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 [Page 3] 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.

[Page 4] 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 'tis 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 'twill 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; [Page 5] 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. 'Tis 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 [Page 6] 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.

[Page 7] This, an exact Table of the Sun's Right Ascensions does demonstrate, for by that 'twill 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 'tis 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 [Page 8] 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 Cross­ways 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 'tis 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.

[Page 9] And accordingly 'tis 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 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 [Page 10] 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 'tis 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 [Page 11] 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. Tis 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 [Page 12] 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.

[Page 13] 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, [Page 14] 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 'tis 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 'tis pos­sible [Page 15] 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 'tis 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, 'twill 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 [Page 16] 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 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: [Page 17] 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 'tis 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 [Page 18] 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, [Page 19] may be equal to the true 24 Hour-Day: To do this, let the Clock be set right to the Sun, and note the Day on which 'tis 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 'tis 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, [Page 20] 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 [Page 21] 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-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, 'twill sometimes be found to differ very much from the same Dial 'twas 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 'twas 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 [Page 22] time 'twill go always too fast till just the same Day Twelve month: Set at some other time, 'twill 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 'tis 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 [Page 23] going between the Sixteenth of July, and the Twenty first of October. 'Tis like­wise as plain, that if a Clock be set right the Fourth of May, 'twill 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 'twas 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 [Page 24] 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, [Page 25] 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 [Page 26] 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 [Page 27] 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.

[Page 28] 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 [Page 29] 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) 'twill, 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 [Page 30] 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 'twill 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 [Page 31] 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 'tis 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 [Page 32] false Shadow on the truest Dial; so that these particulars considered together, 'tis 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 'tis 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; 'twill 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 [Page 33] 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 [Page 34] 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 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: 'Tis 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 [Page 35] 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; [Page 36] 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; [Page 37] 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 'twill 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 [Page 38] 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, 'twill 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, [Page 39] 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.

SInce 'tis so easy to be furnished in London with both these Sorts of Weather-Glasses, I judge it need­less, now, to give any Directions about their Making; only thus much I shall take notice of, That the Goodness of a Baroscope or Quick-silver Weather glass does consist wholly in the Largeness and Depth of the Cestern below, and the Quantity of Quick-silver contained there­in. Now, that you may know whether a Cestern be large enough, cause the [Page 62] Workman, that makes it, to fill the Tube about 3 Inches, with part of the Mercury designed for its Use; fill the Cestern with the best part of the rest that remains, and then clapping across the Brims at the Cestern, a Gage, that shall have a Pin drove into it, reaching just down to the Surface of the Mercury, let the Mercury, which before filled the 3 Inches of the Tube be put therein; and if you find it not to raise the Mer­cury in the Cestern above the thickness of a Six Pence, then is the Cestern of a sufficient Capacity.

A Cestern of about 2 Inches and a half Diameter, generally, is large e­nough for any Tube, that has not a Bore above a quarter of an Inch Diame­ter, which is as large as is needful; for if it be so large, as that when the Quick-silver in the Glass, by rising and falling, do raise that in the Cestern too conside­rably, then you will not constantly have that Distance between the Surface of the stagnant Mercury below and the numbred Figures on the Register Plates of the Weather-Glass; for if the Glass be a good Glass, measure that Distance when [Page 63] you will, and you will always find it just 28, 30 or 31 Inches from the Divisi­ons so numbred to the Superficies of the Quick-silver, in the Cestern below.

Note likewise, That the End of the Tube ought to be emerst at least three quarters of an Inch within the Cestern of Quick-silver, else the Air will be in danger of getting up into the Body of the Tube: For this reason there ought to be at least 28 Inches and 3 quarters Distance between the Figure 28, on the Register Plate and the Bottom of the Cestern.

Now, in order to set the Weather-glass up, let the Frame be first fixed fast to the Place you design for it; which is done by first driving therein a Nail or Tenter-hook, fitted, for that purpose, upon which the Frame is to be hung or suspended, and, with a Screw, let the Bottom thereof be firmly fastned to the Place, or, in want of a Screw, by some­what else that may perform the Work well.

