A Specimen of A NEW ALMONAC FOR EVER: OR, A Rectified Account of TIME, by a Luni-Solar Year. That is, By the Moon's Monthly Course primarily, so as the First of the Month shall al­ways be within a Day of the Change; And yet adjusted to the Sun's yearly Course also.

LET the New Year, or Account begin with March 10, 1680/1 the New Moon and Vernal Equinox in the Meridian of Windsor-Castle, being also near the same, viz. the former being about ¼ of an hour after Midnight; and the la­ter near as much before it: or it may begin at any other Epoche when the New Moon and Equinox, or Solstice (if that be thought a better time to begin the year,) hap­pen both near the beginning of the Civil Day, which perhaps they very seldom will be found to do. From such Epoche or Beginning, let the following Months, which in ordinary Years are Twelve only, have days 30, 29; 30, 29, &c. alter­nately: But in Fourteen Years of a certain Period or Revolution completed in Thirty eight Years, viz. in the Years 2, 5, 7, 10, 13, 15, 18 21, 24, 26, 29, 32, 34, 37 let there be intercalated or added to those extraordinary Years, a Thirteenth Month, consisting of Days 31, 30; 31, 30, &c. alternately also: And so on, Period after Period, for ever, as the Moon, &c.

Once every Century, or to one Year of 100, add one Day, viz.

To near about the first 50th Year, or middle of the Century, and then to every 100th Year following. Which additional Day being omitted every 230th, or 240th Century, or thereabouts (according to the Latitude of the differing Opinions of Dissenters in Astronomy) that is, once in 23 or 24000 Years (only the first omission to be about the middle thereof, if any one should require such great exactness) will balance the Account for ever. But we need not be solicitous about that remote consideration.

The DEMONSTRATION.
(Which may be passed over by those not accustomed to Mathematical Demonstrations.)

BEsides common known Principles denyed by none, I suppose, or take for granted only two things, viz.

1. That the Motions of the great Bodies of Heaven, particularly of our great Lu­minaries, the Sun and Moon, are Regular or Vniform, or at least do approach some­what near towards being so.

2. That in taking the measures of their Motions, especially that of the Moon, all the famous Astronomers, Ancient and Modern, have not been much mistaken.

This Account of Time being made up by continued Addition or Multiplication, the Truth or Exactness thereof may be casily Examined or Demonstrated, only by Division of the number of Dnys of the Period (or number of Years assigned) by the number of Months contained in the same; and the Quotient shall be (the Days, and parts of a Day in) a Month; or the Time, at a Medium, between Change aud Change, according to the exactest Astronomers, ancient and mo­dern. E. g.

In 38 Years there are Months or Lunarions, 470, viz. (38 times 12) or 456 and 14 intercalar ones: And Days, 38 times 12 times 29½, that is 13452; and 14 times 30⅓, or 427, that is 13879 whol Days; together with 38 hundredth parts of a day, viz in all 13879:38, because one day is to be added every hundred years. Divide 13879:38 by 470, and the Quotient will be 29:53059574468, &c. that is 29 d. 12 h. 44 m. 3 sec. 28 thirds.

Which is about 18 thirds only too much in a Month, or 1 min. in 16 or 17 years, or about 1 hour in 1000 Years, or (24 hours or) one Day in about 24000 Years: And yet is above eight times more exact than even the Gregorian Refor­mation, as they call it.

Nevertheless if greater exactness be required, subduct 1/530th or 1/240th part of a 33/100 part of a Day from the said 13879:38 (because the additional Day is to be omitted every 230th, or 240th Century) and so in my thirty-eight-years Period or Cycle, there will be days and decimal parts of a day, viz. 13879:3783478† in the first case; and 13879:378416666† in the second case: Divide the said days, &c. by 470, and the Quotient in the first case shall be 29:53059223— viz. 29 d. 12 h. 44 m. 3 sec. 10 third. 7 fourth. that is greater than the Month of Ricciol. and less than that of Dechales; but in the second case 29. 530;9236—viz. 29 d. 12 h. 44 m. 3 sec. 10 third. 52 four. that is a little greater than the Month of Kepler. Now between the one and the other is probably the just quantity of the Mean Month of Conjunction. However, tho it should hereafter be found out to be less than the one, or greater than the other; yet the Account of time by me proposed will hold good for about twelve thousand years yet to come; at which time the said Additional Day being omitted (only some few years sooner or later, as by experience shall appear best before that time) will keep right, and balance the Account for millions of years after.

