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 ... how thereby precisely to adjust royal pendulums ... : with a table of pendulums, shewing the beats that any length makes in an hour ... / by John Smith ... ; 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. Smith, John, fl. 1673-1680. 1694 Approx. 123 KB of XML-encoded text transcribed from 55 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-12 (EEBO-TCP Phase 1). A60473 Wing S4106 ESTC R17047 12727289 ocm 12727289 66373 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A60473) Transcribed from: (Early English Books Online ; image set 66373) Images scanned from microfilm: (Early English books, 1641-1700 ; 369:3) 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 ... how thereby precisely to adjust royal pendulums ... : with a table of pendulums, shewing the beats that any length makes in an hour ... / by John Smith ... ; 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. Smith, John, fl. 1673-1680. [4], 92 p. Printed for Richard Cumberland ..., London : 1694. Includes one folded table of equations. "Licensed, January 17, 1693/4, D. Poplar"--P. 2. Reproduction of original in British Library. 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Horology -- Early works to 1800. 2005-04 TCP Assigned for keying and markup 2005-04 Apex CoVantage Keyed and coded from ProQuest page images 2005-05 Judith Siefring Sampled and proofread 2005-05 Judith Siefring Text and markup reviewed and edited 2005-10 pfs Batch review (QC) and XML conversion 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 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-Day , which is the 24 Hours , of its own Motion will be finish'd before the 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-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-Day , on which let Him be Set backward if the Figures on the 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 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 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-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-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 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 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 Pe●●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 58 3027 59 3001 60 2976 61 2951 62 2927 63 2904 64 2880 65 2859 In this Table , the first Row of Figures , in each Colume , are the Inches of a Pendulum's Length : The second Row are the Beats that a Pendulum of that Length makes in an Hour . Thus one of 41 Inches long beats 3600 times , and one of 64 2880. The Table of Royal Pendulums continued , from 3 Foot long to 30 , for the Use of such as make Church and Turret-Clocks . Feet Beats 3 3842 4 3327 5 2976 6 2716 7 2515 8 2353 9 2218 10 2104 11 2006 12 1912 13 1845 14 1778 15 1718 16 1664 17 1614 18 1568 19 1526 20 1488 21 1452 22 1429 23 1387 24 1353 25 1331 26 1305 27 1288 28 1257 29 1235 30 1215 In this Table , the first Row of Figures are the Feet of any Pendulum's Length , the second Row are the Beats that that Length makes in an Hour ; as 10 Foot long beats 2104 in an Hour , so a Pendulum of 20 Foot long beats 1488 Blows in an Hour . The foregoing Table of Pendulums I was , in some measure necessitated to publish , in order to demonstrate why heretofore it has been found so difficult to adjust a Clock to the Table of Equations . But , besides this , I thought it might be of good Use to some , who , in contriving Numbers for new Clocks , or for old Clocks altered into Pendulums , are often at a loss what Length of Pendulum to fit their Number to . Perhaps my so doing may anger some , but the pleasuring of more will countervail that Mischief . The Table of Crown-Wheel'd Pendulums is calculated from a Standard of the same sort , 6 Inches and a half long , that strikes 9000 Blows in an Hour : And that of Royal Pendulums from one of 41 Inches , that strikes Seconds , or 3600 Blows in an Hour . In both the Tables you may perceive , That a Pendulum that strikes but half so many Blows as another is four Times as long : This noted , gives you a true insight into the Nature of the Pendulum . The Tables are exact , as to their whole Numbers , and would always give you the exact length , did not different ways of making Clocks cause an Alteration , insomuch that sometimes a Pendulum that strikes Seconds shall be above a quarter of an Inch longer than another shall ; we must bear with what we cannot avoid . The best Rules for the ORDERING and USE Both of the Quick-silver and Spirit WEATHER-GLASS . SInce 't is 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 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 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 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 't is 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 . 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 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 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 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 . 