\ for the founding cf a College ifl. 'Ml Colony"

A
NEW MET H O D
OF
'..'*; STATING and EXPLAINING
THE
Scrwpture Chronology,
UPON
Mofaic Aftronomieal Principles, Mediums and Batay
As laid down in the Pe n tat e u c h.

Ethnicis igitur nullum , tempus proprie* hiftoricum audiat,
nifi quod primam olympiadem fequitur^. Nos autem qui
Mofaicu gaudemus Ratioc'mih, ab ]ip$ primo homine,
mundoque condito hiftorias noftras exordiamur. Et
idcirco totum temporis, quod abipfii motuum \ ccelejlium
\r);^r't'iribus.i ad' hanc ufque Metam, five prafens tempus
effiuxerit, hiftoricum jure nominamus.
.}}¦'¦' Beveridge's67^W. Infl. I.i. c. 2.

By 7 OHN KE N'NE D r, Redjor of
Bradley in the County of Derby*

1 ^A**"*' LO N D O N:
Printed for the Author. Mdccli.

P R E F A C E.

THE importance of the point, the fetling of which
is the attempt ofthe following iheets, fully, ap
pears from it's having employed the refearches and pens
of the moft learned and inquifitive in all ages ; arid
. the difficulties, with which it's determination is attended,
are no lefs apparent from all 'humaji calculations hav
ing been hitherto devoid of agreement, and their en
deavours unable to bring it to any precife regulation.
T^o afcertain then a branch of- fcience no lefs difficult
than ufeful to be adjufted, may be thought well to
claim- the divine interpolation.
¦—— .  Deus Jnterfit.—^— Dignus vjndice Nodus
flncidit.  — ,
I therefore prefent the reader with a fyftem of chro
nology built, upon Mofaic principles and data ; and dp
requeft of him to lay afide, fopa while, ,all preconcep
tions of difficulties and objections, 'till he has viewed
. my' whole fcheme, and confidered^it in all* it's parts.
It has feldom or never happened, that a fcheme of
, any kind, has been brought to perfection in the firft
attempt. But here it muft be remembered, that the
, fcheme of genuine facred chronology, is of too refined
and delicate a nature to admit of any mean ; and the
proof of it, like the fource and fountain from whence
it was derived, muft be perfeS in it's origin.
My calculations, founded on the terms, principles
and data of the Pentateuch, lay a claim to a juft exadi-
neisj and .fhould they, upon a due examination, be
found liable to. produce erroneous conclufions in Sun,
.and Moon aftronomy, they cannot be Mofaic, and I
,muft acknowlege myfelf to have been guilty of a very
<,higk Mifnomer, fm. giving them fuch a facred appella
tion. And therefore the conviction of a fingle error in
time from. the creation to this day, w^ch, upon no-
a 2 tice

IV

P R E F A C E.

tice give«7 rannot ' be corrected upon the -principles
laid down, -muft be admitted as a confutation of this
whole performance, and there will be no plea left,
but only, Quod ft non tenuit magnis tamen exciiit aufss. ^
The more immediate view of this work is to' evince,
amongft others, the following propofitioris, which
"were drawn up by me nearly in the "fame form and
"publimed'forne time ago, when feveral' fubferiptioris
we're taken in upon them ; and forry I am that I could
hot difcharge my obligations foOner to thofe, who
were lb kind as to encourage my defign, which I cer
tainly would have done, had I not "in this interval met
with many unexpected interruptions.
1. The original pbfitiori of the two great luminaries,
the Sun and Moon, with refpect to the EaVth/'on the
fourth ofthe Hexaemeron, deduced from the firft chap
ter of Genejis, and afcertained' in the Levitical law,
by Mofes, when he enjoins the obferva tion of thefeaft
of the In- gathering on the 15'th day of ' the "month, in
-the revolution, i.e. end of the year: here the nurrhber
15 (which is the Scripture full-moon day, and was
its quality on the 4th of the Hexaemeron,) does really
and in fKct, with a true aflrOriomical exactnefs, ex-
prefs the 'diftance of the Mofaic cardinal, /. 6. autumnal
aequinoctial point, from the evening of the Moon's
vifibility, — '¦  =^= ® O
II. An aftronbmical determination on what day of
'the week was the 4th of the Hexaemeron, collected and
ftated from the Mofaic terms of computation, viz.
days, weeks, and years ; beginning his account of
. time, arid his Chronology, from a cardinal point of
the heavens, viz. the autumnal axjuinox ; and from
a cardinal point of the day, viz. noon, with refpect to

PREFACE. v
tothe Mefuic<mtri$im, which is geographically defcrib-
ed, Gen. ch. 2. ver. ro. &c.
III. Mofes meafures the lives of the; patriarchs, by
the courfe of the Sun, or tropica!' folar . years ; and
records all hiftorical tranfattions and events, by the
<rrrbnfhs: and days of the lunar year, computed from
hew'Moon(0 to new Moon (C).
IV. Jn- confequence1 of Hie preceding propofition,
it will'appear'from-Gw. i. i^.-bni-Mofes-s account of
the deluge, that* W&ah .was in the ark, part of two
diftjnct felar,- and partof two diftinct lunar,, years.
3 N?Rs ( 1 ft) -The two diftinct folar years are exprefTe'd
by the riumbers €00 and 60 1 . Gen.ch. y?Ver.n. and
ch.v8\i/er.'i2. "'TKe-^wo diftinct -lUfrar years are thus/pointed out:
iVtfs^'eritered'tnto'the'ark, Gen. ch. 7. ver. 11, on the
17th day of the 2d month of that lunar year, which
-was -concurrent with the 'folar year of his life 600 ;
and he received the -divine command to come out of
the ark, Gen. ch. 8. ver. 14,15, on the 27th day of
the 2d month of that- fanar year, which was concur
rent with the folar year of his life, 601.
(idly) In the year of Noah 600, in which the de
luge began and ended, there was a co-incidence of the
lunar year with the folar, the epact at the conclufiqn
of that year being 11, and is plainly deducible from
the Mofaic account, according to the Hebrew text.
(3dly) The Mofaic hiftorical narration of the circum-
ftances,procefs and conclufion ofthe deluge, is extremely
curious, and will be found to be the key, whereby we
may open many, if not moft, of the fecrets of the fcrip-
ture computation, as,- (1) not only the number of
days in a month, but alfo the manner of computing
and adjufting the months,, both of the folar and ofthe
lunar year. ,(2) The quality ofthe Moon which enn-
' ftjtutidi the head or beginning of the lunar year. (3)
-•'-' - The

vi PREFACE.
The primitive -and true aftronomical law, of connect
ing the lunar years with the folar. •,
V. It will appear from1 the Calendar of the year of
Noah 600, -when rightly collected from th& rMofaic
narration, that the feveral characters, by which any
,given fcripture year, is diftinguifhed from another, are,
the day of the month, the day of the week, and the
cardinal point of the day in which the Sun crofTes the
Mofaic cardinal point- of 'the heavens : from Jience it
comes to pafs, that the. day of the week never occurs
in <tht Pentateuch^ or throughout the ift^racrfcriptures,
becaufe it is not only included in (general, but aftrono-
mically given, as I fhall prove, in the day of the
month; e.g.- when Mofes tells us, Gen.ch.8. ver. 4.
that the ark refted on (one of) the mountains oi Ara
rat on thef 1 7th day of; the 7th month of that year in
which the dekige began, he had no occafion to add, •
'that it was on the 4th day of the week. Points which
may be juftly 1 reckoned: amongft the fecrets of ,the
antient and original computation,
VI. Mofes's canon (i. e. lift, roll or catalogue) of pa
triarchs, from Jdam to Jofeph'ixvAxxfavc, containing an
interval of 2369 years, according to the Hebrew text,
is a moft accurate aftronomical canon ; and may be
proved to be fo, independent of any .period,*, epocha,
• or computation, except what is founded on. the terms
and principles of the Pentateuch, and the given < charac
ters of the world's sra.
VII. The Mofak genealogies, both before and after
the flood, conftitute an uninterrupted, and, fucceffive
chronology, which, aftronomically afcertains the true
extent of the world's paft duration •, becaufe,
1 ft. The years of the patriarchs run parallel iwith
the years of the world,
2dly. Every Mefaic (and Scripture) Sbanab is a true
folar revolution. VIII. The

PREFACE. vii
VIII. The' quantity of the folar tropical year may
be afcertain'd with the minuteft exaetnefs, to an indivi
sible point, from a year of commenfuration, fuggeftcd1
by this text of Scripture, and othersof the like import;
Gen:c.^,.v:zy. All the days of Methufahh^rtrt'^6c)years,
And it may be neceffary to obferve, that the*
exact commenfufation of the annual and diurnal re
solutions, has happen'd but 3- times fince the creation:
the- fourth will be completed A. D. 1 y^, at the au
tumnal asquinox. (
IX. There can be no chafm in the Scripture-chro
nology, becaufe it may be demonftrated that there is ,
no interruption > in the Scrip ture-aftronomy.
X. The form of the patriarchal twofold ft. e. both,
folar and lunar) year, is no where to be found, but in
the patriarchal line.
XI. The year of 360 days, which, for many ages,.,
fb generally prevailed in the poft diluvian world, will.,
appear to be, probably, nothing more than a mutilation
ofthe original and patriarchal folar tropical year ; be
ing the only part of the primitive, computation, which
the defcendents of Ham and JappetYs and .fome branches
of the family of Shem, retained in their feveral, difper-
fieas, Mr. Whifi.on\i2& frameda plaufible and, ingeni
ous theory upon this fingle article, but, it has no foun-.
dation in Scripture.
XII. The terms Antediluvian, Mofaic^ and Scrip
ture aftronomy, are not to be underftood, as relating
to, and comprehending, the planetary fyftem; they
are, to be confin'd to the Sun (and Moon) confidep'd
as the natural adequate meafure of time, by its an
nual revolution. To which office it was originally
defigned and appointed by God himfelf at the creation;
and to which it is conftantly and with great exaetnefs
applied in the chronology of the Pentateuch. N. E.

yln PRE F A C;E, t;
¦ ,N. B. To render my aftronomicalcatculationSTplain
and eafy to be underftood, I have infertecl and explain
ed a concife aftronomical tabj-e,, both folar and lunar,-
conftructed froni the inverted pofition ofthe lumina-,
ries,- A, M. i. and A. M., 1656. {See Page 14-I
And fhould the world continue any definite, number
of, ages, the table, founded on this inverted pofition
will ftand in need of no alteration or correction.
The 'purport of this-undertaking, will not lead mej
to treat ofthe origin, or to fettle the chronology, of the-
moft antient. kingdoms and. nations, where the Scrip
tures are filent. Pf or fhall I attempt the connection
of the Sacred Hiftory with the Profane: and indeed**
was I defirous'-to do it, I know not of one inftancOof*
that kind,, which Can be depended upon with certainty,
(excepting the sera ofthe Olympiads, ofthe building^
of" Rome, according to Varro, and the sera of Nabonaf-
far,) before the expedition of Nebuchadnezzar, into
Judeea, &c. mentioned by the prophet Daniel ch. 1,
ver. 1, and is confirmed by the much noted fragment
ofBerofus. Neitheris it neceffary to make .a digreffion,1
in order to ftate and explain the moft antient forms
of year, which have been in ufe fince the flood 5 but
T fhall entirely confine my enquiries to the Mofaie and
Scripture year ; and it will be my peculiar province
to collect the principles and data, which lie difperfed
thro' the Pentateuch,- and to undertake to prove* by
their affiftance, that the whole of Sacred chronology*
is built upon amoft fure, and truly aftronomical, foun*
dation. Thefe are fome of the particulars which may
be ftill reckoned amongft the neceffary and effent-ial
iefiderata, notwithftanding the many learned' andJ
elaborate volumes^ which have been wrote and pub
lifhed 'upon the fubject of the Scripture chronology.

:71

A Table of the moft material Errata. For two other
Corrections, vide Poftfcript.
)AGE 69. I.26. for, polar  revolution, read,
polar revolution, without a feparating line.
P. 70. I.17. for, Befhanim, read, Vefhanim.
P. 84. J. 10. for, September 8+ October 31, read,
November 8+ October 31.
P.87. 1.8. dele, which.
P.90. I..5. at intelligible, place a coma for the period ;
and for, now, read, nor.
P. 105. k24. for 59 h. 8 m. read, 59' 8".
P.i 12. l.i. for, 9+30, read, 9X30=270.
P.163. l.io. after 360, add the word, days.
P. 18S. l.io. for, ben fomo, read, benjomo.
P.199. I.21. for the 15th day after the 1 6th of Nifan,
read, the 50th day.
P.213. I.9. for, Mogdanim, read, Mognadim.
P.368. I.16. the references fhould be 351, 353.
P.396". 1. 2. for p. 351, read, p. ^go.

NEW METHOD O F,
STATING and EXPLAINING

THE
Scripture Chronology, &c.
[Ccording to the Hebrew (which is the
only true) chronology, We are now
in the. fixth millenium of the world's
paft duration, viz. in the 5758th
current year. .And yet, even in thefe
latter times, in a philofophical, aftronomical, and
mathematical age, neither the learned of our
own, nor of any other, nation, (as experience tef-
tifies) have been' able to teach us, how to accom
modate by fixed and determinate rules, the true
meafures of the annual periods of the two great
luminaries, either to civil or religious ufes : I mean,
not with that exaetnefs and certainty, by plain,
fimple, and yet, unerring laws, which the pri-
A mit'ive

( 2 )
mitive patriarchs were originally taught and prao
tifed ; as will demonftrably appear from the Pen
tateuch of Mofes.
Firft then we are to ftate' and determine the
Original pofition of the 3 orbs, the Sun, Moon, and
Earth to one another ; which' is the fundamental
datum of the Pentateuch, and to us, a neceffary
and important point of knowlege.
Mofes concludes his hiftorical account of the
Hexaemeron j with this remark, And Godfawall
that he had made, and behold, it was very, good,
i. e. every part of the univerfal fyftem, whether
inanimate, animate, or rational,, was created in a
ftate of original perfection.
As the two great luminaries are ever varying
their mutual afpects to each other, their relations
and diftances ; was I to afk the aftronomer, what
we might infer from nature, to be their firjl fitu-
ation, with refpeft to the Earth ? He would, it;
is probable, fmile at my fimplicity \ or, perhaps,
give me fome fuch ferious anfwer as this, viz.
j[n a circle there is no firft point by nature, but
only by pofition.
But was I to afk the fame aftronomer,, what
was xhfmojl perfeEi, and therefore, by juft ratio-*
cination and inference, the original pofition, I do
not think he would look upon this queftion as
abfurd, or treat it with ridicule.
I will endeavour to deduce this point from fome
particular expreffions made ufe of by Mofes in the
firft chapter of Genejis, and afterwards confirm it
by certain texts in the Levitical law.
Gen.