Then make the in side of the Glass Tube very clean and dry, by means of a bright and clean piece of Wire, made [Page 64] red hot at the End in a Fire, and turned down for about half an Inch, like the Eye of a Needle, through which draw a long slip of fine softLawn Paper, which I find best for this purpose, because 'tis not apt to leave any Lint behind it, as Linen Rags will; which Lint will al­ways cause a small Bleb of Air to remain round it, so that in spite of all your Care and Pains you shall never obtain a per­fect fine Cilender of Mercury.

With this Paper, in the Eye of the Wire, let the Bore of the Tube be well cleansed, by drawing of it to and fro, from one End to the other, till you are sure that you have not mist any Part thereof: And if you find, when you have drawn it out, that the Paper be any whit soiled, put in a fresh Piece, and after that another, till you find the Paper come out as clean at it went in, for should any Foulness or Moisture be left behind the Mercury will not play freely up and down.

When you have cleansed the Tuble very well, then prepare and make the Mercury fit to fill it with, which you are to do in the manner following.

[Page 65] Take an earthen Bason or Dish, and put therein half a Sheet of clean white Paper; then put the whole Quantity of Mercury which the maker of the Ba­roscope has fitted thereunto, and having put it into a clean linen Cloath, strain out gently so much of it as you judge will fill the Bore of the Tube and no more, for should you twist and wring the Cloath, the Quick silver is in, to strain it all through, you will, in so do­ing, find much Lint fall off from it, and foul the Surface of the Mercury strain'd out, so that you cannot fill the Tube with it without conveying some of the Lint along with it, which will spoil the perfect smoothness of the Mercurial Cylender within the Glass.

When you have purely strained out about one half of the Quick-silver, take the Tube, and resting the closed end in some large wooden or earthen Vessel, to save the Mercury, should any spill in the filling; then graspe the open end of it between the Root of the Thumb and Fore-finger, somewhat low, that the hollowness between may serve instead of a Tunnel; then fill the Tube with [Page 66] the pure clean-strain'd Quick-silver, by by taking of it up with the clean Bowle-end of a Tobacco-Pipe, or by putting of it into the Cestern-Glass, first wiped clean, and so pouring of it in till it be full, within a quarter of an Inch of the Top of the Tube.

Then, to cleanse it from Air and Wind-Blebs, stop the End with your Finger, and raising the other End up, somewhat above a Level, let the Air, included in the empty Space, at the open End, rise up very gently towards the Top or seal­ed End, and this will take into it self all the other Blebs of Wind that lye in its Way; and when this Bubble of Air is risen up quite to the End of the Tube, let it return again, by depressing a lit­tle that End which before was upper­most, turning the Tube also, at the same time, that the Buble may take in its way all the Blebs of Wind that may yet re­main on the other Sides of the Glass; and, thus, by turning the Tube a little, and making the Bubble pass and re-pass from one End to the other, the Cylen­der of Quick-silver, will be at last clean­sed from all those little Blebs of Wind [Page 67] that appeared by the Sides of the Glass, any of which, should they remain in, would in Time work themselves up into the Head of the Tube, and be very injurious to the Quick-silvers true Mo­tion.

But if, as I noted before, the least Moisture or Lint be left in the Tube, the greatest Care and Skill that can be used will not be able so perfectly to cleanse it from Air, as not to leave the least Speck remaining: In which Case there is no Remedy but to empty the Tube and cleanse it a new, according to the Method before prescribed. Note, when the Tube is perfectly cleansed from Air, then turn the open End up, and fill it quite full with Quick-silver.

Then Wipe the Cestern very clean, and set it in its Place, in the Cestern-Box, then put therein all the remaining part of your Mercury, which you need not take care to strain, for Dust or Foul­ness in the Cestern signifies little; then take the Glass Tube, filled as before was taught, and stopping the End of it with your Finger, invert it so that you may immerge or put the End, stopt with [Page 68] your Finger, the more easily into the Cestern Mercury, which ought to be done so that both Glass and Finger may touch the Cestern Bottom at the same time, keeping the Tube in the mean while as near an upright as you can, then of a suddain take away the Finger you stopt it with, and as suddainly, at the very same instant of Time raise the Tube just upright, the which, if you perform nimbly and well, will be done before the Mercury in the Tube is all sunk down to its lowest station, and so the Tube will be put up well, without any admittance of outward Air.