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 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 , 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 Head of the Glass when you set it up , you will find the same Defect , as Dr. Beale has observ'd . Wherefore 't is 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 . Of the Uses of the Baroscope , or Quick-silver Weather-Glass . AND here it may not be amiss in the first place , to shew you my Opinion concerning the Reasons of that different weight of Air which is now generally believ'd , ( and that with good Reason too ) to be the cause of the Quicksilvers rising against fair , and falling against foul Weather : Now the Reasons or Causes of this , I take to be principally two ; the one is the Dilating and Contracting of the Air ; and the other is the Airs being empty of light Vapours , and sometimes filled with them . That the Air is capable of Contraction and Expansion , is plainly apparent by its dilating with Heat , and contracting by Cold in the Bolt-head of a Thermoscope , or Water Weather-Glass . Now if the Air be Contracted into a less room , by what cause it will , the Adjacent Air flows in to make good the Level of the Atmosphere , and so by the Addition of more Air , the Cylender which bouys up the Mercury in the Weather-Glass becomes heavier , and by consequence makes the Quicksilver rise ; and though in Summer-time it may be thought that the Heat we feel should rather Expand than Contract , yet in this we may be deceived ; for though the Air be Hot just at the Earth by the Sun's Reflection , yet the upper Regions are still as Cold as ever , witness the Snow which continues all the Year round on the Tops of some very high Mountains , and so the Air may very well be accidentally contracted in the hottest time of Summer , as well as in the coldest Winter , and be one occasion of the Airs being then as heavy in dry Weather , as in the fairest time of Winter . And as the Air is made heavier by Contraction , so 't is made lighter by Expansion ; for when its Body is rarified from what Cause soever , the Swelling thereof causes the highest part to flow off ; or , as I may say , run down on those Parts of the Atmosphere that are below it , by which means the Cylender , or Pillar of it that presses on any Place becomes lighter , and so the Mercury in the Baroscope is suffered to sink down or descend . And that the Airs being sometimes full of watry Vapours , and sometimes empty , is another and the chief Reason too of the Quicksilvers rising and falling , is manifest from this Principle in Philosophy , That what-ever Rises up and Swims in any Medium , must Bulk for Bulk be lighter than the Medium by which it is sustained : Hence it follows , that all kinds of watry Vapours must be lighter than the Air , else they could never rise up therein , nor be suspended there , till by another Principle in Nature they are made to descend in Rain or Snow . Now if Water thus Rarified be specifically lighter than Air , then 't is plain , that when the Air is filled therewith , it must become less weighty than it was before : As a Glass filled with half Water and half rectified Spirit of Wine , a much lighter substance , shall not weigh so much as when fill'd with all Water ; so the Air is always lightest in wet Weather , because the Spaces above us are then full of Vapours , much lighter than the Air is , and by consequence the Body of Air and watry Particles mixt together , must weigh less than if the whole were only an unmixt and pure Air. On the contrary , when the Air is dry and free from being thus fill'd with watry Vapours , it must then be most heavy at such times : Indeed we may perceive many large white and curled Clouds sailing aloft over us , but these are only a Collection of some few Vapours in the very upper Region of the Air , the Spaces below being in the mean time very little , or not at all filled therewith ; whereas in very wet Weather , when the Glass is low , and the Air very light , we see not only the upper Region full of compacted Vapours , but find also the whole Atmosphere even down to the Surface of the Earth filled therewith ; as is manifest by the Sweating of Stones , and other tokens of the Airs extream Humidity , and by consequence the fuller of light matter , the Spaces above us are , the less will the Weight be that presses downward ; and for that Reason the Glass in the wettest Weather always sinks lowest . This being premised , I come to the more particular Uses of the Glass ; and first , you may perceive by what has been said , That the Glass gives a very good account of the Temper of the Air as to its Moisture or Driness , the Moisture thereof , or its Fulness of watry Vapours , being always proportionable to the lowness of the Quicksilver , and every Degree of Sinking is an argument of the Airs being filled more and more with Moisture , and the lower its Station , the more full of Moisture the Air