But if any one will assign me the exact quantity or measure of the Mean Month of Conjunction, I shall tell him precisely what Century (or Year if he please) the said Additional Day is to be omitted: For the best Astronomers do differ a little even upon that Account, as may appear by the following List.

[Page 3] is none, and the prejudice or prepossession of the mind with the old way of Reckoning.

My greatest labour and pains has been to make this work easie to others; the work, I say, I have cut out of the hard Rock, without any other help from first to last, (except common Observations, long since Printed) but what I had from the Division or Powder of the Rock it self, or rather from the Rock of Ages, Cui sit laus in secula seculorum. Amen.

As for all other possible ways of Measuring Time, whether such as have been already practised in some part of the world, or not; I shall venture to say this of them in general, viz. that they will either want a Foundation in Nature, or else come short of mine in point of Exactness.

But if any man shall discover a better way of measuring Time, or find a ma­terial fault in this my Contrivance (tho 'tis easie to find faults almost in any thing, or to add to any Invention) I'll promise him a better Reward for his la­bour, than I expect for mine, tho no such Error, or better way can be found.

In a thing of so universal Use or Convenience to all Mankind, as the Reckoning of Time, it is matter of Wonder, that the best way of doing it has not hitherto been found out in so great a number of Ages as the Earth hath lasted, especially since so many excellent Wits in several Parts and Ages of the World have em­ployed their Endeavours therein: But I see that Time and Chance, which happen to all, happeneth also to Time it self.

I shall now in few words give you my Contrivance (and that two manner of Ways, one for the Pen or Memory with the Demonstration; the other contrived into the Honourable Garter for an Instrument or Clock-work:) and afterwards I shall add, by way of illustration, some further Remarks thereupon.

A NEW-YEARS GIFT, IN A NEW ALMONAC FOR EVER: OR, A Rectified Account of TIME, by a new Luni-Solar Year. That is, By the Moon's Monthly Course primarily, so as the First of the Month shall always be within about a Day of the Change; and yet adjusted to the Sun's yearly Course.
(A larger Discourse hereof was lately Published)

LFT the New Year or Account begin with March 10, 1680/1. ^* From such Beginning, let the following Months, which in or­dinary Years are Twelve only, have days 30, 29; 30, 29, &c. alternately: But in Fourteen Years (of a certain Period or Revolution completed in Thirty eight Years,) viz. in the Years 2, 5, 7, 10, 13, 15, 18, 21, 24, 26, 29, 32, 34, 37, let there be intercalated or added to those extraordinary Years, a Thir­teenth Month, consisting of Days, 31, 30; 31, 30, &c. alternately also: And so on, Period after Period, for ever.

Once every Century, or to one Year of 100, add one Day, viz. to near about the middle of the first Century, and then to every 100th Year following.

Which additional Day being omitted every 230th or 240th Century, or thereabouts (accord­ing to the latitude of the differing Opinions of Dissenters in Astronomy) that is, once in 23 or 24000 Years (only the first omission to be about the middle thereof) if any one should require such great exactness, will balance the Account for ever. But we need not be solicitous about that remote consideration.

The Demonstration.
(Which may be passed over by those who are not accustomed to Mathematical Demonstrations.)

BEsides common known Principles, denyed by none, I suppose, or take for granted only two Things, viz.

1. That the Motions of the great Bodies of Heaven, particularly of our great Luminaries, the Sun and Moon, are Regular or Uniform, or at least do approach somewhat near towards being so.

2. That in taking the measures of their Motions, especially that of the Moon, all the famous Astronomers, Ancient and Modern, have not been much mistaken.

