THE Vibrations of a long and weighty Pendulum, although it be justly esteemed to be the most exact and steady of all Natural Mo­tion; yet is it not capable of regula­ting the Index of a Clock to such a pitch of Perfection, as continually to point out the same time that shall be given by the Sun on the Lines of an exact and true Dial.

The truth of which is sufficient­ly [Page 2] made evident by the most exact and critical Experiments: For, let all the moving parts, of a Pendulum Clock, be contriv'd with the great­est Skill and Judgment, and then made up by the most cunning and curious Hand, and after all this be adjusted by the utmost Care and Di­ligence of Man; yet shall not the Motion of it correspond so continu­ally with the Hours given by the Sun, but that in some considerable quantity of Time you shall be sen­sible of gain or loss in the Motion of it.

The true Reason of which Va­riation proceeds not from any De­fect that may be attributed to the Motion of the Pendulum, (of whose exactness we are by many curious Experiments sufficiently sensible;) but rather from an Unequality le­gible [Page 3] and easie enough to be dis­cover'd in the diurnal Motions of the Sun.

Vulgarly, for the most part, the Sun is indeed accounted to be the Standard and Measure of all equal Time, and Men generally esteem Natural Dayes to be all of one length, as containing the just time of 24 Hours; but upon a more ex­act and curious Scrutiny, these vul­gar Suppositions are found to be false: For, neither is the Sun's Mo­tion found to be exact, being in ap­pearance to us, sometimes swift, and at other times more slow; nor are the Dayes themselves, accounted from Noon to Noon, of equal lengths, some Dayes containing more Time than some, and others less; there being a natural necessi­ty, that the unequal Motions of the [Page 4] Sun should produce such inequali­ties in the lengths of those natural Days that are bounded by it.

For a natural Day being com­posed of that space of Time, in which any one Place or Point of the Earth is moved in its diurnal Motion East-ward, from the Meri­dian Sun of any one Day, to that of the next; it will follow, that these Dayes can never be equal, un­less the Sun in that space of Time be so mov'd in her annual Orb, as to cut out equal Divisions on the Aequinoctial upon the Meridian of every Day; which Divisions so in­tersected, are by the Learned term­ed, the Right Ascensions: For when­ever the Right Ascension either of Sun or Star is mentioned, we are to understand by it, those Degrees of the Aequinoctial that are intersect­ed [Page 5] by that Meridian, on which ei­ther Sun or Star have then their place.

But that the Sun between each Meridian does not move such just and certain Spaces in her own Orb, as thus to intersect equal Divisions on the Aequi-nox, upon every Me­ridian, needs no other evidence than what either Calculation it self af­fords, or Globes by an occular In­spection demonstrate to us. By Calculation, if an exact Table of Right Ascensions be composed, for the Meridian, or Noon-time of each particular Day, there will be found almost a continual difference in the length of those Intersections that are made by the Sun on the Aequi-nox, upon every Meridian; so that there will by this means be found no­thing but an almost continual une­qualness [Page 6] in the Right Ascensions▪ Which will be the more apparent, if you make an Estimation of the Right Ascensions of about 10 Dayes together, and compare that with those of the same Number. The like will appear plainly, if tryed on the Globe; for if you mark out on the Ecliptick any 10, or more Day's Motion of the Sun, accord­ing to his true place found out in an exact Ephimeris, and passing these 10, or more Days motion under the Me­ridian, noting what Degrees on the Aequmoctial are then traced out, which compared with the Degrees traced out, by making the same number of Day's Motion in some other part of the Ecliptick, to pass the Meridian, and the difference of Right Ascensions in­cluded between those two equal number of Dayes will plainly ap­pear.

[Page 7] All which Irregularities, or differ­ence in Right Ascension, proceed from two principal Causes: 1. From the different Positions: And, 2. From the different Centres of those Orbs in which, and according to which the Sun and Earth do move; from whence arises a natural necessity, that be­tween two such regular and equal Motions, whose Position is thus ob­lique, those appearing differences should still arise; for though both Sun and Earth, the one in his an­nual the other in it's diurnal Re­volutions, be rationally supposed to be regular and equal in their own Motions; yet in regard of the dif­ferent Positions of their Spheres, the Right Ascensions that are made by them cannot be equal; it being im­possible that the Sun, when near Aries and Libra, where he moves [Page 8] cross the Equinoctial, should then in any particular number of days make so great an alteration in Right As­cension, as he must do near the two Tropicks, where both Equinoctial and Ecliptick run paralel one to the other; and accordingly by the best Tables of Right Ascension, 'tis found that the Right Ascensions of 10 daies motion of the Sun near the Tropick of Capricorn, shall arise to above 11 degrees 30 minutes, whereas that of the same number of daies near the Equinoctial Point of Aries shall scarcely amount to 9 degrees.