still is ; and you shall always observe , That the lower the Quicksilver descends , the more listless and out of order Men's Bodies are , because the Air is then full of that which is disagreeable to the Nature of Man , who was not made to live in a Watry Element : and therefore the more Watry the Medium is in which he lives , the more is his Nature disturbed at it . On the contrary , The higher the Quicksilver is , the drier still is the Air ; and by consequence Men's Bodies are then found to be more Brisk and Lively , because the Medium in which they live and move , is free from what their Nature abhors ; so that by the Weather-Glass may be known in great part , whether the Disorder and Melancholy , or the Periodical Pains and Aches to which we are sometimes unavoidably subject , is really occasioned by a new bodily Distemper or not ; for this happening when the Quicksilver is low , may be judg'd to be occasioned rather by the Air , and by consequence will go off naturally of it self when the Quicksilver rises ; a too moist Air has stranger Effects on Men's Bodies , than is generally taken notice of by them that understand not the Reason from whence it proceeds . In the next place observe , That as the Baroscope Predicts only fair and foul Weather , so that you may be the better directed which of these to expect ; you must still note the rising and falling of the Mercury ; for its rising in any part of the Glass , betokens a tendency to fair , as its falling down foreshews an inclination to Rain and Wet : As for the Words engraven on the upper part of the Register Plats , they are then only to be noted when the Mercury removes from Changeable upwards , and those on the lower part are to be noted only when the Quicksilver falls from Changeable downward . In other Cases the Words are of no Use ; for if it is Rising in any part , foreshews a Tendency to be Fair , and its Falling in any part , a Tendency to foul Weather ; then it follows , that if it fall from settled Fair to Fair , it may yet Rain a little , though the Quicksilver still stands as high as Fair ; the like may be said , if it rise from the Word , much Rain to Rain ; for though its Rising betoken a Tendency to Fair , yet since 't is still so low as the Word Rain , there may be yet be some Wet Weather , though not so much as there was before the Quick-silver began to rise . But if the Mercury mount upwards from Changeable , then will the Weather for the most part be such as the Words in the upper part of the Register Plates Import ; and if from Changeable it falls down , the Weather likewise will be much the same , as the Words found in that Part do express ; but in the Mercuries rising up to Changeable when 't is below it , or falling when 't is above it , the Words as I said before , signifie nothing . If the Mercury rises very high , the Weather will continue Fair , so long as it stands at that pitch , and you will not find the Weather change much , till the Mercury falls down a good Space lower : So likewise when 't is fallen down very low , you must expect Wet Weather during all the time of its so continuing ; in both these Particulars you will be certain , provided the Wind and the Moon Concur . For both the Wind and the Changes of the Moon are to be well observed in order to make the truer Prediction : And first , for the Wind ; this is found to be of very great Moment ; for if the Glass fall , and the Wind sit in those Quarters , from whence much Rain is observed usually to come ; as with us about London are the South and Southwest , then 't is not to be doubted but Wet will follow . On the contrary , if the Glass rise when the Wind blows from a dry Quarter of the Heavens ; as with us are the North and East , then 't is a hundred to one but the Weather will be Fair ; but if the Glass rises , and the Wind be South , the Case is doubtful : So also if it falls , and the Wind be North , for then it often happens that the Weather does not prove always such as the Rising and Falling of the Glass Predicts . As to the Moon , 't is well observed , That the Weather is generally inclinable to Moisture , about three Days before , and three Days after , both the New and Full Moon ; if therefore the Glass Falls , the Wind be South , and the Moon near the New or Full , the certainty of Rain is still much the greater . If the Mercury be high in the Summer-time when the Weather is hot , and does of a suddain fall down a pretty considerable Distance , then certainly expect great and sudden Storms of Rain and Thunder to follow soon after . VVhen the Glass is Risen very high in Winter , and the Wind sits then North and East , it certainly presages Frost to ensue , and the same will continue as long as the Mercury stands thus High ; but when you see it begin to sink somewhat considerably , then be assured a Thaw will quickly follow . If in a Frost the Air becomes Overcast , and the Quicksilver Rises of a suddain yet higher , when it had stood high for a time before , then look for Snow , for the Cold above , which is the Cause of Snow , causes also the Air to become more heavy by Condensatition . If the Glass Rise and Fall but a little , or it be unsettled in its Motion , it then argues an unconstant Season , and the Weather will not then long continue in one state ; the like happens when it is about the Word Changeable , or Uncertain , for then no true Guess can be made what the VVeather will be . The Mercury is always observed to be lowest in extream high and strong Winds , that happen when the Air is full of Moisture ; but the Glass does no way predict Winds before-hand , for the extreme lowness of the Quick-silver happens only at the very Time the Wind Blows , and as soon as the Wind Ceases the Mercury is then found to rise apace , but such a Rise that immediately follows Storms , are no signs of fair Weather , except it rises much higher than it was at the Time of the Wind 's beginning to blow . Note , That when Wet is predicted by the Glass , or by any other Sign or Token , it generally begins to rain either when the Moon is due South , or else when the Sun comes to be upon the same Quarter from whence the Wind blows ; and if it rains not at the Time of the Moon 's Southing or Northing , nor when the Sun and the Wind comes together , then 't will hardly rain till the same Times do again return ; which is a good Note in time of Harvest , and very seldom fails , though it sometimes may . Note also , that most great Changes of the Weather happen with us , either at the New full Moon ; and if the Weather change not then , 't will hold on as it is till the next New or Full Moon comes : Frost generally breaks at the Changes , when it does break , and 't is commonly at the Change or Full that Rain comes , after a dry Season has long continued . An Addition of some Natural Predictions of Fair and Foul Weather : And first of Fair Weather . THe much hooping of Owls , after Sun-set , in the Summer-time , and in the Night also , foreshews a fair Day to follow . Swarms of little Gnats and Flies , sporting themselves together , in the Evening , is a certain token that the Day following will be fair . If the Sun set red in the Evening , and the Place be free from Clouds , and the next Morning rises clear and bright ; these are good tokens that the Day will be fair . The Soaring of Kites aloft in the Air , is a Sign of dry and hot Weather . When the Bat Mice are seen to fly to and fro , in the Evening , it shews that the next will be a fair Day . If , in the Morning , Mists descend from the Hills , and settle in the Vallies , 't is a Sign that the Day will be fair . If it rain in the Summer , and Horses and Kine do thereupon leave off Feeding , 't is a certain Sign the Rain will not continue long . Crows , if they caw or cry early in the Morning , with a loud and clear Voice , it shews that the Day will be fair . Signs of Rain and Wet Weather . IF , in the Evening , the Sun set behind a dark black Cloud , and her Body appear also greater at that Time than usual , it certainly betokens Wet the next Day . If Water-fowl wash themselves much and dive more than usual under Water , and also flutter and clap their Wings , and oil their Feathers more than usual , 't is a Sign of Rain . If Toads are , in the Evening , found leaping in the Paths or High Ways , or if the great black Houseless Snails are found creeping about more than usual , it foreshews Rain . An unusual Circle of Light about the Moon or Stars , when no Mist or Fog appears below , is a Sign of Rain soon to follow . If the Sun , at her first rising , or some Time after , shine waterish , that is , paler than ordinary , 't is a Sign of a wet Day , especially if the Air be soon after obscured with thick Clouds . If , in the Summer , in a fair clear Day , you perceive the Clouds to gather of a suddain on all Sides , and appear black and curled , then prepare your self for Storms of Rain and Thunder soon after . Hoggs crying in an unusual manner , and running unquietly up and down , with Litter in their Mouths , foreshews Rain and Storms at Hand . If Crows cry much in the Evening , 't is a Sign of Rain the next Day . Any of these , or the like Signs , happening in the Summer time , will , if the Baroscope concur , help you to make the more certain Guess at what Weather will after ensue , especially if the Glass be at Changeable and Uncertain , for then , by these you may the better guess at what Weather will follow . Some particular Places have also Signs of Rain and fair Weather , which others have not , which observed , together with the Glass , may make your Guess more certain than they can otherwise be ; the Nature of Countries also differ , for whereas in England , especially near London and the Southern Parts , a South Wind always brings most Rain , and a North or East Wind dry Weather ; on the contrary , at Edenburgh it Scotland a South Wind brings the fairest Weather , and a North or North East the greatest Wet ; these things considered , every Man that lives in Countries which differ in Temper from that for