly proceeds from the exceeding niceness of rectifying the Bob exactly when you have already brought the Clock to go pretty near the true Time as suppose for example that a Royal Pendulum were so well rectified that being kept going the whole Year round it should be just at the same Day Twelve Month but 6′ 5″ too slow for the Sun which some perhaps will account a great matter now this turn'd all into Seconds makes just 365 and by consequence the Clock has gone each Day but a Second of Time too slow Now by the following Table of Pendulums we find that a Royal Pendulum 41 Inches long each Blow of which is a Second of Time strikes just 3600 Blows in an Hour Now this Pendulum will go faster by 45 Blows in an Hour if screw'd up an Inch shorter which is faster in a Day near 1080 Seconds now if an Inch shorter makes a Pendulum go near 1080 Seconds in a Day faster 't will then require the Bob to be screwed up but the thousand and eigtieth part of an Inch to make it go in a Day but one Second faster or so much as the Clock is said to have lost which is so very small a matter that no Man living can by guess hit it exactly the least Turn that shall be given it may perhaps make it go ten Times as much too fast as it before went too slow Now to the end that this may if possible be done by some more certain Rule Method than any yet commonly known I will here make bold to propose a way by which this may be performed more exactly than heretofore and by which you may make a near Estimation how much a Royal Pendulum that strikes Seconds for this sort only is here intended ought to be made shorter or longer to go faster or slower a Second in a Day and the same Rule by which you know how to alter it one Second will direct you how to alter it 2 or 3 or more if occasion require it By the forementioned Table of Pendulums we find that a 41 Inch Pendulum goes 45 Blows which are all nearly Seconds in an Hour faster if screwed up an Inch higher and being let down an inch longer it then goes 43 Blows slower that is strikes so many Blows less in an Hour now if between these 2 Numbers we take a mean one which is 44 't will be suitable to the Lengths near 41 Inches for so many Blows will a Pendulum 39 and an half strike more than one of 41 Inches and an half long Now 44 difference in an Hour makes in a Day 1056. divide this number 1056 by the number of Turns which the Screw of your Pendulum makes in an Inch and the Quotient shall be the Number into which the Nut of that Screw must be divided now one of these Divisions turned about shall alter the Motion of that Pendulum a Second in a Day But to avoid the Trouble of thus dividing I have here added a Table by which knowing the Turns your Screw makes in an Inch you may by Inspection only know how to divide the Nut that belongs thereunto the Table reaches from 15 Threds or Turns of the Screw in an Inch to 40 within which Numbers I suppose all Screws will be comprehended that belong to Pendulums that strike Seconds The Table for dividing the Nut of a Pendulum Screw Turns Divisions 15 70 16 66 17 62 18 58 19 55 20 52 21 50 22 48 23 45 24 44 25 42 26 40 27 39 28 37 29 36 30 35 31 34 32 33 33 32 34 31 35 30 36 29 37 28 38 27 39 26 40 25 The Uses of the Table for dividing the Nut of a Pendulum Screw Find out how many Threds or Turns of your Screw are contained in an Inch by applying the Inch-Division of a Rule thereunto which number of Turns seek out among the first Row of Figures on the Left Hand and against it in the second Row you have the Number that the Nut must be divided into that belongs to that Screw Now the Nut turn'd about but one of these Divisions will alter the Clocks Motion a Second in a Day so that let the Screw
be finer or courser yet by this Table you may readily know into how many Divisions its Nut must be divided Note that if the Clock has got or lost in a Day above one Second then you must turn the Nut about so many Divisions as if it have lost in 60 Days 4 Minutes which is 4 Seconds in a Day turn it then upwards 4 Divisions and that will make it go 4 Seconds in a Day faster or so much Time as it had gone too slow And the like must be done for any other Number lost or got Now though this Rule be ten times more exact than any yet known yet for all that it may be yet found difficult to make a Clock go exact especially for a long time together for though a Royal Pendulum be the most excellent Contrivance in the World for exactness of keeping Time yet the different degrees of Rarity and Density in the Air does oftentimes alter the nature of the Pendulums motion a thick Air not suffering it to vibrate so freely nor so far as a thin Air does the Motion of the Pendulum may be also somewhat altered by the Oyl growing drier and thicker with which the Penets are moistned for when a Clock is clean and the Oyl thin and free from foulness the Pendulum plays differently from what it does when the Clock is foul and the Peuets dry and dirty But here you are to note That not withstanding the Royal Pendulum is subject to be altered