(3 )
Gen; ch. i. Vei\ 14, And God faid, 'lei there
be lights (Heb. and Gr. luminaries) in the firma
ment (Heb. expanfe) of the Heav,ehs\ to divide the
day from the night. (Heb. between the day, and
between the night) and let them beforfigns, and
fof feafons, and for days ¦, and for years.
Ver. 1 5. And let them be for- lights (Heb. and'
Gr. luminaries) in the firmament (Heb. expanfe)
ef the Heavens, to give light upon the Earth,
(Heb. lehair(£on]apit.h\ph.i\)gnalhdaretz, to caufe
to fhine over the wholeEarth, even to enlighten the:
whole extent of its furface, from the one pole to
the other) and it wasfo.
Ver.^ 16. And God made two great lights^
(Heb. and Gr. luminaries) the greater light (lu
minary) to rule (Heb; for the dominion of) the
day, and the lejfer light, (luminary) to rule (Heb.
for the dominion of) the ¦ night* He made the
Jlars alfo. (Heb. and the ftars.)
Ver. 17. And God Jet them in the firmament
(Heb. expanfe) ofthe Heavens, to give light upon
the Earth (Heb. to caufe the whole extent of the
Earth to fhine.)
Ver. 18. And to rule over the day, and over
the night, and to divide the light from the dark-;
nefs. (Heb. between the light and between the
darknefY.) AndGodfaw that is was good. s
Ver. 19. And the evening and the morning
was the fourth day.
Should we enlarge our ideas of the univerfe into
as many fyftems as modern philofophy fuggefts,
A 2 into

(4)
into a numberlefs hoft of funs, and" an indefinite
plurality of worlds, thefe words of Mofes, may be
fairly extended to comprehend them all.— — -
Let there be luminaries in the expanfe, of the
Heavens. — Upon a bare perufal of them, our
thoughts immediately begin to range the whole
circuit of the fky, and we raife our contempla
tions to the Sun,, the Moon, the planets, the co
mets, the fixed ftars, and all the hofts of Heaven :
and we can fcarce help indulging a pleafing hope,;
that Mofes is about to draw the veil, and open to
our intellectual view the fecrets of the univerfal
fyftem. But the following words, in the begin
ning of the 1 6th verfe^— And 'God made two great
luminaries — effectually refirain all fuch fpecula-
tive excurfions ; the fcene immediately clofes, and
we are, in a moment, convinced, that Mofes, in
ftead of multiplying fyftems, and enlarging our
ideas of the uniyerfe, contracts his aftronomy
within narrow limits, and labours to fix our en
quiries and contemplations upon the Sun, and the
Earth's conftant fatellite, the Moon.
Ver. 1 6. And God made two great luminaries.
Mofes, it is manifeft, takes, no fmall pains, to
let the reader know, that he is not delivering to
the world, a fyftematical aftronomy; and thefe
words — God made two great luminaries— are evi
dently wrote, not in exclufion of, but in contra-
diftinction to, the fixed ftars,. and the planetsr
which are ranked amongft them. The numeral
twdt is fet in direct oppofition to their multitude j
and

(5)
and the epithet great, is fet in direct oppofition
to their apparent diminutive magnitude.
Firft, to their multitude ; when in a clear win-f
ter's evening, we lift up pur eyes to the fpherjcal
concave, we fee it befpangled with ftars, innu,
merable as the fand upon the fea fhore ; and the
Pfalmifi, Pf. 147. ver. 4. fpoke a literal truth
when he faid, It is God who telleth the number
of the ftars, and calleth them all by their names.
Secondly, to their apparent diminutive magni
tude. Though it fhould be admitted, that every fix
ed ftar, in itfelf confidered, is a great luminary,
and that it fhines like our Sun, with its own na
tive and inherent light ; yet, with refpect to the
evidence of fenfe, they are comparatively very
fmall. Take a ftar of the firft magnitude, fup-
pofe Sirius-, view it through a telefcope, and it
will be found to have no diameter, but appear on
ly as a lucid point. This diminution of their
magnitude, arifes from the immenfity of their
diftance ; nay, fo immenfe is the diftance of the
fixed ftars from the Earth, in the aftronomer's ac
count, that he affures us, the whole diameter of
the great orbit, will not furnifh him with an angle,
of observation. But Qod, fays Mofes t made two
great luminaries.
Ver. 16. The greater luminary for the domi
nion of the day, and the leffer luminary for the
dominion of the night.
Mofes does not ufe thefe terms — the greater lu
minary, and the leffer luminary — for want of
ap-

(6 )
fcppellatives ; fince afterwards, Deut. ch. 4. ver.
39. he calls the one Shemejh, the Sun; and the
other Jareach, the Moon. He was guided here
in by a divine wifdom and direction. For had it
been faid — let the Sun and the Moon be in the
expanfe of the Heavens ;— and God made the Sun
for the dominion ofthe day, and the Moon for
the dominion of the night;— this, with refpect
to us, would have been undoubtedly true : yet,
might it not with fome colour of reafon have been
objected, that God made all the hqfts of Heaven,
Gen. ii. 1. as well as the Sun and Moon ? Mofes
therefore, has wifely evaded both the cavil and
the objection, by writing, not in exclufion of, but
only in contradiftinction to, the more remote parts
of the univerfe, with which we have not either
art immediate or known connection.
In the former part of the 16th Verfe, the Sun
and the Moon are fet by Mofes j in a ftate of Com-
parifon, with the fixed ftars and planets; in the
words immediately following, they are compared
with each other; and in this laft ftate of compan
ion, the Sun is the greater, and the Moon the
leffer luminary, in refpect of the different light
they afford.
Ver. 16. And the fiars. (Heb. vococabim.)
Our Englifh tranflators have inferred in this
place the words — he made alfo — which is a mif-
take. And had there been any difficulty in un-
derftanding the fenfe of the words, as they lie in
the Hebrew text, the comment 'of the Pfalmifl.
would have cleared it. Pf. 136. ver. 8, 9. who
made

(7)
made, the Sun for the dominion of the day, the
Moon i^Ttd the ftars for the dominion of the
night. ,.
Mofes includes both the fuperior and inferior
planets, under the general denomination1 of (co-
cabim.) ftars. And, in truth and matter of fact,
is not the planet Venus, for inftance, our moft.
bright, both morning and evening ftar ? Do not
the fuperior planets, Saturn, Jupiter, and Mars,
regularly rife above the horizon, in the form and
appearance of ftars ? Do not the fixed ftars,
with their united radiances and fcintillations fhare
with tl^e Moon, in the dominion over the
night? And as it is plain that Mofes ranks the planets
with the ftars, fpeaking from appearances and
the evidence of fenfe, we have no grounds to ex
pect a formal account of their magnitudes., denfi-,
ties, diftances, periods, fatellites, &c.--of all which
there is a moft profound filence. .
Whatever worthy and exalted apprehenfions
of the author of nature, the infinite perfection of
his attributes, or of the extent and magnificence
of his works, reafon and philofophy may dictate
and difcover to us ; to whatever important ufest
God, in his infinite wifdom and power, may
have deftinated the planets and the fixed ftars (in
the difcovery of which, we have no other light
to 'direct us, but bare conjectures, and arguments
drawn from congriiities) Mofes, by divine direc
tion, has withdrawn our thoughts- and fpecula
tions, from all fuch far diftant objects ; not only be-

(8)
becaufe we have no vifible relation to, nor per
ceptible connection with, them, but rather (as
we may with certainty and confidence affirm ) be
caufe, they do not meafure our time, either by
their real or apparent revolutions. God has crea
ted and ordained two great luminaries, the Sun
and Moon, to be unto us, for figns, and for fea-
fons, for days and years ; and to this motion only
Mofes, with great judgment and accuracy, confines
his aftronomy.
From the beginning of the 2d verfe to the end
ofthe firft chapter of Genefis, the facred hiftorian
treats not folely of creation ; but evidently *&f/ t««
J'tctx.oa-iJitiffiac, de ordinatione, of the orderly and re
gular difpofition, of the moft eminent and con-
fpicuous parts of the world, as they were fitted
up and prepared, by a moft exquifite fkill, wif-
dom, and contrivance for our benefit, and for our
accommodation : hence the world in Greek is
called w^, ornament, order, beauty. And par
ticularly in the 4th ofthe Hexaemeron, the Mo
faic hiftorical narration, treats notfo much ofthe
actual creation and production of the greater lu
minary, the leffer luminary, and the ftars, as of
their pofitions, ufes, offices or ordinations, and
final caufes : the hiftorian never fails indeed, as
he proceeds in the narration, to point out the ef-
"ficient caufe, and is very careful, in every in
ftance, to inform the reader, that every thing'
which exifts, was caufed to exift by the power
of God's word.
Ver. 1 5. To give light upon the Earth. Shpuld

(9)
Should a man, fix feet high, ftand upright up- •
on an even extended plane, the radius of the cir
cumference or circle of his obfervation, would
not reach (as it is faid) above 3 miles ; within the
limits of this horizon, the furface of the earth,
and every object prefented to his View, would be
illumined by the rays of the Sun.; and he would
perceive that the Sun by day, and the 'Moon by
night, did, in a literal fenfe, give light upon the
Earth, as it is exprefs'd in the Englifh tranfla
tion : But fuch a limited horizon, cannot con
vey to the mind a full, adequate, and fufficiently
comprehenfive idea of thefe words in the original.
We muft here abftract our thoughts, and to ufe
the words of Mr. Keil, " We muft rife in our
" imaginations in a line perpendicular to the eclip-
" tic, as far above the Sun, as the Sun is diftant
" from the earth ; and from this celeftial obfer-
" vatory, we fhould fee the Earth defcribing the
" fame great circle in the Heavens about the Sun,
" as the Sun feems to" us now ' to defcribe about
" the Earth." And we fhould moreover perceive,
that the words of Mofes, iehair gnalhaaretz, taken
in the full extent of their fignification, exprefs
thus much, viz. And God faid, let the great lu
minary in the expanfe of the Heavens, caufe the
whole Earth to fhine, and diffufe the light, warmth,
arid influence of its rays, from pole to pole.
Having thus far prepared-the way, and clearly
fhewed, that Mofes confines his aftronomy to the
Sun and Moon ; which he calls the two great lu*
minaries, not in exclufion of, but only in con-
B tra-

( I0-)
tradiftindtion to, the planetary fyftem; I fhall now
colled and confider, the terms and expreffions
made ufe of by Mofes, in his account of the 4th
of the Hexaemeron, which evidently and ftrong
ly infer (nor can it efcape our diligent attention)
the pofition of the two great luminaries, with
irefpect to the Earth, at their creation; and this,
before I cite thofe particular texts, in the Levi tical
law, which directly ascertain it.
Had not the original pofition of the Sun and
Moon (the fubject of our prefent refearches) been
an exprefs datum ofthe Pentateuch j and could it not
have been evidently and ftrongly infer'd (as it
certainly may) from the terms and hiftorical nar
ration in the firft chapter of Genefis^ yet I cannot
but think, that a competent knowlege of the doc
trine of the fphere, and abftradt ratiocination,
muft foon have difcovered to us, that the moft
perfect (as all things were conftituted in the be
ginning, by the moft confummate wifdom) muft
neceffarily have been the firft pofition : and the
only queftion to be difcuffed, would be, what is
the moft perfeB pofition of the Sun and Moon, with
refpect to the globe of the Earth ?
Ver. 1 5. Let them be for lights in the firma
ment of Heaven to give light upon the Earth. (Heb.
Let them be for luminaries in the expanfe of the
Heavens, to enlighten the whole globe of the
Earth ; to fpread the influence of their refpedtive,
though different degrees of light, from the one
pole to the other.) The words of Mofes in the ori
ginal

( II )
ginal do, I am perfuaded, include the whole of
this fenfe.
Now it is certain, from the doctrine of the,
fphere, that neither the one .nor the other of the
two great luminaries can perform this office; nor
could they have difcharged this primary ordination
of their creator, directly and at once, but from
the middle points of declination and of latitude ;
from the sequinoctial point, with refpect to the
Sun ; and from the point of interfection, or near
it, with refpect to the Moon.
Ver. 14. And God faid, let there be (two
great) luminaries in the expanfe of the heavens,
to divide between the day, and between the night.'
Heb. lehabdH ben haijom, itben hallaijelah. Gr.
Is it poflible to read thefe words— to divide
between the day, and between the night — and
not perceive the Sun in the aequinox, and the
Moon near the nodes ? If thefe are not equinoc
tial terms, we have no language to exprefs
them. At the end of the 1 5th verfe, Mofes fubjobs
vaijehi chen, and it wasfo. Thefe words are but
few, but they are very emphatic, and may be
faid to conclude the argument. The Scriptures
teach a firft-caufe philofophy, above the reach of
human language : we learn from hence, that
with God vofpeak, is to aft ; amar vaijehi, fays
the Pfalmift. Pf. 33. 9- he Jpake, and it was;
and that with God, to will is toperform; zivvah
vaijagnamod, he commanded, and it (the world)
B 2 was

( 12 )
was eftablifhed. When God fays, be itfo, it is Jo.
We may therefore, upon juft and folid grounds
expect to find all thefe points to be literally true,
exactly as Mofes has expfefs'd and ftated them ;
and they will moft , furely be proved to be fo.
Vaijehi chen, and it wasfo.
Here it may be proper to recollect the charter
of dominion given by God, to the Sun and Moon, -
immediately at their creation.
Ver.' 1 6. And God made two great luminaries,
The greater} } day.
and ^-luminary, for the dominion of the >
The leffer ) J niSht-
As there are 29 different epacts, the pofitions of
theMoontotheSun, at the end, or in the revolu
tion of every year, are various, and confequently
muft produce various degrees of illumination : but
when the Sun is in the aequinoctial point, and the
Moon near the nodes ; in other words, when the
Sun enters libra, on the 15th day, computed
from the evening of the Moon's vifibility (which
is the Mofaic and original full- moon)
Then is the night commenfurate to day,
Then the two regents bear diyidedyw^y.
This diftich (no matter for the poetry) contains a
fine aftronomy; and it contains moreover the true
aftronomy of the original pofition of the Sun and
Moon (with, refpect to the Earth) on the 4th of
the

,( >3 )
the Hexaemeron, which was (as J. fhall" (hew
hereafter) the autumnal aequinodtial day.
On the evening .of this day, the moon arofe
upon the germinating and fruit-bearing earth (be
ing recovered by the divine command, , from the
incumbent deep) in its original ftate of decreafing
perfection. By this means, the whole circumference and
extent of the globe,- and every point of it, was
enlightened by the two luminaries ; by the Sun
in the one hemifphere, and by the full Moon in
the other. And thefe words of Mofes, lehair
gnal haaretz, to enlighten the earth, were effec
tually made good in their utmoft extent of latitude
and fignification.
This furely is the moft perfeB, and it was, as
furely, the original pofition of the two great lu
minaries; and had 1 no other proof of it, I fee
not how it can be confuted.
The fon of Sirach has given us a beautiful and
elegant defcription of the Moon, which is thus
exprefs'd, Eccluf. ch. 43. ver. 8. » o'exiwi — ?,»*«?
i. e. The Moon is a luminary, which decreafeth
at its perfection, viz. after the full ; encreafing
wonderfully «**<>;»«-« in its various phafes, viz.
after the change.
This defcription plainly refers to the two prin
cipal lunar phafes,- we. the full Moon, and the new.
In the Pentateuch We have both, of .them. In
the beginning of the old world, or at thccreation,
the Sun began its courfe from the autumnal aequi-
nocW

( H )
nodtial point, on the Scripture full-moon day,
which is the 15th from the evening of the Moon's
vifibility, as has been already obferved; and at
the conclufion of the old world, A. M, 1655,
the Sun finifh'd its revolution at the fame cardinal
point, with a new Moon(() fo that the original
pofition was there inverted.
I will here fet down, though by way of anti
cipation, the aftronomical characters at the begin*-
ning and conclufion of the old world, that -the
reader may fee what kind of aftronomy he is to
expect in the progrefs of this work.

Adam — — O 130 ©
Seth  105
Enojh ¦ 90
Cainan ¦ •¦ 70
Mehalaleel  65
fared ¦ ¦ 1 62
Enoch — — 65
Methufalah  ¦ 1 87
Lantech ¦  182
Noah ¦ 599

s-*V.

0 A. M. 0 » ; 4
C, 15 O 15 C. 3^655 O 15 C 15 O
I will now prefent to the reader's view the
whole aftronomy of thofe two remarkable years
of the creation, and ofthe univerfal deluge, A. M.
r. and A. M. 1656. V. Noa 600 ; in the fame.
method, as he will find ufed by me all along, in
the following calculations. The

C 15 )
The: following is the pofition ofthe lunar year to
the folar, A. M. 1 . as computed from full Moon to
full Moon, which is the. facred and ecclefiaftical
lunar year : and likeWife, as.computed from new
Moon to. new Moon ; .by the months and days of
which lunar year, all .hiftorical tranfadtions and
events are recorded throughout the Scripture hif
tory/ I defire this observation may be remark'd.

(1) 1 A. M. o The Sun in the ^
Mofaic cardinal point, or libra. — ©
(2) The full Moon arifing upon
the earth. . .  — O
, (3 ) The chaotic newMoon epadt C 1 5

I.
A.M. 1.
./v
,©
354 ° 11
339 c 2°

The pofition of the lunar year to the folar. A.
M. 1656. V.Noa 600. II.
(1) The Sun in the Mofaic
cardinal point, or libta. A. M. ^
1655, ending — — — 0 A.M.1656
(2) The diftance of the full
Moon from the Sun. O 15339 O 26
(3) The new Moon epadt o. <[354 C 11
He that will examine, with fome fmall degree
of attention, thefe two fhort tables, muft im
mediately perceive that the full Moons and new
Moons have changed their places, and that diffe rent

rent fymbols are, therefore, prefix'd to fimilar fi-
' G ®
gures, viz. 6 1 1 . A. M. i . i . 1 1 . A, M. 1 656.
The difcovery of the inverted, pofitions of the
Sun and Moon, at the beginning and conclufion
of the old world, and of the1 co-incidence of the
liinar year with the folar, as computed from
full Moon to full Moon, A.M. 1. (fee the table)
and as computed from new Moon to new Moon,
! A. M. 1656. (fee the table) is of too great ufe
and importance, to be exprefs'd in a few words,
as the feqMel will fully fhew, nor is this a proper
; place for it.
He that can convict either of thefe tables of er
ror, muft neceffarily overthrow my fcheme, be
caufe the whole of the following demonftrations
depend upon them, and proceed by them. If no
one can, then it muft ftand its ground, as being
built upon a true and fure foundation.
Having laid before the reader a fpecimen of
; that perfection of aftronomy, which Mofes expli
citly teaches in his Pentateuch (as I hope clearly
and fully to prove by degrees) I fhall go on to
confider the 17 th and 18 th yerfes of this chapter,
which contain the remainder of MoJ'es's account of
the effect, which the two great luminaries, were
ordained immediately to produce, at their creation,
upon the globe ofthe Earth.
Ver. 17, 18. And God fet them in the expanfe
ofthe Heavens, (1) To enlighten the whole fur- face

/( i7 )
face of the earth. (2) To rule over the day a,nd
over the night. (3) To divide between the light
and between the darknefs. And God faw that it
was good.
Before I endeavour to account for thefe fimilar
expreffions, and feeming repetition of what was
faid before, I fhall collect thofe terms, made ufe
of -by Mofes, in the 14th, 15th, and 16th verfes,
and fet them down in one column ; and thefe laft in
another over againft it, that in this view of them
together, we may be able more readily to form a
judgment about them.