Moreover, from the eccentrici­ty of these Orbs, another irregula­rity does happen in the Right Ascensions, for the Centre of the Earth, upon which it turns round in it's daily Revolutions, being not [Page 9] the same with the Centre of the Suns Orb, it follows that the appa­rent Equinoxes pointed out by an imaginary line drawn through the centre of the Earth, and intersect­ing the Ecliptick, shall divide that Circle into two unequal parts; from whence it arises, that the Sun must spend more daies in passing through one half of the Ecliptick, than he does in passing through the other; and accordingly by experience he is found to move through that part between Libra and Aries in 179 daies, but in passing between Aries and Libra he takes up 186, which is 7 dayes more; so that in that part of the Year between Septem­ber and March, he seems to us to be swift in motion, but in the other part between March and September his apparent course is more slow; [Page 10] which seeming swiftness and slow­ness of the Suns motion, is the cause that the Right Ascensions near both the Tropicks are not alike, but dif­fer much, as do also those that are nigh the Equinoxes: for the Right Ascension of 10 daies motion near the Winter Tropick, is more by 60 Minutes, than that of the same number of daies near that of the Summer one; so also the Right Ascension of 10 daies time near Libra, amounts to above 30 Mi­nutes more than those of the same number of daies near Aries does.

Having thus plainly demonstra­ted that natural daies must needs be unequal, and laid down the Causes from whence those unequalities do still arise; I suppose it may now be concluded to be extreamly unrea­sonable, for those that are so Nice [Page 11] and Curious as some are, to expect an exact correspondence between the times given by the motions of a Clock, and those divisions of it that are made by these unsteady motions of the Sun on the Lines of a Dial; for if from the Reasons before laid down, there be in nature a necessity for those diffe­rences of Right Ascension before asserted, and that the daies which they bound, must differ also in length, correspondent to what those differences in Right Ascension do amount to; how then is it possible that those exact and regular moti­ons of a Pendulum, to what pitch soever it be set, should agree with these motions of the Sun, and true­ly divide those daies that are not so regular as it self is: For,

Suppose a Clock should be ad­justed [Page 12] to the hour at a time when natural daies are shortest, as about the middle of March, this Clock with the same pitch of motion, shall in June or December finish it's diurnal Revolutions sooner than the day shall do, by reason the natural daies are now longer than those of March, to which the Clock had been formerly adjusted; and by conse­quence it shall now gain upon every day, just so much time as these daies in December are longer than those of March. So on the contrary, if a Clock be adjusted to go true with the Sun in the Month of December, at which time the na­tural day is alwayes longest, this Clock when natural daies are short­er, as in March or September, shall not finish it's daily Revolutions so soon as the day it self shall be accom­plished, [Page 13] and by consequence go each day so much too slow, as those daies of March or September are more short than them to which the Clock before had been exactly adjusted.

Since therefore there is no tole­rable exactness in thus adjusting Clocks to the Sun it self, because being thus adjusted at times when daies are either shortest or longest, their gaining or losing will be the more extream in the contrary parts of the year: for Example; Clocks adjusted to the Sun in March shall upon most daies in December gain almost 50 Seconds, which in the Months time shall amount to near half an hour; and on the contrary, if adjusted to go true with the Sun in December, it shall in March lose the same time, and so for any [Page 14] other, according as daies do differ in length.

That Clocks therefore may be reduced to a more exact pitch of motion, that their gain or loss may never be so extream, it will be ne­cessary to adjust them, so as that their motion may be agreeable to that of a middle day, or such a one as is a mean between natural daies that are most long, and those others that are most short; to which pitch if a Clock be once adjusted, it's gain or loss shall then be the less sensible (for gain and lose it will still) amounting in December but to about 15 Minutes in the whole Month, and in March to but about 9, which is vastly more exact than when it shall happen to be adjusted to the longest or shortest of Natural daies, or to any other [Page 15] that is not equal to a mean or middle day, of which there are but few, which in the Table are ex­prest by the Character ☉ Sol.