somewhat in its Motion by the aforesaid Causes that 't is nothing in comparison to what happens in the common Crown-wheel Pendulum for these are apt to be varied ten times more than the other which still makes very much for the Reputation of the Royal Pendulum Since then the Air and Oyl and Dust are apt to cause the best Clock to go less certain than it otherwise would I have thought fit to propose a way by which it may be known when any thing considerable of this nature happens and that is thus Screw or fasten to the back of the Case a brass Plate with 2 sliding Indexes fitted to it that may be set exactly to the Compass which your Pendulum fetches and by that you may perceive whether your Pendulum alters in its Compass for should it do so in the time of your adjusting of it you will find it a very hard matter to rectifie it well and if nothing of this happens till it be brought to go compleatly true yet if the Compass of your Pendulum does afterwards differ you will certainly find it not to keep the same time it did when first adjusted and the best Clocks that are will sometimes be subject to these unavoidable Accidents But although those little Irregularities in the Motion of a good Pendulum may sometimes happen and prove some hindrance to the exactness of its Motion yet when you come to know how much it varies from the truth you may soon correct it by the foregoing Rules if you see occasion Indeed a constant Inclination to go either too fast or too slow argues rather a not being well adjusted at first for if it vary from the Influence of the Air that aptness to go false will continue no longer when the temper of the Air returns to its former state and then the Clock will return to its old pitch of Motion but if it happen through foulness which may be guest at by its having gone true a long time before then 't will continue to go Irregular till the Clock be made clean new oyl'd and put in order But when all is said that can be said on this matter if the Clock be a well made Piece of Work all these Alterations in the Motions will be so inconsiderable as not to be worth the noting if you observe constantly to set it according to the Design of the Second Table and Correct it once or twice a Year by the Sun but for base and ill Work no Art of Man can make that go exactly and well one Quarter of the time that the other will From all that has been spoken hitherto concerning the Royal Pendulum we may gather that the same Exactness of keeping Time is not to be expected in short Crown-wheel Pendulums Indeed if fuch are good Work they may be made to go very well but yet not so exactly as the Royal Pendulum for the shorter the Pendulum is the more difficult it is to adjust it exactly And when the adjusting part is done never so true yet the uncertainty that this kind of Pendulum is subject to in the Compass it fetches will not suffer it to keep so equal a Time as the Royal Pendulum the different Temper of the Weather will alter it very considerably if compared with the other and 't will also be sooner out of order in the going from the foulness and thickness of the Oyl that the Penuets are moistned with The best and easiest way to adjust such a Clock as this is by a Royal Pendulum already Rectified for a Standard to Adjust other Clocks by for when by that you have brought a short Crown-wheel Pendulum of which sort all Spring-Clocks are for the most part pretty near to the Truth take exact notice how much it differs from it in either one Day or two Days as you please then give the Bob just a whole turn about upward if it go too slow or downward if it go too fast and see how much that Turn will make it differ from the Standard above what it did before in a Day or two Days time Now knowing how many Seconds in a Day a Turn of the Bob will alter you may soon bring it to keep true time by turning it so many Turns or parts of a Turn about as shall answer the Time it has gone too fast or too slow As for those Pocket-Watches which are now so improperly called Pendulums there is less to be expected from them than from a Crown-wheel Pendulum for though this delicate Invention of the Ingenious Mr. Robert Hook does strangely Rectifie the Motion of the Balance yet must it not compare with either of the other as to the Truth of going for 't is the hardest thing in the World to make a Watch keep the same Time when laid on what part or side soever you will be pleas'd to turn it which rightly considered may reasonably obtain for them some grains of allowance All that I shall add more is that if you know but nearly how much the turning of each Division on the Justning Plate will make it go either faster or slower you may then at any time with greater certainty adjust it to a Standard Pendulum and this any one may attain to with but the trouble of a little Observation for if the Watch for example have gone too slow two Minutes in a Day turn the Justning Plate about one Division faster and if that Division make it go four Minutes too fast in stead of the two which before