But in case any Air should get into the Tube, in your attempting to set it up in its Place, as sometimes happens, then you must take it down again, by getting your Finger under the open End, to stop it, before you lift it out of the Cestern Mercury, and so repurge it of the Air got in, according as you were taught in the foregoing Method, and then try a­gain to set it up well; and if you should miss this second time, then try a third, for Experience will at length make you perfect.

[Page 69] When the Tube is put up observe whether it stand well in the Cestern, for some Cesterns are so ill plac'd that the Tube, by reason of its being set too near the Side, cannot be well surrounded by the Cestern Mercury, by which means the Air will be apt to insinuate it self, and get up into the Tube, and spoil the Mercury's true Motion.

If the Glass be already adjusted to your Hand by the Workman that made it, you have then no more to do but to put into the Cestern all the Mercury that remains when the Tube is filled; but in case the Glass be not already adjusted, or that some part of the Quick-silver should be spilled or lost, you must then provide to adjust it, according as the Rules of Art require: Which is done thus, Take a small streight Rod of Wood, of the just length of 28 Inches, this is generally called, An adjusting Gage, put one End of it into the Ce­stern, and raise the other up till it touch the Division on the Register-Plate num­bred with the Figure 28; then observe whether the Quick-silver in the Cestern does touch the other End, if it does [Page 70] not, you must put in more Mercury, till it does; but if the Mercury be already above the lower End of the Gage, then you must, with the clean Bowle-end of a Tobacco-Pipe take out so much of the Quick-silver as that that in the Cestern may but just touch the End of the Gage, and then is the Glass compleatly and well adjusted.

In case you have occasion to remove a Baroscope, or Quick silver Weather-Glass, out of one Room into another, you need only loosen the Frame and take it from the Place to which it is fixt, and so, upright, in the same Posture it stood in, let it be carefully conveyed by Hand, so gently, and with a careful Step, that the Quick silver may not surge over the Sides of the Cestern, another Man, in the mean Time, making all things fit to set it up in its new Place, according to the Directions before given for setting of a Weather-glass up.

But here note, That if the Baroscope be to be removed from one House to an­other, it must be quite taken down: In doing which observe, Frst, To incline the Tube so low as it stands in the Ce­stern, [Page 71] that the Quick-silver may rise up quite to the top, then lift it out of the Cestern and let the Mercury run out, for should you lift the Tube out in the Po­sture it stands in, when going, the Mer­cury, by the Force of the Air's Pressing in at the open End, would fly up to the top with such Violence as to endan­ger the breaking off of the top of the Glass.

Note, That if the Glass Tube be not well purged of Air, the Quick-silver will, by long standing, be apt to move contrary to the true Nature of a Baro­scope, by reason that the Air which has been left in the Tube, has by de­grees got up into the Head or empty Space of it, where being expanded by any accidental Heat of Air, it occasions the Mercury to sink, though the Weight and Pressure of the Air be no ways alter­ed; this is observed by Dr. Beale, Phyl. Trans. numb. 9. p. 157. That a Baro­scope ascended higher in the cold Morn­ings and Evenings than at Mid-day; which doubtless proceeded from the a­foresaid Cause; for if you leave, for tryal-sake, a little Bubble of Air in the [Page 72] Head of the Glass when you set it up, you will find the same Defect, as Dr. Beale has observ'd.

Wherefore 'tis necessary if you are doubtful of the like, to Rectifie your Weather-Glass, when it has been set up about a Twelve Month; which is done by taking of the Tube down, and re­purging of it of Air, as you were taught in first setting of it up: but that you may not be put to more trouble than needs, you ought to be first certain that your Weather-Glass does want Rectify­ing, which you may know thus; Let the Tube as it stands in the Cestern be stoop'd down so low, till the Mercury rise quite up to the Head, and if you perceive a Bubble of Wind at the top above the Quicksilver, that is the cer­tain sign of its wanting to be new Re­ctified; clap then your Finger under the open end in the Cestern, and take it out and purge out the Air, as before was directed, at its first setting up.