This Account of Time being made up by continued Addition, or Multiplicati­on, the Truth or Exactness thereof may be easily Examined or Demonstrated, only by Division of the number of Days in my Period or number of Years assigned, by the number of Months contained in the same; and the Quotient shall be (the Days, and parts of a Day in) a Month; or the Time at a Medium between Change and Change, according to the exactest Astronomers, ancient and mo­dern. As for Example,

In 38 Years there are Months or Lunations 470, viz. (38 times 12) or 456 and 14 intercalar, ones. And in 38 Years there are Days (38 times 12 viz.) 456 times 29½, that is 13452, and 14 times 30½, or 427, that is in all 13879 whole Days; together with 38 hundredth parts of a Day, viz. in all 13879:38, because one day is to be added every 100 years: Or more plainly thus, In (100 times 38, viz.) 3800 years, there are 47000 Months, and 1387938 Days. Multiply the said 3800 Years by 6, and likewise the said Months and Days by 6 respectively, viz.

Divide 8327627 by 282000, the Quotient will be Days 29:53059219854, that is 29 days, 12 h. 44 min. 3 sec. 10 third. (almost) viz. the Month of Ricciolus.

But if to each of the above Years, Months and Days respectively you add a twentieth part, there will be near 24000 years, viz.

Divide 8744008:4 by 296100, the Quotient will be Days 29:530592367444, that is 29 day. 12 h. 44 min. 3 sec. 10 third. 50 fourth. (almost) viz. between the Months of Copernicus and Kepler, &c. Near which, or between both, is probably the just quantity of the mean Month of Conjunction. However, tho it should hereaf­ter be found out to be less than the one, or greater than the other; yet the Account of Time by me proposed will hold good for about twelve thousand years yet to come; at which time the said Additional Day being omitted (only some few years sooner or later, as by experience shall appear best before that time) will keep right, and balance the Account for millions of years after.

But if any one will assign me the exact quantity or measure of the Mean Month of Conjunction, I shall tell him precisely what Century (or Year if he please) the said Additional Day is to be omitted: For the best Astronomers do differ a lit­tle even upon that Account, as may appear by the following List.

A New AL-MON-AC for Ever; or A Rectified Account of Time, (beginning with March 10 1680/1) by a Luni-solar Year, or by both Luminaries: That is By the Moons Monthly Course primarily; so as the First of the Month shall always be within about a Day of the Change: And yet adjusted to the Suns yearly Course also; viz Keeping within about a Week thereof at a medium: DESCRIBED in, & DEDICATED to the most Honorable ORDER of THE GARTER.

The GARTER shewes the Number [...] Da [...]s [...] 30, 29. &c.) which each of the Twelve Month's of the year is to containe: And in the Buckle is discovered, through a Hole, the days of a Thirteenth Month (31, 30, [...] 30 &c) to be added to Some years, viz to Fourteen of Thirty eight, or more particularly to the years 2, 5, 7, 10, 13, 15, 18 21, 24, 26, 29, 32, 34, 37. of a certain Period or Revolution completed in 38 yeares; as in a Cycle or Rundle behind; which is supposed movable one 38^th part, every year, backwards or contrary to the Months in the Garter: And the year of the Period or Cycle, or what 38^th year is Current, is shewed through another Hole. & so on for ever

Once every Century, or to one Year of 100, adde one Day viz to neer about the middle of the First Century, & then to every 100^th year following. Winsor Castle▪

Some farther Remarks on the preceding Account.
(Formerly published in the Philosophical Collections. N. 2.)

THe Egyptian Hieroglyphick of the Year was a Serpent curv'd into a Circle or Ring, with Tail in Mouth: but the Emblematical Garter will be much more proper for England, &c, and is so exactly fitted to the Moon's motion, that perhaps it will be hard to judge, upon consulting a whole Jury of Astronomers, ancient and modern, whether it will prove too streight or too large a measure of Time; and the exceeding small difference between this Account and some of their Calculations on one side or other, may rationally enough be ascribed to the imperfection of Instruments or Observations, 'till the farther experience of future Ages, many thousand years hence, shall evince the contrary.

This Almonac measures Time principally by the Moon, but with a great and near respect to the annual motion of the Sun or Earth: The Unite or least Mea­sure is a Day; and the Garter or Luni-Solar Year will be, at a Medium, within about a Week, or half a hundreth part, of the true Solar Year; that is, so near that the difference will not be discern'd by ordinary popular Observation, (and therefore must needs answer the ends of Husbandry, and other civil Affairs, well enough;) And at certain periods balance one another, and have a kind of coinci­dence or agreement, much better than the Suns course has with the Iulian Ac­count, so much magnified by Scaliger and others.