I.
Ver. 14. And God faid,
let there be luminaries in
the expanfe of the hea
vens. ( 1 ) To divide between
the day and between the
night. (2) For the dominion
of the day, and for the
dominion of the night
(3 ) To enlighten the
whole furface of the
earth. (4) And it was fo.

II.
Ver. 17, 18. And God
fet them in. the expanfe
bf the heavens.

( 1 ) To di v ide between
the light and between
the darknefs.
(2) To rule over the
day and over the night.
(3) To enlighten the
whole furface of the
earth. (4) And God faw that
it was good.
Some, perhaps, may think they have a right
here to" charge Mofes with a vain tautology : and
C in-

( i8)
Indeed it muft be acknowleged, that there is the r
appearance of a bare repetition, excepting princi
pally and chiefly, that he fubftitutes the words —
light and darknefs— -in the 18 th verfe, for thofe
Xii— night and day— in the 14th.
: When we examine the particulars of the two
columns, we muft obferve, that this is the only
confiderable variation ; and I will venture to fay,
that this one is of fuch importance, as muft, I
think, itfelf convince us, that Mofes could not have
made it* or have wrote in this manner, either
without the affiftance of a divine director, or be
ing able to penetrate, hy an extraordinary philo-
fophic acumen, into the inmoft depths andfecrets
ofthe fphere, as he lived before we have any ac
count of the cultivation of fcience.
y To evince this, I fhall firft fhew, that thefe
fimilar expreffions, viz. (1) To enlighten" the ,
whole furface of the earth. (2) To rule over
the day and over the night, cannot, if taken to
gether, be applied to the Sun, in any point, but
the sequinodtial; nor to the Moon, but in or near
the point of interfections of the 3 circles, of the
asquinodtial, ecliptic, and the Moons orbit.
Secondly, That the fubftitution of the terms—
light and darknefs, inftead of — day and night—
are to be look'd upon as Mofes' conclufive proof,
of the confummate perfection of the original po
fition. Firft, I am to fhew that thefe fimilar expref
fions, cannot, if taken together, and as Mofes has
connected them, be applied to the Sun, in any point but

(19)
but the aequinodtial, &c. I am obliged to add,
if taken together, becaufe if taken feparately, one
of them may be truly applied, in any given de
gree of its oblique circulation ; as is obvious to
apprehend, and, may eafily be made to ap
pear. Ver. 1 8. (2) To rule over the day and over the
night. Where there is no elevation or depreffion ofthe
pole, there Can be no variation in the length of
the days. Hence it comes to pafs, that thofe,
and only thofe, who live under the aequator, con
ftantly experience 12 hours night and 12 hours
day. But in more diftant climates, this unifor
mity will not hold : on the contrary, the day is
ever lengthning or fhortning, according to the
Suns more remote departure from, or nearer ap
proach to the asquator. But let the degree of de--
clination be more or lefs, the Sun has as full a
dominion over the longeft, as over the •fhorteft
day ; whilft the Moon and ftars govern equally
the longeft as the fhorteft night.
Between the poles and the polar circles, there
is but one day and. one night, throughout the year j
and each of them of fix months continuance. But
the Sun has an abfolute dominion over the fix-
month day ; for during that fpace of time it never
fets; whilft the Moon and the ftars, have the
like fovereignty over the fix-month night, fince,
in that fpace of time, the Sun never rifes. Con?
fequently,
C 3 With

( 20 >
With refpect to the fix-month day, and the
fix-month night, between the poles and polar cir
cles, thefe words of Mofes — limfhol baijom ubal-
laijelah— are literally true.
Though all this be readily admitted, yet ftill it
may be afked, where, in thefe intermediate ftates
of declination, is the equal dominion ofthe Moon
by night; and ofthe Sun by day ; which was the
original dominion, with which they were invert
ed by the divine charter?
In order to underftand the words of Mofes
(when he writes as an aftronomer) we muft ever
have recourfe to, and diligently examine the efta-*
blifhment of nature ; and without fome previous
knowlege of the one, we can never be qualified
rightly to comment upon the other.
Ver. 17. Lehair gnal haaretz. (2) To en
lighten the whole furface of the earth.
When the Sun is in the greateft extreme of its
declination, it fhines beyond the pole ; but then
the oppofite, in the mean time, is equally invol
ved in darknefs. On the other hand, when the
Moon is in its utmoft extent of latitude, it fhines
alfo beyond the pole; but then that which is op
pofite to it, is at the, fame time deprived of the
benefit, in an equal degree.
Therefore, if thefe words be applied to them in
thefe fituations, they muft be varied, without any
authority from the text, in fome fuch manner as
this, viz.
When the Sun is in the folftices, and the Moon
at itsgreateft diftances from the ecliptic, they do
not

(21 )
not fpread the influence of their refpective, tho'
different degrees of light, from the one pole to
the other, but interchangeably or by turns. Not
in the moft perfect manner, from pole to pole,
directly and at once, as— in the beginning.,
From what has been faid laft, it is fufficiently
clear, I think, that Mofes in the 17th and 18th
verfes ftill refers to the Sun in libra, and to the
Moon in cries, as we fpeak.
. I am now to fhew, fecondly, that the fubfti-
tution of the terms, light and darknefs, ver. 18.
inftead of night and day, ver. 14. is to be look'd
upon as Mofes' conclufive proof of the confummate
perfection of the original pofition.
Ver. 18. (3) To divide between the light and
between the darknefs.
This equal divifion of light and darknefs is the
fecond circumftance recorded by Mofes, in the
original conftitution of nature.
Ver. 3 . And God faid, let there be light, and
there was light. (Heb. And God faid, let light
be, and light was.)
Ver. 4. And God faw the light that it was good:
and God divided the light from the darknefs.
(Heb. between the light, and between the dark
nefs.) There is a vifible difference in the introduction
to thefe words, as they lie in the 4th verfe, and
in the 18th ; in the firft cafe, the effect is refer'd
to the immediate act of God; God, fays Mofes,
divided. — In the latter, the effect is refer'd to
a fecondary and inftrumen^al caufe, ordain-

(22 )
ed by God. . Ver. 18. God placed them,, fays
Mofes, in the expanfe of the Heavens, — /. e.
fo placed them,' under fuch determinate laws of
motion, fuch peculiar circumftances of pofition,
lehabdil,. &c.: to divide conftantly and invariably,
&c. - We muft carefully bear in our minds that Mo
fes reftrains his aftronomy to 3 orbs : to the orb
of the Sun, and to the orb of the Moon, which
are his two great luminaries ; whilft he ever
confiders the orb of the earth, as the whole and
fole object of their diftinct illuminations.
Ver. 3 . God divided between the light and be
tween the darknefs.
Let us now, in the interpretation of this text,
confult the fettled ftate of nature, and Mo/es' nar
ration of its primary conftitution.
Here then I fay, that light and darknefs (fo far
as we are concerned) are relative terms ; and the*
relation arofe (and neceffarily muft do fo) from
the divine and primary application, of the orb of
the earth, to the firft exifting light. Suppofe the
earth to be fix'd (motionlefs) in any one point of
its orbit whatever ; this light though at ever fo im-
menfe a diftance from it, muft needs illumine one
hemifphere ; whilft that which was turned from it,
muft as neceffarily (by reafon of the interception
of the rays) lie in darknejs. And there conftantly
ifi, and ever muft be in nature, a darkned and an
enlightned hemifphere with refpect to the orb of
the Earth, and in the now fettled ftate of nature,
to the orb of the Sun. In

(23 )
In this ftage of our progrefs, we have, as yet,'
but two oppofite terms, viz. light, on the one
fide ; and darknefs, on the other fide of the
globe. But Mofes thus proceeds in his narration : Ver.
5. And God called the light, day; and the dark-
nej's, he called, night.
Calling and being, in the idiom ofthe Hebrew
language, are, as is well known, fynonymoUs.
God, fays Mofes, by the power of his word, com
manded the light to become day; and, by the power
ofthe fame Word, he commanded the darknefs to
become night ; i. e. he imprefs'd the diurnal motion.
We have now 4 diftinct terms, viz. darknefs,
night, on the one fide of the globe ; and light,
day, on the other.
And do we not often familiarly fpeak, of the
darknefs of the night, and of the light of the day,
without confidering in our minds, at the fame
time, in what a curious and divine manner (by
antecedence and confequence) Mofes has' inform
ed us, both of their origin (with refpect to us and
our habitation) and of their diftinction, as found
ed in nature.
Here the comment of the Pfalmift is this, Pf.
74. ver. 16. The day is thine, and the night is
thine. Attah hacchinotha hammaor vafhemejh.
The -day is thine; that is, of thy ordination
and appointment, for thou calledft the light, day;
the night is thine ; that is, of thy ordination and
appointment; for thou calledft the darknefs, night.
Thou, O God, in the- beginning, willedft th©
vicifli-

(24)
viciftitudes of light and darknefs, the conftant
and agreeable fucceffions of night and day. <
The latter part of this verfe has been, I per
ceive, a great ftumbling block to tranflators and
expofitors. The Greek verfion renders it thus,
iru x.a.Tct?Tt<re> tov nMov >y *>a.\>aiv. Thou haft prepared the
Sun and the light. But the word which they
have render'd (rov »\m) the Sun, in the original
is — hammaor, the luminary : and the word, which
they have render'd {$m<tiv) light, in the original
is (Jhemejh) Sun.
On the contrary, our Englijh tranflators, have
given it this conftruction. — Thou haft prepared
the light and the Sun. But the word which they
have render'd — light — in the original is — the lu
minary. Might not the latter part of this verfe, be in
terpreted in the following manner? Attahha-
chinptha hammaor vafhemejh, thou haft prepared
the (great) luminary, even the Sun j the recep
tacle of light, and, by means of the diurnal mo
tion, the parent of day.
Although Mofes does . not teach us -to philofo-
phize, after the manner of men ; yet the Penta
teuch conveys to the mind clear, diftincl, and de
terminate ideas of his principles, data, and terms;
and this, independent of the aids and affiftances,
of technical language; without which fupport,
invented fcience would become lame, and arts
muft keep filence.
There is an effential difference, in the efta-
blifhment of nature, between light, day-, dark nefs,

(25)
fiefs, night. For day, includes and infers the
conftant, regular rifing and fetting of the Sun ;
and night, vice verfd.
Should the diurnal motion be entirely ftop'd,
night would be loft in the primitive darknefs ;
and day would refolve into the primitive light.
But notwithftanding the law of diurnal motion,
and its advantageous effects, I mean, the con
ftant fucceflions of night and day ; Mofes is care
ful to acquaint us, that the equal divifion of light
and darknefs, (which was a primary conftitution
of the creator, and is the fame the aftronomers
call the circle of illumination) was far from be
ing abrogated or cancell'd.' It was fo, in the be
ginning, and it is fo to this day. Suppofe all mo
tion to be this moment fufpended ; yet the Sun
would be ftill in the center of the enlightned he
mifphere ; and a perpendicular drawn from the
orb ofthe Sun to the orb of the Earth, would
ftill fall in the center of the circle, which bounds
light and darknefs, which are the very words of
Mofes, ufed by the aftronomers in the very fame
fenfe, and applied in the very fame manner.
This equal divifion of light and darknefs, arifes
invariably from the original divine caufe mention'd
above. But,
* The equal divifion of night and day, arifes from
the Sun's ingrefs to the aequator. Therefore,
when the Sun annually returns to the autumnal
sequinoctial (/. e. the Mofaic cardinal) point, then
the equal divifion of light and dafknejs, becomes
D exactly

(26 )
exactly coincident, with the equal divifion of night
and day.
Thus I have illuftrated thofe different expref-
fions of Mofes, ver. 14. and ver. 18.
Ver. 14. To divide between the day and be
tween the night.
Ver. 18. To divide between the light and be
tween the darknefs. And
I have had the fatisfaction to find them, in ex
act agreement and conformity, with the true doc
trine of the fphere.
It is worthy of our remark, that Mofes has ju-
dicioufly referved one of the moft important par
ticulars to the clofe of his account.
This is all I have to offer in relation to the
fourth of the Hexaemeron. And upon a review
ofthe whole, may we not with reafon, and up
on juft grounds fay ? That the Mofaic pofition of
the Sun and Moon to each other, and to their di-
vided dominions, the Earth, in their firft goings
forth, is too curious, not to be admir'd ; andvtoo
promifing, in the whole and in every part, to be
doubted or called into queftion. Whilft the re
fearches in philofophy, and the calculations in
aftronomy, claim not the privilege of giving, but
labour to find out, from fome fixed radix, the
true pofition of the two luminaries to each other,
in a given time, either real or imaginary.
I will now fubjoin a fynopfis of the contents of
the firft chapter of Qenefis, in the light in which it
appears to me ; tho' I cannot help thinking there
are fome things, not only hard to be underftood, but

( 27 )
but above the penetration of the acuteft reafon,
and the moft philofophic genius : and no wonder-
fince Mofes is entirely filent about the motives of
creation, and only fays, in general, that the Earth
was — tohu and bohu. This confufed congeries
and fluid mafs, is the fubject and bafis of his nar
ration ; order, beauty, harmony, and perfection
all arife from this ground, by the efficacy of the
omnipotent Fiat. And therefult is, — God faw
all that he had made, and behold it was very good.
In truth, it would have been the greateft miracle.
of all, if in the hiftorical account of a rifing world,
not one fingle circumftance had been found, which
furpaffed the human comprehenfion.
jr.
A fynopjis of the contents of the firft
chapter of Genefis.

Gen. ch. i. ver. HPHE creation of the Hea-
j. c. 2. v. i. JL ¦ vens an(l tne Earth, and
all the hofts of them, by the power of God's
word: He fpake, and it was ; he commanded,
arid they were created.

v" I. The Earth without form and void. II. Dark
nefs upon the face (furface) of the deep. III. The
v fpirit of God moved Upon the face of the waters.
IV. Light. V. The equal divifion of light and
darknejs. VI. The origin of the diurnal motions
and its effects, the ^ucceffions of night and day.
VII. Jom (i). the fpace of time which flows
D 2 frorn.

- ( 28 )
from Sun-rifing to Sun-fetting, or, (at the asqui-
nox) a femi-diurnal revolution.
The firft, compleat diurnal revolution, or
Jom (2). 1
VIII. The expanfe ofthe Heavens in the midft '
of the waters. IX. The divifion between the
waters, which were above the expanfe of the
Heavens, and between the waters, which were
below the expanfe of the Heavens.
The fecond, compleat diurnal revolution, or
Jom (2).
X. The congregation of the waters into
one place, and the conftitution of the terraqueous
globe. XI. The furface of the Earth (now be-*
come dry land) cloathed with grafs, herbs, flow
ers, plants, fhrubs, and fruit-trees, after their
kind; bearing feed, whofe feed is in themfelves,
upon the Earth.
The -hird, compleat diurnal revolution, or
Jom (2).
XII. Two great luminaries in the expanfe of
the Heavens: XIII. The equal divifion of day
and night, or the (autumnal) aequinodtial day.
XIV. The dominion of the greater luminary over
the day. XV. The dominion of the leffer lumi-
na:y and the ftars over the night. XVI. The
diffufion of light from pole to pole ; by the Sun,
from the aequinodtial; and by the full Moon,
from the point of interfection — nearly. XVII.
The equal divifion of light and darknefs, (the pri
mary refult of the Earth's fixed pofition to the
Sun,

(29 )
Sun, co-incident with the equal divifion of night
and day. XVIII. Haju laothoth, i. e. predeter
mined future events, to be afcertain'd in their times
by the periodical revolutions of the two great lu
minaries. XIX. Haju lemognadim, i, e. the ap
pointment ofthe two great luminaries for the re
gulation and determination of the periodic returns
of folemn affembly days, inftituted in the begin
ning. XX. The commencement of the annual
motion, and the radix of time, from whence to
compute, by days and by years. XXI. The
diftinction of years, or the folar and the lunar.
The fourth, compleat diur-nal revolution, or
Jom (2).
XXII. Fifli, after their kind. XXIII. Wing
ed fowl, after their kind. XXIV. The divine
benediction of them.
The fifth, compleat diurnal revolution, or
Jom (2).
XXV. Animals, wild and domeftic, reptiles,
infects. XXVI. The creation of the firft hu
man pair (for God called their name Adam, in
the day they were created, ch. 5.) in the image
of God. XXVII. Male and female created he
them ; but man the firft in order and in dignity.
XXVIII. The charter of dominion granted to
man, the Lord of all. XXIX. The folemn di
vine benediction of the firft human pair. XXX.
The appointment of food for all. XXXI. The
original perfection of all things.
The fixth, compleat diurnal revolution, or
Jom (2). Gen.