But to this exact pitch of moti­on, that may thus correspond to a mean day (the greatest exactness that a Pendulum is capable of be­ing brought to) there is no way certainly to adjust a Clock without the help and assistance of a Table of Equations, that give the daily diffe­rences between a mean day and those which are either longer or shorter than the mean day is; which Equa­tions having formerly been compu­ted by the Worthy and Ingenious Mr. Christian Hugens de Zulechim, (who is reported to be the first that ever applyed the Pendulum to regulate the motion of a Clock) and not long since Printed in num­ber [Page 16] 49. Philos. Trans. I have made bold, in regard of its exactness, to transcribe in it's more natural form of an Equation, by only expressing the Equations themselves, without adding them together, and sub­stracting, as Mr. Hugens has done for a particular use, to shew the nature of a Pendulums going, when set right the first of February, and let go the whole year round, without setting afterwards.

Now for their sakes that desire to know the manner of Compo­sing such a Table themselves, that thereby they may the better under­stand the nature of it; they may Note, that the Equations are to be found out, and a Table composed in the manner following: First find out a mean Right Ascension, by di­viding the 360 degrees of the Equi­nox [Page 17] into 365 parts, and a quarter, equal to the daies of a year, and the product shall be the mean Right Ascension desired, which will be found to be about three Minutes 56 Seconds (according to Sir Jonas Moors account of it in his Mathema­tical Compendium) then by the help of an exact Ephemerides (here lyes the difficulty) let the natu­ral Right Ascensions of the Sun be computed by Calculation, for the Meridian Position of the Sun for every day, to Minutes and Se­conds; which having done, com­pare the daily differences of these Natural Right Ascensions with the mean one, by still substracting the lesser from the greater; and what remains shall be the Equa­tions desired; still noting down either the excess or defect, that is, [Page 18] whether the natural be more than the mean or less: as for example; Suppose the Right Ascension between the Meridians of the 1 ^st. and 2 ^d. of January be found to amount to 4 Minutes, 20 Seconds, this com­pared with the mean Right Ascen­sions, 3 Minutes, 56 Seconds, and by substracting the lesser from the greater, the remainder will be found to be 24 Seconds, and so much the Natural Right Ascensi­on does then exceed the mean one; this 24 Seconds is the Equati­on for that day, it being from noon to noon 24 Seconds longer than a mean day is; and shews you, that a Clock when well adjusted to a mean day, shall then gain 24 Seconds, because it finishes it's Diurnal Revolutions sooner by 24 Seconds than the day it self does: [Page 19] on the contrary, when the Right Ascensions of Natural daies are less than the mean ones, as they are about the middle of March, by almost 20 Seconds, this 20 Se­conds being the Equations belong­ing to such a day, shall shew you, that upon such a like day a well adjusted Clock shall then lose 20 Seconds; for the mean day to which it is adjusted being longer than the natural one by 20 Seconds, the Natural Day shall be finished sooner by 20 Seconds than the Clock at that time shall accomplish it's diurnal or daily Revolutions, and by consequence it shall then lose 20 Seconds. The Equations thus found for every particular day, and a Ta­ble composed of them, shall re­semble that which is here insert­ed, [Page 20] whose Use we now come to shew more particular in some Cases.

For Explanation, take notice, that the first Column contains the daies common to every Month, the other 12 Columns that belong to the several Months themselves, con­tain those Seconds of time that all natural daies are either longer or shorter than the mean day. Note, that in four parts of the Table are placed this Character ☉, which de­notes the times wherein natural daies having before been longer than the mean day, do then begin to be shorter; or having before been shorter, do then begin to grow more long: Note also, that those daies upon which this Character ☉ is affixed, have no Equation, they being equal in their length to the [Page 21] mean day; as for the words insert­ed among the Columns, they are at sight to inform you, that the Equations in those parts of the Ta­ble are either more or else less than the mean day, as the words themselves do fully express; they also note, that where the Equations are more, there Clocks shall gain each day so much as the Equation belonging to it does then express; but if the Equations are less, they then shall lose; and how much this gain or loss for every particular Months time shall amount to, is by continual addition of the Equations belonging to each day summed up, and the quantity of time it amounts to, set down apart at the bottom of every Column.