which these Rules serve , ought to frame Rules to himself , by observing the Changes that follow the Glass's Rising and Falling , the Change of the Wind , and the Southing of the Moon . Note , If the latter End of February and the Beginning of March be constantly Dry , it betokens a very Dry Summer . Also a hard Frostly and Snowy Winter makes the Year following to be very Plentiful and Healthy , but a Warm and Moist Winter makes the Summer after to be very sickly . Some Uses of the Spirit Weather-Glass . THE suddain Rising of the Spirit in the Day , in Summer , foreshews an immediate Approach of Thunder and Storms of Rain , and in Winter Snow . If it rises much in the Day and falls but little in the Night , then expect , the Day following , excessive Heat , if not Thunder and Storms . If it rises never so little in the Night-time , expect next Day either Rain or Snow , as the Season is . If it rises no more in the Day than it falls in the Night , 't is a Token that the Air is Temperate , as to the Heat and Cold. If it falls in the Day-time , and the Weather be fair , expect a Frost the next Night . The like happens also generally when the Liquor is very low . The more it rises or falls at any Time the more remarkable will that Change of Weather be which follows . All the other Uses of it are only to shew the present Temper of the Air , as to Heat and Cold , and farther than this my Experience has not as yet led me , neither by Enquiry do I find any other useful Observations made on them . I shall only add , That these Glasses might be made as strong as the Tube of a Quick-silver Weather glass , provided the Ball be proportionable to the Bore only . It may be , if the Glass were thicker , they would not move so nicely ; but this would not signify much , because little Judgment can be made from small and little Alterations . JUst when the last Sheet was ready to be printed off , that which follows was communicated to me by Mr Watson , the Person before-mentioned in this Work , which in respect of its Nature , being not only plain and useful , but also free from all Objections that Tables may be liable to , I have thought fit to add it hereunto , upon his Recommendation , and in the Words penn'd by himself . SIR I Rather communicate this to you , because many Gentlemen have the Convenience of Places fit for this way of Observation , which I take to be the most exact Way yet found to adjust a Pendulum Clock well . If you think it may be serviceable to those that are the most exact and curious in Time-keeping , you may do well to insert it in that laborious and curious Tract of the Equation of Natural Days , that you are now publishing . I am , Your real Friend and humble Servant , S. W. The Way of finding how much a Pendulum Clock has gained or lost in a Day , Week or a Month , to the nicity of Two or Three Seconds , &c. N. h. ′ ″ 1 0 3 56 2 0 7 52 3 0 11 48 4 0 15 44 5 0 19 39 6 0 23 35 7 0 27 31 8 0 31 27 9 0 35 23 10 0 39 19 11 0 43 15 12 0 47 11 13 0 51 7 14 0 55 2 15 0 58 58 16 1 2 54 17 1 6 50 18 1 10 46 19 1 14 42 20 1 18 38 21 1 22 34 22 1 26 30 23 1 30 25 24 1 34 21 25 1 38 17 26 1 42 13 27 1 46 9 28 1 50 5 29 1 54 1 30 1 57 57 31 2 1 53 TAke a Piece of thin Brass , and file therein a Slit or Notch , about half a quarter of an Inch deep , but somewhat wider at the Top than at the Bottom , as thus 〈◊〉 , knock the End of it into some Post in your Back-side , or else in some Window , that ye think convenient ; then look through the Notch at any Star of the first or second Magnitude , and wait till the Star comes to the Edge of any Chimney , or the Side of any House , and you will see the Star vanish in a Moment ; then mark what your Clock is at when the Star vanishes : Then at any other Night afterwards ( as the next Night , or a Week or a Month afterwards ) wait for the same Star again till it vanish behind the Chimney or House , as before , and then observe what your Clock is at , then your Clock should shew the second Time of vanishing so much sooner than the first , as this Table shews ; now the farther off the Chimney or Wall is the more exact will the Observation be . Let the Distance be Ten Yards at least , let the Observation be made in any part of the East , South or West , but little towards the North Pole , because the Polar Stars are not so fit for this Purpose . EXAMPLE . Suppose a Star vanishes this Night at Nine Hours , Three Minutes and Four Seconds , by my Clock , and Eight Nights after I observe it again , and it then vanishes at Eight Hours , Thirty four Minutes and Forty two Seconds ; by my Clock , against Eight Nights , in the Table , I find Thirty one Minutes Twenty seven Seconds ; that is , so much sooner should the Star vanish at the second Observation than it did at the first ; therefore substracting 31′ 27″ from the first Observation 9h . 3′ 4″ . there 's left 8h . 31′ 37″ , the true Time that the Clock should have been at in the second Observation ; therefore seeing the Clock was then at 8h 24′ 32″ , it has gained 2′ 55. FINIS .