( 30 )
Gen. ch. 2. ver. 3. And God bleffed the feventh
day, and fandified it, becaufe in it he refted from
all his work.
Before any one be too follicitous to know, why
God appointed fix compleat fucceffive days, for
the creation and conftitution of the univerfe and
the fyftem of 7 days ; firft, let him afk the moft
fagacious enquirer int6 nature, why the creator
appointed fix primary planets, together with the
Sun (che center of their refpective motions) to
conftitute likewife a feptenary fyftem.
The precept to obferve the fourth command
ment, is ufherd in with this finr-luri/V of expref-
fion, Zacor — remember the fabbiv'h day to keep it
holy : why fo'? Becaufe, had the ancient Ifraelites,
either through careleffnefs, or a total apoftacy
from the worihip ofthe true God, the creator of
Heaven and Earth, once fuffered this divinely
inftituted memorial to have flipped out of their
minds, they could not poffibly have recovered it
again, either by the light of nature, or the powers
of reafon, or the periodic motions of the lumina
ries. And we plainly -fee, that the deifts, the
zealous abettors of the light of nature, and the
all-fufficient guidance and direction of unaflifted
reafon, acknowlege no ftated public memorials,
either of creation or redemption. Thefe works
of the Lord, and the wonders he hath done, for
the children of men, are neither the objects of
their faith, nor their regard, nor contemplation.
Here the light of nature, becomes a moft profound ,
darknefs, and difcovers nothing. 1

( 3^ )
I donot prefume to grafp the extent, or pene
trate the depths of the Mofaic cofmogeny : I (hall
content myfelf, with being able to demonftrate,
that Mofes dates the beginning of time, and his
chronology, from the fourth of the Hexaemeron
(when the annual motion commenced) and yet fo,
as to exclude it from the computation, in the
collected number of days.
This remarkable circumftance, viz. of the ex
clufion of the fourth of the Hexaemeron, from
the collected number of days (though I am fenfi-
ble that the peculiar meaning of it is not yet un-
derftood) is fo far from being a precarious hypo-
thefis, or a fanciful and groundlefs conceit, that it
felf eftablifhes a general rule, for the carrying on
and aptly connecting a continued feries of folar
revolutions, without perplexing the account (as
Sofigenes was forced to do) with an intercalary day,
at the end of every fourth folar year ; which is of
no fmall ufe in the civil computations of time; and
I may venture to fay, is abfolutely infcrutable up
on any other principle. It never yet has been,
nor poffibly can be obtained by all our moft ex
act obfervations of the phaenomena of nature, and
phyfical ratio of things.
The not apprehending, and in fure confequence
of that, the not expecting to find, a clofe, connec
ted and demonftrable fcheme of Sun and Moon
aftronomy, both in the Pentateuch, and through
out the Hebrew bible, has been the grand obftacle
and impediment, why fo many have entirely over
looked, and fcarce any one has fufficiently at
tended

( 32 )
tended to and confidered the inherent aftrono
mical fenfe and fignification of the Mofaic and
Scripture terms of computation, which would
long e'er this have laid open and completed the
facred and important fcheme.
From the Mofaic terms, Gen. ch. i. ver. 14, 15,
16, 17, and 18, we infer'd the Sun in the aequi-
nox, and the Moon a little paft the full, or at fuch
a diftance from the node, as not to fall into the
Earth's fhadow. But waving all advantages which
might be taken from the precedent reafonings and
deductions, I fhall ftep a little further into the
Pentateuch, and fee What difcpveries may be made
from thence to afcertain the firft pofition of the
Sun and Moon to the Earth, as contended for
above. Mofes, in the 23d chapter of Leviticus, rea
ches, in an orderly manner, mognadei Jehovah,
ver. 2. which I interpret the folemn affimbly
days, and fet feafts of the Lord; i. e. which'
were inftituted and ordained, (fome of them, in-
the beginning) by the authority and command of
Elohim, Jehovah ; the God of the Patriarchs, the
God of the Hebrews, and the God of Ifrael.
Should a queftion and doubt arife, whether
fome ,of them were inftituted — in the beginning,
then I afk, whether haju lemognadim — Gen. i. 14.
is not exprefily found amongft the original ordi
nances, laws, ftatutes, and decrees of the fupreme
legiflator ? Can it be reafonably, and upon appa
rent juft grounds difputed, whether the Pfalmifi
refers to that original law, Gen. i. 14. when he
fays,

(33)
fays, Pf. civ. 19. (Jehovah) Gnajhah Jareach
lemognadim; God has made and appointed the
Moon, (/. e. as I fhall hereafter prove) the months
and days of the lunar year, for the regulation and
determination of the periodic returns of folemn
affembly days.
Levit. ch. 23. ver. 33, 34. And the Lord
fpake unto Mofes, faying, vtx. 34. fpeak unto the
children o/*Ifrael, faying, the 1 $th day of this fe
venth month Jhall be (chag haffuccoth) thefeaft of
tabernacles. Ver. 39. Alfo in the 15th day of the feventh
month, when ye have gathered in the fruit of the
land, ye Jhall keep (chag> a f eaft unto the Lord.
The month and day of the month, fpecified by
Mofes, carries back our thoughts, through all the
intermediate months, to the beginning of the
year; but yet, whilft we only compare thefe two
texts together, we cannot fo much as form a pro
bable conjecture, much lefs are we able to deter
mine, of what kind of year, this is the feventh
month ; i. e. whether of a folar, or of a lunar,
or of a mere civil and political year: nor is there
one circumftance, that can give us any farther in
formation than this, viz. that we here read the
15th day of the feventh month of a year.
To thefe therefore let us add the following
texts, and fee what light may be gained from
them. Exod. ch. 23. ver. 16. And thou Jlialt ob ferve
(chag haafiph) the Jeafi of in-gathering, which is
E in

( 34 )
in the end of the year. Heb. bezteeth hafhanah,
in exitu cujufque anni.
Ch . 3 4 . ver . 2 2 . And thou Jhalt obferve (chag
haafiph) the feafi of in-gathering, at the year's
end. Marginal reading, revolution of the year.
Heb. Tekuphath hajhanah, in revolutione cujufque.
anni. By comparing all thefe texts together more
than a fingle ray of light begins to break in upon
us. We are now in poffeffion of fufficient data,
from whence we may argue, and from which,
by laying Mofes' fundamental principles together,
we may readily, and with certainty, collect a
diftindtion of years : for have we not the 15th
day of the feventh month of the lunar year, and
the laft day or conclufion of the folar ? Thou
(halt keep, fays Mofes, the feaft of the in-gather
ing, on the 15th day of the feventh month, in
the going out of the year, or in the revolution of
the year.
The preceding obfervations will receive a far
ther confirmation by confidering the Mofaic com
putation of time, prOpos. 2d.
Time may be confidered as a quantity of deter
minate duration ; a duration fucceffive, meafured
by motion : and the apparent revolutions of the
greater luminary are the appointed meafures of a
determinate quantity of time ; confidered as divi-
fible, by the Pentateuch, into days, weeks, and
years. Thefe are the 3 aftronomical Mofaic terms of
computation. Days

(35)
Days and years arife from the apparent diurnal
and annual revolutions of the Sun ; but the dif
tribution of our time into weeks, or fyftems of 7
days, proceeds not, asisallow'd, from the vifible
/Conftitution of things, but immediately derives its
origin from a pofitive divine inftitution. And
fince the number 7, or the hebdomatic meafure,
is an infallible medium of proof, throughout the
Scripture chronology, and indeed the whole courfe
of time, from the fourth ofthe Hexaemeron, to
this prefent day, therefore it is, that I have called,
days, weeks and years, the 3 aftronomical Mofaic
terms of computation.
Mofes, Gen. i. 14. records, by divine autho
rity, thefe fundamental principles of aftronomy —
And God faid let there be luminaries in the expanfe
ofthe Heavens — and amongft - other ufes — haju
lefhanim — let them be for (difttinction of) years.
He adds, ver, 16. And God made two great lu
minaries, viz. Shemejh and Jareach, Deut. ch. 4.
ver. 19.
The verb haju being in the plural number mar
nifeftly relates, and hath an immediate refpect to
both luminaries, and thefe words — haju lejhanim
— may be underftood, as if it/ had been diftinctly
faid, 'Jhaggadol'pLeJhanah.
Jehi hammaor> >
3 hakkaton^LeJhanah.
greater} 7 for a year.
Let the ^ luminary be appointed >
leffer J ^ jforayear.
E z Let

( 3fr)
Let the Sun and the Moon, by their annual re
volutions, meafure each its refpective year.
We are plainly taught from hence, that folar
years and lunar years, have their diftindt foundar
tions in nature, and are equally of divine ordina
tion and appointment— in the beginning. And
we fhall find, that the Hebrew word Shanah, re-
' petition is applied in the Pentateuch, both to
the folar, and to the lunar year.
Now, may I not afk the queftion, are not
thefe amongft the principles of computing times,
which are clearly and explicitly taught in the,
Pentateuch'? And it would have been incongru
ous and abfurd, as well as highly derogatory to
the author of it, as a chronologift and legiflatdr,
not to have eftablifhed his chronology, and to
have afcertain'd invariably, the appointed feafons
of his fet feafts, upon the principles and laws of
aftronomy, revealed to him by the author of na
ture himfelf. But we fhall find no fuch defects
in Mofes, for he has done fo : Thou Jhalt 'obferve,
(fays he) chag haafiph, on the 1 5th day of the fe
venth month, tekuphath hafhanah.
And indeed if Mofes had not made ufe both
ofthe folar and the lunar year ; or if we may fup-
pofe the primitive patriarchs and Ifr'aelites to haye
been ignorant of them, then they never yet an-
fwered the ends of their joint ordination, from
the beginning -till now. The old JEgyptiam,
Chaldceans, Medes, Perfians, Syrians, Phoenicians,
Grecians, Romans, ufed a year purely folar j
which, in different ages, was more or lefs perfect. , The'

(37)
The Europeans continue in the ufe ofthe Julian:
the Turks and Arabians have a year purely lunar
vague and erratic. And we muft be at laft obli
ged to Mofaic principles of aftronomy, and to
the Hebrew bible, for the due regulation, and
juft correction, both of our ecclefiaftical and civil
year. The Mofaic term tekupha is of fpecial note,
and merits our careful examination. The prefent
Jews call the four cardinal points of the ecliptic
tekuphoth. Vox tekupha Hebraice idem valet atq; Grace
T?oirat, viz. punfta eardinalia, duo aquinoftia,
totidemq-Jolftitia. Bo. Bever. Chron. Inftit.
In the aftronomical calculations of the Jews,—
Tekupha tijri, denotes the autumnal aequinox.
Tekupha tebeth; the winter folftice. Tekupha ni
fan, the vernal aequinox. . Tekupha tammuz, the
fummer folftice.
Tekupha is ufed in the Hebrew Scriptures to ex-
prefs both the diurnal and annual revolutions.
Shanah, fignifies to repeat or double. §>uia
file ad punftum, unde digredi caper at, redeunte,
iteretur; & injejua per vefiigia Jemper volvatur
ac redeat. Buxt. Lex.
It is very furprifing, that not one of the many
Scripture chronologifts fhould fo much as think
of applying the tropical year to the Mofaic and
Scripture chronology ; when it is evident, that
we cannot define Shanah, as it is applied to the
Sun, without defining at the fame time the tropi
cal year. If

(38 )
If Mofes was capable of laying down, in the in
troduction to his Pentateuch, the fundamental prin
ciples of Sun and Moon aftronomy, why not of
erecting a fuitable chronology upon thofe princi
ples ? If he was qualified to inform us, that the
God of nature, — in the beginning — ordained the
two great luminaries, to determine each its year,
by their refpective annual periods? though with an
original diftinction, which will in its place be
ftated and explained, what reafonable inducement
have we to imagine, that he did.not know them ?
The abfutdity moft furely -lies, not in the appte?
bending that he did, but in haftily concluding,
as moft have done, that he 'did not. Mofes no
where betrays his ignorance, whilft his language
and ftyle imply fome extraordinary degrees of
knowlege. \ Ex. g.
In the fix hundredth {fohx)year of Noah'* life,
in the fecond month, the feventeenth day of the
month (of the lunar year) the fame day, the foun
tains of the great deep were broken up. .
I fhall reduce my obfervations upon thefe fe
veral texts, which I have collected and laid toge
ther, into thefe following particulars.
(i) If it fhould be afked, and no doubt fome
one would be curious enough to afk, how may
we certainly deduce, from the terms of thefe,
or any other texts, the Tekuphah, or cardinal point,
of the Mofaic (Shanah) tropical year ?
In order to give a fatisfactory anfwer to this
queftion, we muft have recourfe to Mofes' s law ;
u from

(39 )
from whence we learn, that when the IJraelites
were to be fettled in Canaan, they would have 3
fucceffive harvefts.
1. The barley harveft. 2. The wheat har-
veft. 3 . The latter harveft, or the in-gathering
of the olive yards and vineyards. We fay then,
that the terms chag haafiph are equally a peri-
phrafis of the autumnal aequinodtial feafon, as
chodejh abib, are of the vernal. For abib is not
the political name of a month, but an appellative j
as much as to fay, the month of ripening, (vid.
Shuckford's preface, vol.2.) the month in which
the barley was ripe for the harveft ; in which they
began to put the fickle to the corn : which, in the
climates of Palefline and Egypt, and thofe more
hot eaftern countries, was at the vernal aquinox,
(vid. Prid. preface, vol. 1 .) or, in the Mofaic ftyle,
beha chodejh abib. Hence we conclude, that the
autumnal aequinodtial day, was the Tekuphah, or
cardinal point, of the Mofaic (Shanah) tropical
year. (2) Mojes enjoins (by the divine command) the
obfervance of a double feftival, viz. (chag haffuc
coth) the feaft of tabernacles, and (chag haafiph)
the feaft of the in-gathering, on the 1 5th day of
the feventh month. And he explicitly declares
to them the reafons for the obfervance of the for
mer, viz. ver. 43. That your generations may
know, that I made the children oflfv&el to dwell in
booths, when I brought them up out of the land of
Egypt, faith the Lord. But he is entirely filent
as to the other. Why fo ? Becaufe chag haafipfo was

(40)
was an Original feftival, well knbwn to the 2f-
raelifes at leaft traditionally, if not by an imme
morial obfervance, and is to be carried back, quite
through the patriarchal difpenfation, up to the
times of Adam ; Vaijomer elohini — haju lemogna*
dim — Gen. i. 14.
(3) Mofes denominates and diftinguifhes the
months by ordinal numbers, which not only de
termine the fituation of the months in the lunar
year, and patriarchal calendar, (hereafter to be
exhibited as preferved and tranfmitted by Mofes)
but alfo limit their precife diftance, before the
Exodus', from the autumnal aequinox ; and, after
the Exodus, from the vernal.
We have, for inftance, ver. 39. the feventh
month of the lunar year from the vernal aequi
nox; on the 15th day of which feventh month
a feaft was appointed to be obferved : and thou
fhalt obferve this feaft (fays Mofes) in the revolu*
tion of the (folar) year.
(4) In thefe words— tagnajhah chag haafiph
tekuphath haJhanah—MoJes afcertains the utmoft
aftronomical limits and boundaries of the feaft of
in-gathering, and gives us to underftand that it
might fall upon the very day, on which the Sun
finifhed and began its annual courfe ; (For,
Libra novi prima eft, veterifq-, novifjimajolis,
, Principium capiunt Phoebus & Annus idem.)
tho' by the original and immutable law, it never ,
did nor could come before it. (5) From