Note also, that since Clocks do either gain or lose, during the [Page 22] whole number of daies included between those daies on whom this Character ☉ is affixed, the whole quantity of time either got or lost does amount to the summs that follow, viz. Between the 1st of February and the 4th of May, the time that a well adjusted Clock shall lose, amounts by continual add­ing the Equations together, to about 19 Minutes, 29 Seconds; between this 4th of May and the 15th of July it shall gain about 9 Minutes 43 Seconds; from the 15th of July to the 23d of October, it shall lose 22 Minutes 9 Seconds; from the 23d of October to the last of Janua­ry, it shall gain 31 Minutes 55 Se­conds: All this is to be understood of a well adjusted Clock, set right to the Sun at the beginning of each time of either gaining or losing.

[Page 23] By this Table, if you would ad­just a Clock to a mean time, which is the greatest exactness to which it's possible to be brought, do thus: First set it true to the Sun, and note the day, then let it's motion be continued without setting a new, for about 30 or more daies: Ob­serve then the time that it has got or lost by the Sun, then summ up the whole number of Seconds inclu­ded in the Table, between those two daies of first setting and last Obser­vation (allowing 60 Seconds to a Minute) and if the gain or loss of your Clock be equal to the summ of time that it should have gained or lost by the Table, then is it well adjusted; but if it have not, then must its motion be reduced to a more near agreement, by shortning the Pendulum in case the Clock [Page 24] have gone too slow, or letting the Bob down longer in case it have gone too fast: Then set it anew, and try it for about 30 daies more, and then comparing its loss or gain with the summ of those Equations con­tained in the Table, as before you did, let the Bob be again rectified as the nature of it's motion requires; and continue to do thus, till you find its gain or loss exactly to cor­respond with the summ of time given by the Equations contained in the Table, for the time that the Clock has gone.

When it is thus well adjusted to a mean time, it will be so exact, as that, being set right at any time of the Year, and so let go the whole Year about, it shall come right with the same Dial by which it was set the same day Twelve-month; but [Page 25] [...]n all other parts of the Year it shall still differ from the same Dial. For Example: If set right the first of February, and so continued in Moti­on the whole Year about, it shall continually be too slow the whole Year, either more or less, till the same day on which it was set: The reason of this is plain enough; for from the first of February to the 4th of May, it shall continually lose to the quantity of 19 Minutes, 29 Se­conds; then from the 4th of May to the 15th of July, it shall gain; but this gaining amounting to but about nine Minutes, 43 Seconds, it shall still be too slow by 9 Minutes, 46 Seconds; because its gaining now shall not be so much as it lost before, by 9 Minutes, 43 Seconds: Then again, from the 16th of July it shall lose afresh till the 21st of October; which second loss a­mounting [Page 26] to about 22 Minutes, 9 Se­conds, this added to the time that it was too slow on the last account, shall amount to 31 Minutes, 55 Seconds, and so much it shall be too slow on the 21st of October; from whence it shall gain afresh till the last of January, to the quantity of 31 Mi­nutes, 55 Seconds; which being equal to what it was before too slow, shall cause it to come right to the same Dial with which it was set twelve Months before, altho' it went too slow the whole Year be­side.

Again, let a Clock be set right the 23d of October, it shall from thence gain time till the last of Ja­nuary; and this gain shall amount to 31 Minutes, 55 Seconds; then from the first of February to the 4th of May, it shall lose 19 Minutes, [Page 27] 29 Seconds, which being less than the 31 Minutes, 55 Seconds, which before it had got, by about 12 Mi­nutes, 26 Seconds, it shall still be too fast by 12 Minutes 26 Seconds: Then from the 4th of May, to the 15th of July, it shall gain anew to the quantity of about 9 Minutes 43 Seconds▪ which added to the time it was too fast before, shall amount to 22 Minutes, 9 Seconds, and so much it shall be too fast on the 15th of July; from which time till the 23d of October, it shall lose this 22 Minutes, 9 Se­conds, and by Consequence come right to the same Dial with which it was set twelve Months before.

Thus shall one and the same Clock, with the same pitch of Motion, go alwayes too slow if [Page 28] set at one time of the Year, and always too fast if set at another time, if it be let go the whole Year about.