I find the elder World generally computed their Time (and most of the Ea­stern Countries, if not the bulk of Mankind, do so still) by the Moon, or by a Lunar, or Luni-Solar Year; made up of Lunations, or real Months, or some­what near the matter such, (and not such in name only, as ours now are; being, as it were, but the Ghosts and deformed Shadows of their old Moons and Reckon­ing:) Which Months were for the most part 12, and some years 13: This ap­pears from their Kalendars, &c. 'Tis plain (from 1 Sam. c. 20. v. 5, 18, 24. compared with v. 27, 34.) that the days of the Iewish Month, were the same with those of the Moon: And the Grecians (where Astronomy, as well as other Arts and good Learning most flourish'd, and particularly the Athenians accord­ing to the Institution of their wise Legislator, Solon) did thus reckon their Time; and so did the Romans too, till Iulius Caesar alter'd, I cannot say, mended, the Year.

Among the Grecians there liv'd, in three not far distant Ages, three famous Astronomers in their several Times, Meton, Calippus, and Hipparchus; each of whom still farther improv'd Astronomy, and rectified the Accounts of Time more and more one after another respectively, according to their light and the Obser­vations of their own and the foregoing Ages: Hipparchus, the last of them (and unto whom our modern Astronomers, with all their helps and advantages, have been able to add very little as to the exactness of some of his Observations) he flourished about 100 or 90 Years before Iulius Caesar alter'd the Year; yet Caesar, or his Astronomer Sosigenes, followed Calippus in framing the Iulian Year; as I find by examining their Accounts: For Calippus his Period of 76 Years consisted of 27759 Days, and so do 76 Iulian Years. About three Centuries and an half after Caesar, the Council of Nice (first,) and about two Centuries after that, Dio­nysius Exiguus (again) introduced the Decennoval Cycle (called the Golden Number) for the Celebration of Easter; following Meton, the first and least exact of the Three; or rather following both Meton and Caesar, two Masters, who were neither of them the best, and would after some time disagree and part far­ther and farther from each other; tho both Caesar and the Church might have had much better Copy from Hipparchus: Which mistakes of theirs (and their Eyes being dazled with the Sun, whereas they might have looked more safely on [Page 6] the Moon) have occasioned those Anticipations and Differences, that have em­barrassed the Accounts of Time, and these Parts of the World in the succeeding Ages. And tho many have proposed laudable ways of redressing the said Ac­counts, yet still building upon the old Foundations, which were infirm; Pope Gregory XIII, in his Reformation of the Kalendar near 100 years since, was ne­cessitated to wave the Golden Number, and yet has but palliated the Disease; so hard it is to cure an Error in the first Concoction: Wherefore inverting a Dystic of Ovid's, 1 Fast. one may say,

The Council of Nice appointed Easter to be kept the first Sunday after the first Full Moon after the 21th of March; because the Vernal Equinox (which was on the 25th in our Saviour's time, or thereabouts) was then come to be on or a­bout the said 21th Day; and therefore the Gregorian Reformation has reduced the Vernal Equinox back to that Day, or brought that Day to it again, by losing 10 Days, and must omit another Day within 20 Years: But in this Garter or Luni-Solar Year, Easter will always be the first Sunday after the frst Full Moon of the New Year, that is, after the Vernal Equinox; according to the true intent and meaning of the Nicene Council, or as it was in the Primitive Times; and be but a Week moveable, or a Month less-moveable than now, either after the Old or New Stile: Which might perhaps have prevented the Difference, or served as an Expedient for reconciling the West and East Churches.

The three Cycles of Meton, Calippus, and Hipparchus, were all of them too large for the Sun, and primarily intended for the Moon, or for a Luni-Solar Year; however that of Hipparchus was nearest to both, and very near the Moon's Period.