;(4i >
(5). From Adam to Mofes and the Exodus, the
lunar year began at the autumnal aequinox, as
did the primitive and patriarchal folar; which
laft continued" the fame under the law,, after the
beginning of the facred year was transfer'd by
the exprefs command of God, Exod. 12. ver.
1, 2.. to the oppofite cardinal point, or vernal
aequinox. Therefore from 7 m, 1 5th day fub-
ftract 6 m. and there will remain 1 m. 15th day.
Now then, read fhe text thus : Thou (halt ob-
ferve the feaft of in-gathering (inftituted origi
nally) on the 15th day of the firft month of the
Junar year, and bn the tekupha, or cardinal point
of. the folar. For tekupha is, in a ftrjdt literal
fenfes cardinal ; and chag haafiph being added to
it, makes it to become autumnal.
The Mofaic integra.1 number 15 is half 30 ;
but, 30 comprehends the number of days in the
firft month of a lunar year, and is bounded, by
nature, in both its extremes, by the lunar phafes.
X. 30. C. Divide therefore 30 into 15 and 15;
then there will nothing more remaih to compleat
the deduction, but ;Qnly to tranflatei the. .feveral
terms of the collected . Hebrew tex{s, into aftror
nomical fymbols or characters, . and. we ihal! imr
mediately have a fenfible reprefentation of the
original pofition of the two great luminaries, on
the 4th of the Hexaemeron, exactly correfpond-
Jng With th'e precedent interpretation of the terms
there made ufe of by- Mofes.
i-.. ¦.:'.-< '' # Xevit;

( 42 ) .
Levkv c. 23 . v. 3 o. Tagnajhab, chag haafiph. £*.
Thou fhaltobferve the feaft of in-gatheririg.
Exod. 23. 16. Betz eeth ?baJhamk Q
' 34.22. Tekuphath^ -
In the end ~) c . ¦
, .- Cof the year. _
revolution^ J O
Beha chamijhah gnajhar Jom lechodejh. C- 15.
On the 1 5th day of the month.
It is no mean or irrational entertainment to
contemplate (with attention and admiration too)
this revealed aftronomy ; and to be instructed, by
intuitive evidence, how thefe important points
ftood, in the very firft rife and origin of na
ture. It is poffible that fome may confider my inter-
pretation and aftronomical application of thofe
few Hebrew texts, cited above, as an hypothefis
only, though fbmewhat ingenious, and not at all
unfuitable to the traditionary notions of a Jew.
But when it fhall appear, that demonftration gives
its irrefragable fandtion both to the interpretation^
and aftronomical application ; what will be faid
then ? Why, at leaft, as much as is contained in
thefe few Words following :
Tempora quo vetuftiora eo certiora.
And will not this be a great deal to be faid and
admitted ? For I am pretty certain, that neither
the Jews nor the Chriftians, have, at prefent,
any the leaft apprehenfions of feeing fuch a
(feeming)/

('43 )
(feeming), paradox verified by the genuine au
thenticity ofthe Hebrew text.
When we take a more clofe and intimate view
of thefe original characters, we plainly perceive
they determine, that, Berefirith i. e. in the firft
ftate of things, the primaeval feftival chag haafiph,
together with that of the firft day of the feventh
(which was anciently, the firft) month of the
year, was appointed a fettled memorial, Levit.
ch. 23. ver. 24.
After the diffolution of the Perfian monarchy
by Alexander, the Jews, being difpers'd through
the Grecian colonies, became graecis'd or helle-
nis'd in their religion, their ufages, and their
computations ; and fo loft the knowlege of the
Mofaic year. Yet it muft be own'd, that they
have not fo entirely loft all knowlege of it, but
that they have ftill retained, by immemorial tra?
dition, fome general traces and footfteps of it.
For in the famous Rabbi Hillel's aftronomical year,
which was publifh'd about the middle of the 4th
century, Rojh hajhanah, or the beginning of the
year, is that mean new Moon, whofe full Moon
either happens upon, or follows next after, the
autumnal aequinox.
Hitherto I have been endeavouring to eftablifh
the literal truth of my firft proportion ; and I
leave it to the reader to judge, how far I have
contributed towards it, and what grounds he has,
to conclude, F 2 Prop,

(44 )
Prop. I. That the reafon why the 15th day of
the month, is characterize with fo much folem-
nity in Mojes's law, is, becaufe the number 15
does really and in fact exprefs the original quality
and fofiti 'on of the Moon, on the 4th of the Hex
aemeron. It will be to little purpofe to enter upon the
Calculations, and a direct proof> till we have fet
tled the determinate fenfe and meaning of the
diftinguifh'd terms of the Pentateuch relating to
time and its meafures. In order to this I fhall
return back and confider  ,
Gen.ch.i. ver. 5. And God calledthe light,
day ; and the darknefs he called night.
And the evening was, and the morning was the
firft day.
Was it poffible for the Sun to be inhabited, its
inhabitants would ever be in the center of its
light, diffufed all around to the utmoft extremis
ties of the circumference ; and could they view
the Earth from thence, they would only fee its
enlightned face without being fenfible ofthe vi-
tiffitudes of light and darknefs, much lefs, the fuc-
ceflions of night and day. So that with regard
to us,, and our native fituation^ there is a great
propriety, as well as concifenefs, in fpeaking from
appearances and the evidence of fenfe.
Mofes inculcates firft principles, -and lays foun
dations with fuch a fuperior fkill and judgment,
as we muft admire and efteem ; for he pertinently
and judicioufly confiders his reader as a fix'd in-
habkant ofthe Earth, tolwhom, as he well knew, every

(45 )
every phenomenon, arifing from original pofition
and diurnal motion, was merely optical; and that
there was not, nor ever could be, in nature, any
other than an imaginary and fuppofed fpectator of
heliocentric motion. >
And yet, in this chapter of principles, his cau
tion and warinefs is not a little obfervable ; for in
stead of openly mentioning the fetting and rifing
of the Sun, he gives us the term gnereb to ex
prefs the time of the one ; and the term boker, to
exprefs the time of the other ; and I fhall not
fcruple to tranflate directly the one, Sun-fetting;
the other, Sun-rifing. Whilft thofe who think
it neceffary to fpeak fyftematically, have equal au
thority from the Mofaic terms, gnereb and boker,
to tranflate the one by the difappearing ; and the
Other, by the appearing of the Sun ; if they are
peffuaded, that, by fuch affected language, they
jpreferve an important diftinction, and convey to
the readers mind a more ufeful inftrudtion. But
to proceed ;
Mofes uniformly defcrjbes, through the whole
Hexaemeron, an aequinodtial day ; and he termi
nates the boundaries of its equal divifions by
gnereb (Sun-fetting) and boker (Sun-rifing).
That fpace of time which flows from boker
{Sun-rifing) to gnereb (Sun-fetting) is (Jom) the
artificial day, as fome fpeak ; for God called the
tight, sday ; i. e. he imprefs'd the diurnal mo
tion.
• And that equal fpace of time which Rows
from gnereb (Sun-fetting) to boker {Sun-rifing}) is

(46)
(lajelah) night; for God called the darknefs,
night; i. e. he caufed, (by means of the diur
nal motion) the Sun to fet and to rife ; & vice:
ver/a. But the darkned hemifphere and the enlightned
hemifphere being added together, conftitute (alfo
Jom, i. e.) the natural day, or Nudthemeron: for
gnereb (Sun-fetting) and boker (Sun-rifing) were
the firft day.
We fhall find the term Jom, .ufed in both
fenfes, *". e. as it denotes the artificial and the na
tural day, in Mojes's account of the deluge, and
the falling of the rains." Gen. ch. 7. ver. 12. 17.
And the rain was upon the Earth (arbagnim Jom
yzaxha'griimlaijelah) forty days and forty nights.
Ver. 17; And the fioodwas upon the Earth, (ar
bagnim Jom) forty days, or Nudthemerons.
I fhall now confult the fundamental text, Gen.
3. 14. And God faid — let them be for days and
years. A diftindtion of days, not with refpect to the
natural meafure, but fo the law of computation,
muft be the neceffary confequence of a diftindtion
of years ; that is, there muft be the days of the
lunar year, as of the folar. And the not admit
ting this diftindtion into our reckonings and ca
lendar is evidently owing to our not being ac
quainted with, at leaft, to our not making ufe of
the lunar year, together' with and diftindt from
the folar.
The days then of the Scripture twofold year
differ not in their meafure, but in their epochs or

(47 )
or beginning : the folar year, and the folar day,
ever begin together, and they have equally a va-r
riable epoch; whilft the days of the lunar year
are fixed by nature, as well as by Mofes, to an
immutable cardinal point; and the aequinodtial
day is the unchangeable ftandard of the computa
tion. Levit. ch.23.ver. 32. Ye fhall celebrate
your fabbaths, (fays Mofes) megner eh gnad gnereb,
from evening to evening,— as on the aequinodtial
day. Thus far we have confider'd thefe terms as re
lating to both the luminaries, and their refpedtive
-years 5 . we fhall now confider them, as they are
applied only to the Sun ; and in this application of
themMojfo thus records the lives of the patriarchs —
Gen. ch. 5. ver. 27. All the days of Methufalah
were 969 years.
Mofes defines the longaevity of his patriarchs,
as an aftronomer, by the diurnal and annual re
solutions of the Sun ; and none but an aftrdno-
jner can afcertain the precife age of Methufalah, as
ftated by Mofes. Nor can he be faid . to be a mean
.proficient, who is able to reduce folar years, and
lunar years, to days, with the required exaetnefs.
-This law of calculation fo generally prevailed in
the primitive ages, and the patriarchs were fo fa-
miliariz'd to it, that the terms became dialectical,
and intermix'd themfelves with their common
¦ phrafeology. Gen, ch. 47. ver. 7, 8, 9. And
¦Pharoah Jaid unto Jacob, how old art thou f And
Jacob Jaid unto Pharoah, the days of the years of
my pilgrimage, are 130 years. Pew and evil have
Jh the

1 4").
/fo %j */* the years of my life teefi. 'JhdMvi
not attained unto the days of the years ofthe hfe of
my fathers, in the days of their pilgrimage.
¦ Although the diurnal and annual revolutions
of the Sun are motions diftindt from, and en*
tirely independant of, each other • yet in the fet
tled ordination of nature there is an dbvious a-
greement and conformity between a day and a
year. (In prophetic ftyle, the one is, with great
propriety, fubftituted to exprefs a correfpondr
ing number of the other; I have appointed thee
a day for ayear, fays God to the prophet Ezekielj
ch. 4. ver. 6.) For as the Sun in its annual re^
volution paffes over 4 cardinal points of the Hea
vens, fo likewife in its diurnal it paffes over 4
cardinal points of the day. The 4 cardinal points
of the Heavens are by us diftinguifh'd into the
.autumnal aequinox, the winter folftice, the vernal
aequinox, the fummer folftice ; and the 4 cardinal
points of the day, into Sun-fetting (o), Mid*
night (1), Sun-rifing (2), Midday (3),  (4)
The fpace from Sun-fetting to Sun-fetting
(megnereb gnad gnereb) is the invariable meafure
. of the Nucthemeron at the aequinox, accommo
dated to the lunar phafis, eftablifh'd in th& begin
ning, and afcertain'd, by Mofes.
Three compleat quadrants, meafure from Sun-
fetting (6) to noon (3) ; here (with refpect to the
Mofaic Meridian) we meet the Sun, and in the
aequinodtial point ; fo that the 4th quadrant ofthe
Nucthemeron was the firft that was meafured by
the Sun.
We

(49 )
. We meet with no account, in the Pentateuch,
of the artificial fubdivifionof the day into hours,
&c. nay,, there is not a word in the Hebrew lan
guage to denote the hours ; for Shagnah, Dan.
iii. 15. is not Hebrew, but Chaldee. I can recol
lect but one fingle paffage in the Pentateuch,
where Mofes undertakes to determine the precife
time of the day, between the cardinal points ; and
he there ufes very elaborate terms, and fuch a
peculiar Hebrew idiom, as will not admit of a li
teral tranflation into any other language. Exod.
ch. 12. ver. 6. And the whole affembly of the
congregation , of Ifrael Jhall kill ii, (viz. Pefech,
the pafchal \a\x\h)—bin %hagnarbajim. To un
derftand this idiom rightly, we muft remem
ber, that there is a twofold declination of the
Sun, viz. the annual and the diurnal. The for
mer, I need not fay, is reckoned frdm the aequa-
tor to the tropics, and fo is both northward and
fouthward. The latter is not reckoned two ways ;
when the Sun appears above the horizon, it is faid
to afcend ; when it, has reach'd the Meridian, it
is faid to defcend, or to decline : now, faysMoJes,
ye fhall kill the pafchallamb— bin hagnarbajim —
i. e. in the middle point" of the Sun's diurnal de
clinations or tendencies to the weftern horizon.
Mofes, in this place, like a fkilful mathematician,
as well as expert aftronomer, divides Jom, or the
aequinodtial nucthemeron, into octants, and or
ders the paffoyer to be flain, at the end of the
former half of the 4th quadrant; i.e. in the old
Roman ftile, which we read in the gofpels, at
G the

( 5° )
the ninth hour of the day ; and according to us,
at three o'clock in the afternoon. We have here
an inconteftable argument from the Pentateuch,
that the method of computing by hours (however
commodious it may be thought for civil ufe) was
not ufed in the times of Mofes ; though more
than ,2500 years of the world's age were com
pleted at the Exodus.
The vifible eftablifhment of nature, and the
Hebrew Scriptures, unanimoufly inftrudt us to dif
vide Jom, or the aequinodtial Nucthemeron, into
4 equidiftant quadrants ; and the correfponding
cardinal points are explicitly mention'd in their
appropriated terms.
(o) 0) (2) (3)
Sun-fetting. Midnight. Sun-rifing. Midday.
Gnereb. Chatzi laijelah. Boker. Zohoraim,
In the evening, at midnight, in the morning,
and at noon day, (in our ftile, every hour and
minute of the day) fays the PJalmift, will I praife
thee. It may be proper in .this place to remind the
reader, that hitherto I have been ftating firft prinr
ciples, and collecting proper materials to fupport
the fubfequent calculations /and I would beg leave
to fuggeft, that the fubolvifion of Jom, or the
aequinodtial Nudthemeron, is of too great impor-:
tance, in the courfe of this fcheme, to be paffed
over, without fome particular remarks and obfer
vations.
When

( 5i )
When we take a review of the original' cha
racters which have been already exprefs'd in the
©
following manner — < 1 5. — it is evident, I may
fay, to fenfe, that the Sun began to meafure the
year from libra ; nor can the terms chag haafiph,
without offering a manifeft force and violence to
their moft obvious and natural fenfe, be applied
to any other Tekuphah, or cardinal point of the
ecliptic. It is alfo, as intuitively evident (without em-
baraffing the fpeculation with the fubtilties of
Geometry, the operations of Algebra, and the
depths of fcience) that the aequinox fell upon the
15th day, computed from the evening of the
Moon's vifibility.
But here it muft be particularly noted, that the
integral number 15, with refpect to the age of
the Moon, on the 4th of the Hexaemeron, is
wholly chaotic and imaginary ; for the Moon
arofe, and enlightned with a full orb the new
created Earth, after the fetting of the Sun, or on
the beginning of the 5 th. But with refpect to
the Sun, they are not entirely chaotic. The Sun
began its courfe at noon, in the Meridian of para-
dife. Therefore, from 15 days, fubftradt 14 1,
there will remain ¦£• This quadrant thus obtained
was the firft diftindt portion of time, that was
meafured by the annual motion of the Sun, and
the firft folar year muft be reckoned to have
proceeded in this form, viz. .1+365 days. Little
G 2 does

( 52 )
does the reader fufpedt, at prefent, the almoft in
credible importance of this quadrant, collected
from the firft point (both of the year and of the
day) ofthe Sun's going forth on the" 4th of the.
Hexaemeron, and the autumnal aequinodtial day.
And by way of farther explication, it is, ( 1) The
original ftandard meafure of equal time ; for there
was no lenfible declination of the Sun, at his firft
fetting, in the clofe of the fourth day. (2) It is
the leaft aftronomical and natural meafure of time
to us, the inhabitants of the Earth. (3). It is
the only medium, in our portion of the fyftem^
which, in union with the lunar year, can enable
us to carry on a continued feries of folar years
(as was hinted before) without perplexing the ac
count with an intercalary day, at the end of every
fourth year. (;) This feparate quadrant ofthe
4th of the Hexaemeron, thus obtained, manifeft-
ly difcovers to us the diftindtion founded in na
ture, between the (beginning ofthe) days of the
folar year, and of the lunar. ,
As for inftance, in the example before us ; the
firft folar year, and the firft folar day, began to
gether at noon, or in the Mofaic meridian. But
the days of the lunar year (by which the facred
writers, from Mofes to Nehemiah, conftantly re-
ckon'd; are. to be computed (by an exprefs com
mand, Levif. ch. 23. ver. 24.) from evening
to evening. Therefore the firft folar year anti
cipated the beginning of the firft lunar year (as
meafured from full Moon to full Moon) by one
whole quadrant of the Nucthemeron.
As