Moreover, if set at some other times, and then continued in its Mo­tion for a Year, without setting a­new, it shall both gain and lose, be sometimes too fast▪ and some­times too slow: For if a well ad­justed Pendulum be set right to the Sun the 4th of May, by the 15th of July it shall be 9 Minutes, 43 Se­conds too fast: From this 15th of July to the 23d of October, having lost 22 Minutes, 9 Seconds; from which substracting the 9 Minutes, 43 Seconds that it was before too fast, there remains 12 Minutes, 26 Seconds; and so much it shall be too slow on the 23d of October; from which day it shall begin to [Page 29] gain, and continue so to do till the first of January, by which time the Clock having got 31 Minutes, 55 Seconds, which amounting to about 19 Minutes, 29 Seconds above what it was too slow on the 23d of Octo­ber, it shall by Consequence be now 19 Minutes, 29 Seconds too fast; from whence to the 4th of May, it shall lose what now it is too fast, and so come right to the same Di­al with. which it was before set.

Again, set a Clock to the Sun the 15th of July, and if it be well adjusted, it shall by the 23d of Octo­ber be 22 Minutes, 9 Seconds too slow; from whence to the last of January, it being to gain 31 Mi­nutes, 55 Seconds, it shall be then 9 Minutes, 46 Second▪ too fast; from which time to the 4th of May, [Page 30] it losing 19 Minutes, 29 Seconds, it shall then be 9 Minutes, 29 Se­conds too slow; which time by the 15th of July shall again be got, and so the Clock shall come right to the same Dial.

Thus, by this Table, are these great Varieties discoverable in the Motion of the best adjusted Pendu­lum, according to the different times of the Year that it is set in; that the same Pendulum set right upon the first of February, shall go always too slow till the same day twelve-month; but if set right the 23d of October, it shall the whole Year round be still too fast, till the same day on which it was set: The same Clock being also set to the Hour on the 4th of May, or the 15th of July, shall on the following Year [Page 31] be sometimes too fast, and at other times too slow. These are all strange and unaccountable things to such as understand not the Nature of the Unequality of Time, from whence all these Varieties do still arise, and are scarcely to be demonstrated to the Understanding by any other way, than by this or some other Table of the Aequation of Time.

Since therefore there is a necessi­ty for setting Clocks a-new to the Sun, at some times, that they may be kept as near as possible to the apparent time given by a Dial; I advise that this setting may be, if possible, the first day of every Month; so may you the better dis­cern by the Time set down at the bottom of every Column, whether your Clock have gone right to the [Page 32] mean time, and be as exact in his Motion as 'tis possible to bring him to: For if it be exactly adjusted, it will then either gain or lose near that time that is set down at the bottom of every Month, those Sums being nothing else but the Aequa­tions of the whole Month added together into one Summ, as before I directed, when I gave you the Me­thod of adjusting a Pendulum to the true or mean time: But in case you cannot set it right the first day, then must you be at a little trou­ble to add together the Aequations your self, at such time as you come to set it a-new; but when the Clock is well adjusted, there needs little of this trouble, being assured that it's brought to the nearest pitch of Mo­tion it's capable of; and that when it is at any time found to differ [Page 33] from the Sun, it must be lookt up­on as the natural Consequence of the Unequality of Time, and not any Deficiency in the Motion of the Clock.

I speak this of those long and cu­rious Pendulums that vibrate within the Compass of 2 or 3 Inches; for the less Compass a Pendulum takes, the more steady is it's Motion, not being so subject to rise and fall, as others are, that vibrate in a larger Compass. As for those shorter Pen­dulums of a Foot long, or under, although they may go very steady for the most part, if Frost or foul­ness hinder not, yet are they not at all intended in this Discourse, their Motion being apt to an Al­teration in some Cases; for a short Pendulum that goes well when clean, [Page 34] shall go faster than the mean time when foul, because the Pendulum is by the foulness hindred from taking its wonted Compass: The same ef­fect does Frost produce; for by con­gealing the Oyl in the Pevets, its freedom of Motion is interrupted, so that the Pendulum not fetching it's wonted Compass, shall go too fast; but those long and curious Pendulums of 40 Inches, that fetch not above three Inches compass, they are so exact, that being once adjusted they shall alwayes keep the same time, if their motion con­tinue; for if the Pendulum should fetch a smaller compass, their Mo­tion would cease, and themselves stand still.