Perhaps at first view, my 38 Years Period may be looked upon but as a dou­ble-Metonic, or semi-Calippic one, &c. but upon farther consideration, it will be found otherwise; for Meton and Calippus, their Periods, as also that of Hippar­chus, were all of them too big, not only for the Circuit of the Sun, as I said be­fore, but for that of the Moon also; whereas mine, on the other hand, was too lit­tle for either, and needed one additional Day in near about every 100 Years: Meton's 19 Years Cycle, or Enneadecaeteris, had 6940 Days, the Double whereof is 13880 Calippus his Period, or 76 Years, had 27759 Days, the half whereof is 13879½ Hipparchus his Period of 304 Years, had 111035 Days, the Eighth part whereof is 13879⅗ Whereas my Period hath but Days 13879:38—

So that it may easily appear, to any one who shall please to examine it, where­in my Cycle or Period differs from all theirs: But the Frame of my Contrivance of this so nice matter, for the easie Explication thereof, even to the grossest Ca­pacities, as to Practice and Use, is wholly different from theirs, and every ones else I ever yet heard of.

I am not so vain, as to perswade my self, that any such Account of Time will be used, and therefore do not set down the Uses of this; which otherwise I could do, and shew how the Practice thereof need not make any disturbance in Civil Affairs or Contracts.

For 'tis not unlike but that, after 1700 Years Prescription, prudent Men may judge it better to let the Year and World go on without alteration; as Physicians say, Some Chronical Diseases in old Folks may with more safety be continued, than their Cure endeavoured; and that one had better follow old beaten High­ways, tho crooked and foul, than seek out, or make new ones: And perhaps I should have thought so too; but Pope Gregory XIII having already chang'd the old Iulian Account, and his new Model having taken place, and obtained in the major part of all the West of Europe, or Christendom; We, who are Reform­ed in other things, seem now to be left almost alone, or with some few other Pla­ces, [Page 7] in this. And several Persons having from time to time offered their Propo­sals towards the amendment of the erroneous Iulian Year, I thought I might without offence offer mine also; which are not so novel, but that the like there­of, tho framed with less artifice, have endured the Test in many well policed Na­tions for several Ages.

It may afford one Argument, by the by, against the old Way, or Year, That like a Finger-Watch, it needs so frequent setting, and must have a New Almanac got every year; whereas one Direction in this Luni-Solar Way may serve for all Ages; and the Garter may be so well buckled once for all, that it may last for e­ver, as the Moon, &c.

I chose rather to take the Revolution of the Moon, than that of the Sun, for my chief and primary Measure of Time; because, First, the Lunar Phases, and consequently Months, are more easily discerned, than the Sun's annual Period, even by the most ignorant vulgar Eyes, who need but look up almost any night, to see their Almonac: Next, the Observations upon the Moon, made by more knowing Men, have been more in Number, more exact and of far greater An­tiquity; Astronomers having also had the help of Eclipses of very distant Ages, for their Guide in finding out very near the true measure of the Moon's mean Motion: Lastly, keeping an Account by the Moon, we may reckon by the Sun al­so, that is to say, by Months and Years too; whereas on the contrary, reckoning by a Solar Year, the Months are but empty Names, and in measuring of Times and Seasons the Moon is rendred of no use; tho some inanimate Bodies (so con­siderable, that they take up and possess perhaps half this our Clobe) as the Sea, do exactly observe the Moon's Course; and there are living Creatures also, thought perhaps no less considerable at Land, that do the like; which I need not mention, nor take any farther notice of the near Affinity, if not Consanguinity with the Garter.

To conclude; the Sum of what I have done, is, after the finding a Par or Equation, or a very near Approach thereunto, between Days and Months, in whole Num­bers, with a respective balancing the Sun's Annual Motion also, To render the use thereof very easie and ready for Practice. I could in larger Periods keep a more re­gular balancing Account with the Sun, by a small addition, or very little alteration of one Rule of these Cycles; or by other great Cycles I could perform all that these do; or by a farther Decomposition of Cycles I could, I say, approach to a yet greater exactness, nearer and nearer to any given quantity, in infinitum; But ne quid nimis.

Upon the whole Matter, I judge an Account of Time by the Moon to be much better than any such Account by the Sun; because (setting aside other considera­tions) I have reason to doubt, that, as we are in the dark in reference to divers other particulars about the Sun, so likewise the Measure of the true Solar Year is much taken up on trust, or is not so well known, perhaps never will be, or at least is not so universally agreed on, to near that degree of exactness, as that of the Moon, which God appointeth for Times and Seasons, as the faithful Witness in Heaven.