( 53 )
As I have claimed the tropical, to be the Mofaic,
folar year, I fhall undertake in the calculations
(which proceed upon Mofaic principles and data)
toafcertain its quantity, from a medium in nature,
fuggefted by the terms and ftile of Mojes's chrono
logy. Gen.ch. v. ver. 27. All the days of Methufa
lah were g6gyears.
We are inftructed by this text, and others of
the like import, to compute the times by days
and years ; and although a day is not the aliquot
part of a year, yet may they be reduc'd to an exact
commenfuration to each other ; and from hence
may be extracted the true quantity of the folar
year. This commenfuration of the diurnal and
annual revolutions of the Sun has happened but
three times fince the creation, and the fourth will
be completed, A. D. 1753, at the autumnal
aequinox. It is well known, that Pope Gregory XIII. re
formed the calendar, A. D. 1582, when he threw
off 10 days; ever fince the beginning of A.D.
1700, we have reckoned 1 1 days difference be
tween the old ftile and new, or the Gregorian
and Julian account ; but though this is the 51ft
current year fince this reckoning commenc'd, 1 1
days are not yet completed ; now if the aftrono
mer can fhew, from his tables, by which he cal
culates the Sun's annual revolutions, when they
will be exaftly completed, he will be able, at the
fame time, and by the fame means, to determine
the true meafure of the Sun's year.
The

( 54 )
The revelations of the Pentateuch will evi
dence to us, that there are more fecrets than one
in our allotment in the fyftem, which philofophy
founded upon obfervation has not yet (fully) dis
covered to us.
Felices anima! quibus hofcogriofcere motus,
Non ars, non ftudium, Jed deusipje dedit.
I fhall now proceed to examine the grounds on
which the latter part of my fecond propofitioh isi
built ; which fome, perhaps, may look upon as
an arbitrary poftulatum, unwarranted by the Pen
tateuch, and fo pafs it by with a total difregardj
viz. II. That Mofes dates the beginning of time and.
his chrOnolbgy ' from a Cardinal point of the"
Heavens, viz. the autumnal aequinox ; and from
a cardinal point of the day, viz. noon. And the
Mofaic meridian is geographically defcrmed, Gen,
ch. 2. ver. 10, &c.
The divine perfection of original aftronomy
will fhine forth moft confpicuoufly from the
demonftrable truth and certainty of this peculiar
(and may I not add unexpected) prOpofition ?
For can there be a nicer point, either ftated Or
fuppofed, than the co-incidence of the Mofaic
Tekupha with Zohoraim ? Or the aftronomical
connection, and exact adjuftment, of a cardinal
point of the year, with a cardinal point of the
day,

day, in a given and determinate meridian t And
fhould it be found, in fact, an exprejs datum of
the Pentateuch, it muft, I fuppofe, enhance its
authority and its value ; fince we might tire our-
felves by fearching for it to no purpofe in any
Other records. The philofopher has never read
it in the expanded volume of the material world,
and if it is not legible in the book of Revelation,
we muft acknowlege it to be an inacceffible truth.
But where the light of nature fails to aid and fur
ther the progrefs of our enquiries, there the light
of Revelation feafonably interpofes, as in theology
fo In aftronomy, and gracioufly fupplies its- de
fects. We have been fufficiently informed concern
ing the divifion of Jom, or the aequinodtial Nuc
themeron, into 4 equidiflant quadrants, and from
hence we are able to exhibit to view every par
ticular, in the following clear, perfpicuous, and
intelligible manner.
A. M- o. the Sun in the Mofaic?^
Tekupha   £©
(o) ' (i) (2)' (3). (4),
Gnereb. Chatzj laijela. Boker. Zohoraim. Gnereb.
. Sun-fetting. Midnight. Sun-rifing. Noon. Sun-fetting.
The meridian of the garden of— Eden.
The full Moon  O
The chaotic new Moon epadt c -1 5
This part of the 2d propofition offers to the
aftronomers confideration as curious a fpeculation and

C 56 )
and difquifition, as can exercife his labours, and
employ his fkill. A difcovery and proof of the
Mbfaic meridian (or that determinate point of
the Earth's furface, in refpect to which the annual
motion commenced, and from which both years
and days are, by divine authority and command,
to be 'jointly computed) muft furely be attended
with ufeful and important confequences. And
although no public ample rewards have been pro-
pofed for its difcovery and proof; yet is it, in it
felf confider'd, of fufficient weight to animate
our endeavours, and to excite our moft diligent
purfuits. It may poffibly be enquired, why I have ex-
preffed myfelf in this fingular manner, in the fore
going paragraph, viz. " And from which both
" days and years are— to be jointly computed."
Was k ever known that their meafures were fepa-
rated or disjoined ?
Here my anfwer is, it is plain from the Mojaic
Narration. Gen. ch. i. ver. 5. That the diurnal
motion was imprefs'd 3 days, and 3 quadrants of
a day, before the annual began ; and that thefe 3
days, and 3 quadrants are not admitted into the
computations of time, nor make a part of Mojes's
chronology. Now if the philofopher can prove,
upon true principles of aftronomy, that it is im-
pofiible in nature for the diurnal motion to exift ,
prior to, diftindt from, and independent of, the
annual, he will effedtually confute my interpreta
tion; and if it will not ftand the teft of true phi
lofophy, it muft and it ought to fall. It

(57)
It may be again objected, that Mofes cannot be
faid to defcribe fix fucceffive natural days, be
caufe, though there was light for the 3 firft days*,
there was no Sun till the 4th ; to which I reply,
that, with refpect to the Earth, covered with
the deep, as with a garment, there was not only
an equal divifion of light and darknefs, but every
one of thefe days had an evening and a morning,
and therefore motion ; and as there was motion,
there muft be a rifing and fetting, an appearing
and difappearing of light, luminous body, lumi
nary, Sun. Should any one be difpdfed to call,
with Milton, this original light, " aethereal, firft
of things, quinteffence pure," this, or any other
fentiments of this kind, will not any ways affect
this, antecedent diurnal motion,, or natural mea
fure. I will here fet down Mofes's geographical de
fcription, and exact determination of his meri-r
dian; Gen. chi ii. ver. 8. The Lord God had planted
(Mikkedem, beforehand) a garden— and there he
placed Adam.
Ver. 10. And a (fingle branch Of a) river,
went out fl/VEden to water the garden, and from
thence (both northward and fouthward) it was
parted, and became into 4 heads.
Ver. 11. The name of the fir fl (river) /;Pi'fb'n — ¦
Ver. 13. And the name, of the fecond river is Gi-
hon— Ver. 14. And the name of the third river
is Hiddekel (Grec. Tigris)— And the name ofthe
fourth-river zYPerath, *. e. Euphrates.
H Now

(53 )
Now when we read this, are we to look upon
it only as a map of the land of Utopia ? As a mere
vifionary and romantic fcene? Or admitting it
(with all interpreters) to be real ; are we to con
clude, that Mofes certainly intended no farther by
it, than to point out that particular place of the
Earth, where the firft human pair paid their ear
lieft adorations to their creator ? Why then did
not the pen of Mofes defcribe, with the fame ex
aetnefs of geography, the land of (Nod) the wan
derer Cain ? Why did lie not record the way of
the ark, on the furface of the deep, and point out
all its bearings ? Why did he not fettle the longi
tude and latitude of, that place, in which Noah-
built and entered into the ark ? Why did he not
fpecify the very mountain on which it refted ?
Mofes never gratifies our vain curiofity ; what
he has recorded, it Would have been a detriment
not to have known, and will fooner or later ma-
nifeft its importance. Weighevery word of the
Pentateuch, and you fhall not find onp of them
light in the ballance.
-If Mofes was inftructed, as a divine aftronomer,
rightly to fiction the two great luminaries at
their firft goings forth ; ,why not alfo, as a divine
mathematician and geographer, to fix and deter
mine the meridian, according to which the ori
ginal pofition was adjufted ? — that very meridian
which firft paffed through the center of the
Sun ? - _ <
A verbal explication of the original characters
will be only a tranferibing (as we fhallprefently fee)

(59 )
fee) the nature, properties, and affections of a
direct fphere. We are immediately directed, by
only cafting our eye over them, to rectify the
globe to the Sun's place in libra, and to bring it
to the meridian, and then mentally .correct our
prefent application of the ecliptic to the terreftrial
fphere. This being done, the Sun immediately
appears in the midft of the prime vertical ; from
whence the divifion of the globe into the eaftern
and weftern femicircles of longitude, and into the
northern and fouthern hemifpheres, arifes. The
Sun is due eafi ; it is due weft ; it is due north ;
and it is duejouth. I need not note its right af-
cention, for we cannot overlook it. Therefore,
Afcentional difference^o. Amplitude, ortive
and occafiverzo. North and fouth declina-1
tion=o. Longitude=o. : ,• ,
Suppofe now the Earth fix'd immoveably in its
orbit, and a right line to be drawn, from the cen
ter of the Sun, to the center of the Earth, it
would (i) Pafs through the plane of the meridian of
the garden of Eden,
(2) It would fall in the center ofthe enlightned
hemifphere, or of the circle which bounds light
and darknefs. Gen. i. 4. Vaijabdil Elohim bin haor*
ubin hachofhec. Ver. 17. Vaijitten otham Elohim,
birkiahg hajhamajim, lehabdilbin aor bin hachofhec.
(3) The circle which bounds light and dark-
nejs would pafs through both the poles. Ver. 17.
-Vaijitten otham Elohim, birkiang hajhamaiim, le-
bairgnal haaretz. H 2 (4) It

( 60 )
(4) It would be co-incident with the rational.
horizon. (5) It would cut the parallels of declination into
two equal parts. — Gen. i. 14. Vaijomer Elohim,
jehi meoroth birkiang hafhamajim, lehabdil bin hai-
jom ubin haliaijelah.
(6) Being extended to the iftarry Heavens, it
would meet that point where the ecliptic optically
interfects the aequinodtial.
Now, I fay, in this perpendicular ray we fhall
find what St. Bafil, with great accuracy and juft
propriety, calls — T* xv>vt TKV ^.^Tw^iywii ; the
firft motion of time: for time and (the annual)
motion are'coaeval.
Thus then, from revealed data, I conclude the
Sun began its courfe, or, if you had rather fay,
the (firft computed) revolution' of the aequator
commenc'd from the aequinodtial point of the
Heavens, and from the meridian of the garden of
Eden; where we muft remember the fingle river,
which ftill remains as a directory.
Here I appeal to the Pentateuch for the meri-:
dian; and to aftronomical calculation for the
proof. And yet the aftronomer will never be able to
calculate the Sun's going forth from the Mofaic.
meridian, unlefs he will take explicit directions
and inftrudtions- from the facred hiftory. He muft
neceffarily take into confideration, however re-
ludtant his faith, may be, that ftupendous fufpen-
fion of motion^ recorded, Jojh. ch. 10. ver.
12, 13. Ver.

(61 )
Ver. 12. Then fpake Jofhua to the Lord — and
he Jaid in the fight of all Ifrael — Shemejh dom- —
Sun hefilent, or ceafe to -fpeak thy wonted lan
guage. Ver. 1 3 . Vaijiddom hajhemejh, and the Sun was
filent. I would know from the aftronomer himfelf,
• what is that univerfal language, which the Sun
feems to fpeak, both to the cultivated and un
cultivated nations of the world, in the interchange
able ftates of light and darknefs, and the con-
ftant viciffitudes of night and day, with bnlyone
interruption fince its firft going forth ; for, ver.
14. there was no day like that before it nor af
ter it.
I would know what language, the Ptolemaic fy
ftem fuppofes it to fpeak. From what ground arifes
the diftindtibn, in the ephemerides, between he
liocentric and geocentric motions ? Whence comes
the double language, in our aftronomy, of Apo
gee and Perigee, of Aphelion and Perihelion ? Do
not the aftronomers fpeak of the Sun's place in
the ecliptic, fifty times for one of the Earth's in
its orbit ?
An autonomy, proceeding upon the evidence
of fenfe, with a feeming difregard to philofophic
realities, and the phyfical laws of motion, may
be thought very unpromifing to the penetration
and acute difcernment of a modern : but be that
as it will ; I fhall offer to the reader this general
remark, viz. That the aftronomical language of
*-¦¦•'• the

(62)
the Pentateuch is plain and fimple, fuited to ap
pearances, and ftudioufly accommodates itfelf to
the ideas and apprehenfions of the vulgar and illi
terate. The peculiar phrafe or diction, in which Mofes
has recorded and tranfmitted to thefe latter ages,
the aftronomical characters of the world's aera, _ is
very obfervable, and will ferve for a pertinent il-
luftration of the truth of my general remark with
regard to fimplicity.
Mofes, for inftance, does not enjoin his If-
raelites to obferve the feaft of in-gathering— Te
kuphath haaretz — in the revolution of the orb of
the Earth about the Sun ; nor— Tekuphath hajhe-
mefh — in the revolution of the orb of the Sun
about the Earth ; the terms have no reference ei
ther to the one orb or to the Other : but abftradt-
ing our thoughts, both from the Ptolemaic and
the Copernican fyftem, he only fays, with a very
furprifing, and I verily beleive, directed fimpli
city,— Tekuphath hafhanah— -in the revolution of
the year. Now, where there is a revolution,
there muft be motion, and a fubject of that mo
tion, but Mofes appropriates it not. Nor can the
terms and language of the Pentateuch be eluded
or tormented, into the confeffion or denial, ei
ther of the truth or falfity, of any philofophic
fyftem. Let us recollect and contemplate the order and
fituation of the four quadrants, and their corres
ponding cardinal points, which we will now fet
down

(63 )
down, with fome fmall difference, in this man

ner,

Night. Day.

* Gnereb. Chatzi laijelah. Boker.
| Sun-fetting. Midnight. Sun-rifing.
> Boker. Zohoraim. Gnereb.
\ Sun-rifing. Midday. Sun-fetting.

Mofes, in exact conformity to nature, divides
the aequinodtial Nudthemeron, into two hemif
pheres; whilft Gnereb (Sun-fetting) ftands at the
head or beginning of the night : and Boker (Sun-
rifing) at the head or beginning of the equal day.
Let us confider thefe three terms. Boker, Zoho
raim, Gnereb.
The MoJ'aic pofition of thefe cardinal points
fully inform us, how we are to conceive, and
what judgment we are to frame of, the formal
manner of diurnal motion.
The whole enlightned hemifphere was never
defigh'd to be the object of our fenfes ; and we
are obliged by the God of nature, whenever we
take a view of , the cceleftial phaenomena, to argue,
infer, and conclude, from geocentric motion.
The Mofaic term Boker conveys to the moft
rude and Uncultivated mind the familiar fenfible
idea of the Sun's rifing in the eaft ; and Gnereb
of his fetting in the weft; which fpace, at the
aequinox, meafures a femidiurnal revolution, the
prior fenfe of Jom. Whilft the middle term Zo
horaim conftantly refers to the Sun in the meri dian.