When such a Pendulum as this is well adjusted, you may trust to [Page 35] it, as to it's correspondence in Mo­tion with the mean time, and only give your self the trouble some­times to set it a little forward or backward, according to what the unequality of Time has made it to differ from the same Dial with which you did use to set it; which times of setting may be, as I said before, once in a Month; yet if the Table be well noted, you shall find, there be some times in the year in which a good Clock may go a longer time without any material difference from the time given by a Dial: For Example,

Suppose you set a Clock right to the Sun the first of January, this Clock if let go till the first of March, shall then be but two Minutes four Seconds too fast; for though it gain [Page 36] in January six Minutes, no great matter, yet losing in the next Month about four Minutes, it shall at the end of that Month be but two Minutes to fast; nay, if let go another Month, as to the last of March is, it shall then differ but about seven Minutes, which is no great matter. Moreover, if you set a Clock the first of May, it shall, if let go till June, lose but two Mi­nutes thirty five Seconds in the whole, though it shall at the begin­ning of May be about five Minutes to slow, which is no great matter; so also if it be set right the first of June, it may well go without set­ting till the first of September; for though it gain five Minutes in June, yet losing eight Minutes in August, it shall then be but about three Minutes too slow in this three [Page 37] Months time; but at some other times, as from February to May, if a Clock were let go 'twill be ex­treamly out, losing above eighteen Minutes; so also in November, De­cember and January, in which time it will gain above thirty Minutes.

By the Table you may also rea­dily find out, what difference there is between the lengths of any two daies in this manner: First, If the daies are both shorter, or both long­er than the mean day, then sub­stract the Equation in the Table belonging to one day from the Equation of the other, and the re­mainder shall shew their difference in length. But if the daies be one longer than the mean, and the other shorter, then add the two [Page 38] Equations together, and the summ shall be the time that they differ in length: Thus the tenth of Janua­ry will be found to be thirteen Seconds longer than the tenth of May; also the fifteenth of September will be found to be fifty one Se­conds shorter than the fifteenth of December.

Note, That if men be very nice in keeping a Clock true to the Sun, they should then make use, if possible, of but one time on the Dial that they set it with, and that pretty near noon; for few Dials being drawn exactly true, great mi­stakes may arise, when a Clock is set to one hour and then compa­red with another; and by reason of refractions great errours may al­so [Page 39] arise; for the Sun by Refracti­ons being made to appear higher than really she is, there can be no certain account taken of the time till near Noon, where Refractions cease: And when all this care is ta­ken, in regard it is so very hard to distinguish Minutes by the shadow of a Dial, you will be much more exact if you do thus: Let two plain and flat plates or boards, about ten Inches square, be joyned so close together that a Six-pence may but just go between; let them be fixed so, that this Cranney between them may respect the true South; this will give you the time to less than half a Minute, by observing the first mo­ment that the Suns beam is darted through it, and cast upon some dark body that is plac [...]d on the [Page 40] North-part to receive the light; so that having thus the exact time, when the Sun comes to every Me­ridian, it will be found a much better way to adjust Clocks by such a device as this, than by the truest Dial.

One use more, and that a Prin­cipal one, I shall add, that is this: When a Clock is once well adjust­ed to the mean or equal day, you may then by this Table keep it right to the time given by the Sun, although you never set it right to a Dial, nor see the Sun above once a Year; to perform this do thus: set your Clock right to the Sun the first day of any one Month, and then the Table still giving you the time it should lose [Page 41] or gain in that whole Months [...]ime, 'tis then but setting it for­ward or backward the first day of the next Month what it either hath got or lost in the Month im­mediately preceding, and it will then be right with the Sun as if it had been set by a Dial, and so from Month to Month you may (by still setting it either forward or backward according to what the Table tells you it will gain or lose) keep it true to the time giv­en by the Sun, though it should never shine so as to give you an opportunity to set it by a Dial above once in the whole Year; but be sure your Clock be first well adjusted, or else there may be some errour: Note, that for this pur­pose it will be very convenient to [Page 42] Paste the Table it self on a board, and then putting it into a handsom Frame, let it be hung up near the Clock, that you may have rea­dy recourse to it on all occasions, especially for this in particular; for without the assistance of such a Table as this, I know no way in the World to keep a Clock right to the apparent time, in case Clouds should intercept the Beams of the Sun for any long time to­gether.