(64)
dian, to which he fticceffively arrives by his ap
parent motion from eaft to weft.
Biit here the philofopher interpofes, and with
ardor and zeal affures Us, that all thefe phaeno
mena, pr appearances, are mere deceptions of
fenfe; that we muft learn to correct bur fenfes
by our judgments, arid muft rightly inform our
judgments from the principles of true philofophy.
If we afk how, with refpect to the rifing and fet
ting ofthe Sun, weare immediately taught a con
trary leffon ; arid now the whole enlightned he
mifphere muft be taken into the account, and the
two extreme terms Boker and Gnereb, muft be
placed in this inverted order.

oa

(A) Eaft. Gnereb. 90°. 0. 90°. Boker. Weft. (B)
Sun-fetting. Sun-rifing.
For the explanation of this fcheme, and inver
ted pofition of the extreme terms, we are to fup-
pofe two fpectators, A and B ; the one (A) fituated
in the eaftern, and the other (B) in the weftern
verge of the enlightned hemifphere.
Now (A) being 90 degrees diftant from the
Sun, immoveably fix'd in the Heavens, it will
appear to him in the edge of the horizon, and as
fetting in the Weft; confequently, this eaftern
point, with regard to the fpectator (A) will be
Gnereb, Sun-fetting^ On

'( ^5 )
On the contrary, (B) being alfo 90 degrees di
ftant from the Sun, it will be feen by him on the
edge alfo of the horizon, and as rifing in the eaft.
Therefore, this weftern point of the enlightned
hemifphere, with refpect to the fpectator B, will'
be Boker, Sun-rifing.
, As to Zoheraim, or the Sun in the meridian,
the philofophic reality is this, viz. The Earth
turns round its axis from weft to eaft, and, meet
ing the Sun, paffes under rt, and revolves eaft-
ward. Thefe things are fo generally known > that I
have only hinted them without regard to minute
exaetnefs, and ftating every circumftance ; but it
may be worth the while to remark, what a tedi->
ous ambages bf words, and labour'd circumlocu
tions, we are forced to have recourfe to, in order
to exprefs philofophically two of the moft obvious
and the moft common phaenomena of nature, the
rifing and the fetting of the Sun.
But if we underftand and apply the terms Boker
and Gnereb in the order they are placed by Mofes,
and as correfponding with the evidence of fenfe
(doubtlefs by the authority and fuggeftion ofthe
creator himfelf, who beft undeftood the opera
tions of his own hands* and muft know what
Was the moft proper., and the moft inftrudtive
mode of human conception) all will be plain, and
level to ordinary capacity and apprehenfion. Then
the intricacies which attend philofophic ftile im
mediately ceafe,. .,!
I I

( 66 )
I would here beg leave to make one obfervation,
and to propofe one queftion, to thofe who fhall
find themfelves difpofed to take notice of it.
The obfervation I would make is this — Sun
and Moon aftronomy were well underftood, and,
with refpedt to ufe and application, with greater
exaftnejs, and higher degrees of certainty, than
arts and fciences have yet been able to recovery
and this, feveral thoufands of years, before pUL
lofophic realities, from aught that appears, were
fo much as apprehended or thought of; I am
fure I may fay, before they were digefted into a
regular fyftem : this is the peculiar honour, I fup-
pofe, of the prefent age, and of our Britifh phi
lofopher. The queftion I would propofe is this. — What
phyfical reafon can be affigned, why the creator
of our folar fyftem, infinitely wife throughout
all his works, fhould have fo deeply fecreted from
the evidence of our fenfes, both the rotative and
progrejfive motions ofthe Earth, (though the day
is meafured by the one, and the year by the other)
that almoft 2000 years werepafs'd, fince the cul
tivations of fcience, or the times, of Hipparchus\
(not to mention the cycles of the Greeks) and be
tween 5 and 6000 years of the world's age, be
fore obfervation, calculation, and fcience, had
taught us to demonftrate, with an abfolute and
infallible certainty, the truth of the Copernican
fyftem, to the entire confutation of the Ptolemaic^
And laftly, to fum lip the whole, what notable
.emolument or advantages, have accrued to Sun and

( 67 )
and Moon aftronomy (I mean, with refpect to
the recovery of the coceval lunar year, its nice and
curious adjuftment to the revolutions of the true
folar, and the more exaft meajures of time) by the
modern demonfiration ?
Was it poffible to eftablifh a fyftem of true phi
lofophy upon the evidence of fenfe (which is im-
poffible) the Ptolemaic muft neceffarily and uni-
verfaliy prevail. And without controverfy, this
fyftem (if any fyftem may be fuppofed to be true,
i. e. exactly conformable to the inward frame and
real conftitution of nature, which muft be, one
Would think, rather a divine than human per
formance) derives an inconceivable honour and
dignity upon this our Earth. For when we eaft
our eyes up to the Heavens, does not the Earth
feem to be immoveably fix'd, in the center of an
immenfe concave fphere? And upon whatever
point of its furface, we may chance to fix our
feet, we are ftill in the center of our own obfer
vations. Does not univerfal nature, both above,
below, and all around us, feem to be created and
ordained for our whole and fole ufe, and is
pleafed to militate in our fervice ? The planets and
the" fixed ftars fhed the influence of their fainter
beams on us by night, whilft the Sun warms, re-
frefhes, and invigorates us by day. The ftupen-
dous circumvolution of the whole Heavens feems
to be unwearied in the meafuring of our days,
and to roll in fubferviency to the Lord of this
important globe. I 2 But

(68)
But fay, that true philofophy, both remon-
ftrates and demonftrates againft all this ; that by
its penetrating, and enlightning powers it awa
kens us from, thefe delufive, felf-admiring dreams
and fuperfedes the hallucinations of fenfe. Be it
ib; yet furely, true philofophy never excites,
much lefs will it juftify, the petulancy of fome
modern aftronomers ; who, more" arrogant and
prefumptuous than either truly wife or knowing,
defile whole pages with rhetorical flourifhes and
ftudied harangues, in degrading the place of their
own habitation, this moft dignified -and diftin
guifhed planet. And all this, under the fpecious
praetext of curbing its afpiring pretentions to any
degrees of pre-eminence and fuperiority above the
reft of its fellow- wanderers.
But I would afk fuch a fyftematical declaimer,
whether he can produce an authentic hiftorical
account or memoir of any other known habitable
world, befides this, from its firft formation to this
prefent day- from whence to trace the funda
mental principles of his own profeffion, back to
their very firft fpring and fountain head, arid there
fix them a priori on their proper bafis ?
The mafters of method have laid us down thefe
two rules, (i) to fhew what a thing is not. (2)
To (hew what it is.
As the antient and the modern aftronomy are
very different from each other in their calculus,
extent, and terms; as widely different, 'I may
fay, as philofophy and no philofophy 5 as art and no

( 69 )
no art; as plain fimplicity, and an oftentatious
pomp and parade of technical language ; it is quite
neceffary to begin with the negative part of the?
rule, and to fhew, with as much brevity as may
be, what particulars do not appertain to the an-
,tient and original knowlege.
Firft, Saturn with its ring and-fatellites. — Jupi
ter with its belts and fatellites — ^ Mars and its re-
trogradations— the tranfits of Venus, like a black
fpot, over the difk of the Sun— the rare phae
nomena of Mercury— magnitudes, denfities, dif
tances — centripetal and centrifugal forces— the
inclinations of the planes of the orbits— opposi
tions, conjunctions, trigoris, quart'iles,. textiles —
In a word, every, phaenomenon, both ofthe fupe
rior and inferior planets, are entirely (and, in
deed, by the very terms, neceffarily muft be) ex
cluded from Sun and Moon aftronomy.
¦ Secondly, center of motion — univerfal princi
ple of gravitation— elliptical orbits — focus — ec
centricity — mean anomaly— proftaphaerefis — ir
regularity of folar days — ecliptic— aequator — ho-
rizon—^conftellations— figns— the ram, the crab,
the ballance, and the goat's horn — degrees, mi
nutes, feconds, &c. — hours, minutes, feconds,
&c. — aphelion, perihelion — polar — revolution j
£fc. — are all modern inventions and difcoveries. >
1 Thirdly, The Moon's anomalies — her accele
rations and retardations in apogee, in perigee, in
quadrature — The inclination of the plane of her
orbits— angle of inclination— dragon's head-.-r-dra-
gon's tail — The retrograde motion of the dine of
the

< 7° )
the nodes — excurfioris beyond the ecliptic — com
menfuration of her diurnal and menftrual revolu-
tions-rdibrations in the perimeter of its orbit —
periods, conjunctions, eclipfes, &c. have no
place, no denomination, are of no account, in
the plain fimple elements of original aftronomy.
Let thus much fuffice for the negative part of
the rule; arid to make a tranfition to the pofitive,
I may juftly obferve, that in all this farrago o£
philofophy, aftronomy, technical terms and fci-
entific principles, there is no exprefs mention, no
note of reference, nor feemingly a remote thought
or apprehenfion of the fundamental text of the
Pentateuch. Gen. i. 14. And God faid, let there
be luminaries in the expanfe of the Heavens, and
let them be —
(1) LeatJooth.. (2) Lemognadim. (3) Lejamim.
(4) Bejhanim.
The fecrets and the depths of this theologico-
aftronomical text, neither human philofophy, nor
all the improvements of modern fcience, have
ever been able to unfold or penetrate; fo per-
blind is human philofophy, fo Idark the light of
nature. It manifefts not indeed the univerfal principle
of gravitation, the center of motion, and phyfical
law ; yet it clearly reads, to the ear that is open
to attention, a much more felf-concerning and
more inftrudtive leffon.
It fcientifically reveals the primary defignation
and the refpective offices of the two great lumina ries 5

<7' )
ries ; the facred and the civil ufes, the high im
portance and final caufes of periodic motion.
Here the gracious ceconomy and tranfactions of
Elohim Jehovah, ad extra, with the whole race
of mankind, are planned, if I may fo fpeak, in the
determinate divine counfel, and fore-knbwlege,
from the very foundations of the world.
And indeed, the Mofaic and Scripture aftro
nomy is rather of a theological than philofophi
cal nature ; for, in this divine difpenfation, the
Sun is not confidered, as the center of motion,
light, and heat, to a chorus of planets dancing
round it; nor is the Moon confider 'd, as a fphae-
rical opaque body, fhining with borrowed and
reflected rays; but both the Sun and the Moon,
are here reprefented as the faithful witneffes in fhe
Heavens ; ever regulating, in purfuance to the
original law of the fovereign legiflator, the perio
dic returns of folemn affembly days and divine
inftitutions ; whilft they never fail to give their
united and illuftrious atteftations to every awaken
ing grand event, recorded throughout the Scrip
ture hiftory, with notations of time, koto. t«
tf-fcTSTa^-Msw x?ow 3^ xst/jKf, in exadt agreement
with before-appointed times and feafons.
The learned and inquifitive deift will not ex
pect, and the Chriftian will rejoice to find, that
the Sun and Moon in their courfes fhine in fub
ferviency to the adorable myfteries ofthe Chriftian
redemption, and glorioufly plead the caufe of re
vealed religion. If

C 72 )
If - ouf 'Brttijh philofopher has^. in thefe latter
ages, taught and dembnftrated a geometrical phi
lofophy; Mofes t the Jewijh legiflator, above
3000 years before him, has clearly and explicitly
revealed the original and proportional aftronomy.
/The patriarchs underftood aftronomy, fo far as
was neceffary ,, for mankind to know better than
.we ; for what they knew, they knew to perfec
tion, becaufe they primarily received it from the
creator himfelf. The God of nature originally
conftrudted the patriarchal year, no wonder that
arts and fciences could never attain to it,
I who am but a novice, and juft initiated into the
perfections of the Mojaic Calculus, cannot avoid
perceiving the vaft and inexpreflible difference be
tween the knowlege of a patriarch and of a modern
philofopher, between the knowlege of one, who
lived near to the fountain and fpring head of truth,
and had imbibed, from his youth, the dogmata of
our great and common progenitor, ultimately re-
folvible into immediate divine revelation, and that
precarious uncertain knowlege, which wasfqueeze^
out, by the gradual and laborious deductions of
'reafon and experiment, a drop or two in an age. .,
Aftronomical hiftory carries us back no farther
than the times of Hipparchus, and in that inter
val of about 2000 years, we have, at laft, . made
a fhift by drudging at obfervation, and by in-,
vented rules of art, to difcover and, determine
nearly the quantity of the Sun's annual courfe-.
'Till the fuperior gertius of Sir I. Newton arofe^
and inftructed this weftern world, what was all
our

(73 )
our philofophy, but the fluctuating opinions of
the current age, the reveries of Ren. des
Cartes f
But let us not imagine that we have exhaufted
fcience, for modern fcience is but in its dawn ;
and we are but juft recovering fome truths, which
were well known to mankind (at firft in general)
above 5000 years ago. Take away the Penta
teuch of Mofes, together with the aftronomical
principles, mediums, and data, which are evi
dently, clearly, and perfpicuoufly taught and in
culcated there, for aught I can fee, the facred
and ecclefiaftical lunar year muft be irretreivably
loft; and that too, in this aftronbmical age. And
yet-^haju lemognadim — is a divine law, enacted
in the beginning.
Should it be enquired, wky the emperor and
Pontifex Maximus entirely difcarded the lunar
(which was the ancient irregular Roman) year,
•need we fcruple to affign for a reafon, the utter
inability of Sofigines (his affiftant and director) to
teach him how to accommodate, by true aftro
nomical laws, the one to the other, or the Moon's
year to the Sun's ? And will any Europaan aftro
nomer kindly ftep in, to fupply this evident want
offkillin the /Egyptian^ Strange and unexpec
ted paradox ! that, even in the age of fcience, we
fhould be obliged to return back to the remoteft
ages of the antediluvian patriarchs, and to their
fuperior fkill in Sun and Moon aftronomy, and to
learn from the laws of primitive fcience how to
reftore the coaeval lunar year, and how to recti-
K fy

(74)
fy our mifapplications of the tropical folar to the
Julian* Six primary planets (fays the modern aftrono
mer) move in elliptical orbits about the Sun, the
center of their motions. Why then 'tis as certain
that there are fixdiftindt fpecies of planetary aftro-r
nomy. And is it not highly reafonable, if not
neceffary, to be, firft, well acquainted with our
own, before we are fo impatient to gratify an uje-
lejs curiofity ? ,, >
The diurnal and annual revolutions of Jupiter,
for inftance, meafure not my days, nor my years,
nor do thecircumjovialsprefide over my nights. .,
After a general account of the feveral periods
and diftances of thefe folid moving orbs, together
with their harmonious and truly divine propor
tional laws (I mean, that the fquares of their pe
riodic times are as the cubes of their diftances)
the aftronomer has not recorded a phaenomenon,
which can merit the privilege of withdrawing our
contemplations and ftudies from the Mofaic two
great * luminaries. I except not the altitude and
diameter of Scturn's ring, whofe immediate ufe
and properties are beyond the reach of conjecture.
Nor, the immerfions and emerfionsof the>fatellites
of Jupiter, a moft enormous planet ; and to us,
(cocab) a ftar of about the firft magnitude.
Had we employed our chiefeft thoughts, upon
this one Hebrew text, Gen. i. 16. Vaijagnafh E-
lohim eth Jhenei hammeoroth haggedolim^ — rather
than in wracking our brains, if haply we might
be able to calculate and determine the diameter and

(75)
and circumference of the extreme orbit of Saturn,
or folve (by geometrical fchemes) the feeming re-
trogradations of Mars, we had long ago attained
to that perfection in Sun and Moon aftronomy,
which the creator intended to be the object of our
knowlege, and of which he has qualified us to
receive the inftrudtion.
Here I dare appeal to the greateft proficients in
fyftematical fcience, whether the civil and the
facred ufes, and the final caufes of periodic mo
tion, are not a more affecting, a more beneficial
and concerning fpeculation, than precarious phy
fical ratio, .and phyfical law ?
The broad fpheriodical figure of the Earth is
owing, fays Sir I. Newton, to the Earth's rotation
about its axis ; but furely, one would rather con
clude, that it's form and motion were both imprefs'd
by the creator of it ; and, when impreffed, could
not be fubject to any mutabilky or changes, with
out the divine interpofition.
Aftronomy, as the creator himfelf has revealed
it to us in his written word, isufeful, felf-con-
cerning, plain, eafy, and obvious to common ap-
prehenfion : whilft the learned profeflbrs have
rendered it perplexed, intricate, and inacceffible to
the bulk of mankind ; as if they affected, like the
old JEgyptian priefts, to become facred and vene
rable to the vulgar, by their efoteric dogrnata,
and their hieroglyphic grammata.
Arts and fcienceshave led us round-about ways;
nay, thoufands and millions of miles out of the
K 2 way;

(76)
way ; into paths, which God requires us not to
traverfe; into remote and diftant regions, which
we were never defigned to reach or compre
hend. We, the Sun and Moon aftronomers of this
terraqueous globe,; are no more concerned with
the Britifh, catalogue of 3000 fixed ftars, than
with the parabola of a comet.
What account the (fuppofed) inhabitants of the
fuperior and inferior orbs might be able to give
of time and its meafures, were it within our reach
to examine them, I do not know, nor can a New?
ton inform my ignorance. It is fufficiept for me,
if I. am able to render a fatisfactory and true aftro*
nomical account of — my days, and — my years-^
from the Pentateuch of Mofes, whofe aftronomi
cal directory is exprefs'd in the Hebrew text,
Gen. i. 14. by a lefs number of words, than there
are primary planets,* 1 Haju lejamim vefhanim, ..

This comprehenfive fcientific text points out
to us a diftindtion of years, and a diftindtion of
days; it confines our enquiries to folar and lunar
years, and to the days of the folar year, and of
the lunar. Add to this text,
Gen. ch. 5. ver. 27. All the days of Methufalaj)
Wpre 969 years.
„ In like manner, by the guidance ofthe Mofaic
#yfe, 1%,
- , All

C 77.)
AH the daysoi the world's paft duration are 5757
years, A. D. 1750 J
Now does it require any extraordinary genius,
any uncommon degrees of penetration and faga-
city, to difcoves, that we are pofitively directed,
by the terms of Mofes's chronology, to reduce
folar years and lunar years to days? And from
this fimple (though Very peculiar) law of reduc
tion, in union with the given radix, and the
terms of the Pentateuch, all founded in nature,
we fhall immediately difcover the moft ufeful,
and the moft neceffary effentials o.f Sun and Moon
aftronomy. It is now time to enter upon the proof of my
3d propofition, which fets forth, that Mofes mea-
fu'res the lives ofthe patriarchs, &c.
In this propofition I muft enter into a critical
account of thofe two diftinguifhed terms of the
Pentateuch, Chodejh month, and Shanah year.
I fhall begin with the explanation of Chodejh, in
doing which I will firft fet afide the Jewijh notion
of k : fecondly, affign to it its true meaning : and
laftly, fhew the number of days it contains.
Buxtorf in his lexicon interprets Chodejh 'by the
Latin — Novilunium, menfis, ab innovaiione Luna.
That Chodefh fignifies renovation, or in a calendar
fenfe, repetition, is eafily allowed, though not of
the Moon? but of a fyftem of days, called month:
that it fhould mean a renovation of the Moon's
light is impoffible to be true, becaufe the months
are equal, as will be proved in its place, which
equality,

(78)
equality, a computation by the lunar periods and
fynodscan never produce. And when Mofes relates,
Exod. i. 2. that his mother Jochebed hid him,
Shehjhe Jerachim, thefe words were not to be un-
derftood to mean 3 unequal lunar months, but 3
equal months of the lunar year, between which
two computations there is a wide difference.
Chodejh occurs aboVe 150 times in the Hebrew
text, yet in all thofe inftances, I fhould fay not
in any one inftance, does it ever refer to the new
Moon any more than it does to the full, and
equally to both. . -
Neither is the Hebrew word Chodejh more mif-
taken than the Greek Neomenia by which it is
fometimes tranflated. There is a paffage in Philo,
contemporary with Jofephus, which will clearly
inform us of its precife determinate fenfe : great
ambiguity and confufion has arifen from the Eng
lifh tranflation, which has rendered it, 2. K. ch.
4. ver. 23, &c. New Moon, Moon inftead of
month. But thefe few words of Philo will teach
us where the error lies, and how to correct it :
Mst& ervvo£ov, mv kouto. tiva ~2,iKwnv vatv, pcoy.ni/ia,. Wbere
Philo writes, ^t* awofov, Mr. Whifton, in his Har
mony of 'the 4 gofpels, tranflates, pi 95,1. 32,—
after the new Moon. Now if this expreflion—
the new Moon. — can with any propriety be appli
ed to o-uf-aJW then the words — ¦z.ihwnv vzm — being
literally tranflated, will alfo fignify— new Moon,
—f And I need not obferve, that — Ntopwa. — is
conftantly tranflated new Moon. > But

(79)
But what inconfiftency of interpretation is here?
After the new Moon, which happens in every
new Moon, is the new Moon. Philo was incapa
ble of writing fuch unmeaning jargon, and what
he means is clear, precife, and determinate.
There are 12 fynodical lunations wkhin the
limits of a lunar year, according to the artificial
calculations and invention of the Greeks. Now,
fays Philo, Neo^iw*, i. e. the firft day of the month,
begins in the evening next after thejynod, and this
in every fucceflive month, throughout the lunar
year. Kara, rtva, Setouw vatv.
We have from the fame antient writer and
gxxcizzcXjew a farther explanation, and even the
aftroaomical boundaries of the Attic term ns^m/*.
Aftronomical, I mean, with refpect to a calcu
lation by the mean motion ; which would fome
times fall on the right day, and fometimes would
exceed it. Whenever this happened as it muft
when the Moon was in conjunction late in the
day, they would begin their month on the even
ing the next but one after the fynod, or when the
Moon was vifible ; although this was not their
law, and ftanding rule, nor did they intend it.
I was induced to remark thus much, becaufe
this very cafe fell out at the vemal aequinox, in
the year of our Saviour's crucifixion, A. D. ^.
and A. J. P. 4746. Mr. Whifton, in his Har
mony of the Gofpels, p. 196, has fixed this paf-
chal new Moon to March, 19 d. 13 h. 30 m. or
to half an hour paft one in the afternoon ; fo that
there

(86)
here wanted but 4T hours to complete the day.^
And/ *
" What is moft material here (fays Mr. WhiJ-
" ton, p. 197) is this: fince the new Moon (fo
" the aftronomers exprefs the fynod) happened
" -fo near to the night on the 19th of March.
" A. D. 33, as by no means to be vifible till the
" evening of the 20th, it feems to follow—
" that not the 20th of March, but the
" 2 1 ft, fhould be the ift day of the month
" of Nifan :"— and fo it adually was. For
whoever will give himfelf the trouble to make
the calculation by Ptolemy's aftronomy, which
was publlfh'd A. D. 140, and adopted by
Rabbi Hillel about A. D. 338, will find Neomenia
Nifan, the ift day of the ift month of the
Jewijh year, to fall on the day after the con
junction, or on March 26, and on the 6th
Feria. 'And confequently, the 14th day 'of the
month, ots iQvov to nra.<%&, fays St. Mark. s> » «/«
6usjr9<tt to int^a., fays St. Luke, will fall on April
3d, and alfo on the 6th Feria, or n? o<ra.^a.rov, in
exact agreement with the gofpel account.
Mr. Whifton feems 'not to have confidered a
material circumftance, viz. that he was able to
calculate this pafchal new Moon by the laws of,
true aftronomy, . whilft the Jews, who were
taught by the Greeks, drew their conclufions from'
the mean motion only, which muft, in other in-
ftances befides this, occafion the difference of a
day, and ever when the conjunction happened in
the afternoon, as this did.
The

(8i )
The prefent Jews to this day, though they
live in the aftronomical age, and in the midft of
aftronomers, acquiefce in Ptolamy's definitions,
and ftill calculate their vio^via.1 by Rabbi Hillel's
laws, and the mean motions of the Moon. To
return to Philo :
The paffage which I refer'd to laft is this.
}infAiviet, yet? etf)(irai <paTi(^&y a/afttira Qtyyi 2SA.HW HA/of.
Idem apud Selden de anno judaorum, c. 20.
" In the end of the firft day of the month
?c (which began the evening next after the fynod)
f f the Sun begins to enlighten the Moon with a
*' perceptible light. And whenever they con?-
fc eluded rightly this conftantly happen'd."
From the writings of Philo Judaus, and the
concurrent teftimony of Jofephus, we may infer,
that thefe expreffions — a lunar month (k*t*2smiw)
and a month of the lunar year, is a charadteriftical
difference between the computations of the an
cient and pf the latter Jews.
I fhall now come clofer to the point, and unr
dertake to prove directly, that the latter Jews in
their difperfions borrowed their unequal months,
and the whole of their computations from the
Greeks. They made ufe of no cycle, either thaf
of 84 or of 1 9 years, as fome have imagin'4 ; nor
did they obferve the <p&yi<r of the Moon. The
more we enquire into this, the more evidently its
truth will appear from Phifo's precife, exact, and
determinate explication of the attic term aioymvut;
whilft the ancient' Jews fhew'd a total difregard
L to

( 82)
to lunar periods and fynods throughout then-
year. I fhall fetch my argument from the table, and
the feveral particulars of Ptolemy's calculation.
Timocharis obferv'd, as Ptolemy has noted, 1. j.
c. 3. p. 170. that the ftar called J'pica virginis
exactly touched the north fide of the Moon, as it
was rifing above the horizon, A. aer. Nabonaf.
466, on the 7th day of Thoth, and on the 6th of
the attic month Pyanepfion, decreafing.
This obfervation of Timocharis then was made
in the beginning of the third year of the reign of
Ptolemy Philadelphus, and in the 42c! year from
the death of Alexander, according to the law of
the canon of kings.
Neomenia Hecatombaonis, or the firft day of
the firft attic month Hecatombaon (for Pyanepfion
was the fifth) began the evening next after that
fynod, whofe 15th day, from thence inclufive,
fell either upon the fummer folftice, or imme
diately after it. "The fummer folftitial days in that
age, in the Julian calendar, were June 26, 27.
We are therefore to afcertain the Nudthernerori of
that fynod, whofe evening next after was neareft,
according to mean motion, to June 27, A. aer.
Nabonajf. 465, and in the 2d year of the reign of
Ptolemy Philadelphus. '<-*•¦ :
Now whether, we calculate from the Mojaic
Molad Tohu, or from Rabbi Hillel's (which are 13
decennoval cycles diftant from each other exactly)
the Nudthemeroh of that fynod, which is neareft
to June 27, will be determin'd by the mean
motion

( «3 )
motion (and the aftronomer will confirm it) to
June 19. Therefore,
(1) Neomenia Hecatombaonis began the even
ing of June 19, the next after the fynod, accord
ing to mean motion, by which Ptolemy calculated.
The fame may be faid of the Jewijh month Ta-
muz, and of the Macedonian month Panemus,
in the fame parallel line, in tab. p. 89.
But we are informed by the helleniftical Philo,
a latter Jew, that this law of computation, i. e.
{AiTatrvvofw, holds equally true, K<tTa.Ttva.%iKwm vatv,
throughout the 1 2 fynodical lunations. There
fore, (2) Neomenia Metagitnionis, or the firft day of
the fecond attic month Metagitnion, will fall,
according to mean motion, and the calculation of
Ptolemy, (as we fhall fee in the conclufion) on
July, 18. The fame will hold equally true of the
Jewijh months, and of the Macedonian month
Lous in the fame parallel line.
(3) Neomenia Boedromionis, or the firft day of
the third attic month Boedromion, will fall, by
the fame law, on Auguft 17, and fo will the firft,
day of tbe Jewijh month Eluf, and of the Mace
donian month Gorpiceus, in the fame parallel
line. (4) Neomenia Maimafterionis, or the firft day
of the fourth attic month Maimafterion, will fall*
by the fame rule, on September 1 5 ; and fo alfo
will the firft day of the Jewifh month Tijri, and
of 'the Macedonian month Hyperberetceus, in the
fame parallel line.
-.- L2 (5) Nez

(84)
(5) Neomenia Pydnepfionis, or the firft day of
fifth attic month Pyanepfion, will fall, by the
fame rule, on Oftober 15; and fo likewife, will
the firft day of the Jewijh month Marchejvan,
and of the Macedonian month Dius, in the fame
parallel line.
(6) Neomenia Thoth, or the firft day of the firft
month of the Mgyptian and Chaldaan year, from
the aera of Nabonaffar 466, falls on November 2,
and the 7th of Thoth on November 8. But Sep
tember 8, x Oftober 31=39 — Oftober 15=24.
Therefore^ The 7th of Thoth concurs with the 24th day
of the Jewijh month Marchejvan, of the Mace
donian month Dius, and of the attic month Pya
nepfion. But the Athenians divided their month
of 30 days, into 3 decads, the 3d of which or
10 laft days, they reckoned in a retrograde man
ner, as the Romans did their calends, nones, and
ides. If the month confifted of 29 days only, then
they computed the 9 laft days from 20, in this
manner. ~E.vva.Tw p&tvovTo?, Nona definentis, or 21. Oyfon
qQivovto;, Oftava definentis, or 22. Ep/o^n <p9/ww,
Septima definentis, or 23. E»tm qQiwto;, Sexta
definentis, or 24 ; which is the day that Ptolemy
has given, and calculated in this manner.
From the whole laid together, we may con
clude, that there is more certainty in the compu
tations of the latter Jews, than many have ap
prehended, or will readily believe. We

(«5)
We are as fully certified, for inftance, that Neo
menia Nifan fell on March 20, and on the 6th
Feria,- A. D. 33, as the aftronomer can be by
the tables, that the Moon was firft vifible on that
evening. And Mr. Whifton's calculation of the
true time of that fynod, Mar. 19 d. 13 h. 30 m.
has enabled me to difcover the grounds of this
certainty. Without the affiftance of that calcu
lation indeed, I could not have eftimated the dif
ference between the mean motion and the true ;
notwithftanding this, when the aftronomer cor
rects the mean motion, he does not at the fame
time corredt, much lefs can he be faid to over
throw, or even to weaken, the conclufion of the
Jew. That ftands as it did, upon its own foun
dation. Thofe who made the metonic cycle the regu
lator of our ecclefiaftical lunar year, whoever they
were, they adopted, it is plain, the computation
of the Greeks and of the latter Jews, who ftand
as diftinguifh'd from the Rabbins and Talmudifis
as they do from the ancient Jews. They have
made fome additions indeed, which have ren
der'd the whole of the account very confus'd, and
I may fay, almoft unintelligible. The proof is
obvious and confifts of the particulars enfuing.
(1) The council of Nice was held, A. D. 325.
(2) March 21 was confider'd as the fix'd im
moveable day of the vernal aequinox. (3) March
8 is the day pointed out by the golden number as
the firft of the vernal Moon, which a latter Jew
would call Neomenia Nifan. (4) March 8 be
gins

(86)
gins on March 7, H. 6. P. M. or the evening
next after the fynod. (5) On the evening of
March 8 the Moon is fuppofed to be vifible, ac
cording to the foregoing determination of Philo,-
N^sc/ot, yd.% a,$yiTa.i qaTi^eiv a,i<rdi/nra Qtyyi Xihnvw Haios.
(6) March 21 — March 7=14. Here we have
what Jofephus expvefRy calls TiSffa.^.(rv.arH%wTw ko.to.
ssahiw, i. e. the 14th day of the month accord
ing to the vernal Moon. <
Thus far there is an exadt conformity to the
pradtice of the latter Jews, and to the language
and ftile of Philo and Jojephus ; but if we pro
ceed to examine more nicely thefe pafchal canons,
and the rule to find Eafier for ever, We fhall find
a confiderable deviation from both ; nor has it
been clearly and fully fhewn (as I know of) from
what antient teftimonies and authorities the day
of the full Moon wds made coincident with the
14th day ofthe month, which Eufebius, as well
as Philo and Jojephus, has kept diftinct. But as
thisdifcuffion would lead me into too wide a di
greffion, and anfwer no important end, I fhall
only obferve in general, that this Athenian me-
tonic cycle has deluded the Chriftian church for
14 centuries and upwards; hanging out but a
falfe light at firft, and it has withdrawn even that,
above 1000 years ago. Although, had it riot
been antiquated and ufelefs, its 19 correfponding
numbers, which were formerly wrote in letters
of gold, could have difcharged no other office
than that of directing us to the evening next after
the fynod, throughout the 12 knationsj accord ing

( 87 )
ing to mean motion, and the calculation of the
Greeks. Jojephus, in the whole courfe of his hiftory,
connects the months of the Macedonian year, with
the months of the Jewijh ; and this he does fo
frequently, that it would be almoft endlefs to pro
duce inftances. Now, fhould a queftion arife,
whether we are to compute them as months of
the Macedonian lunar, or of the Macedonio-
Julian folar year, the following citation from
Jojephus, muft, one would be apt to imagine, de
cide it beyond all contradiction.
Ta cfs [Attn tco %a.i4tx&>, o; vtf<ra.v 7ra$ tt/xiv x.a.KeiTO.1, xai T*
iTx; sr/c <*f%i)j Tnr<*a.$iGKtu J^ko.t» -aato. SsAsiw, iv x.$ia> th
Ha/k jt«t9sr«T0{-, cf« ztsss zko.?* ira,°(a. Qo&v zvo[/.i<rs.. Anticj.
1. 3. c. 10. in the month Xanthicus, which we
call Nifan, and is the beginning of the year on
the 14th day of the ift month (according to the
Moon) which when the Sun is in aries, we an
nually kill the paffover, according to the precept
of the law.
Now, as both Xanthicusand Nifan are months,
%a.Ta. 2&a.«jw according to the Moon, how is it pof-
fible that the 14th day of a lunar month, fhould
fall uniformly on the" 14th day of April, in the
Julian calendar ?
Notwithftanding this exprefs declaration and
atteftation of 'Jojephus, fome learned writers have
fuppofed Jojephus to ufe the Macedonio- Julian
months; fo neceffary is it to fee and examine for
ourfelves. The opinion of every learned writer
ought doubtlefs to have its due weight 3 but I fee no

C 88 )
no reafon why, in every cafe, we fhould impli
citly think it to be final and decifive : if, upon ex
amination, it appears to be true, we fhould glad
ly embrace it as a truth ; if a miftake, we fhould
unite our endeavours to correct it.
The following is a table which exhibits to
view the preceding obfervations on Neomenia ; it
includes the forms of years in ufe amongft 7 dif
ferent nations and people, with their refpedtive
aftronomical adjuftments to the cardinal points ;
and it may be of ufe in the reading of Jofephusi
and Greek writers, (after Alexander had com
manded the intercalary month, or Artemifius
<JWsj« to be introduced ;) to thofe, I mean, who
have not adopted an hypothefis, and are refolved
implicitly to adhere to it.
The learned Bifhop Bever ege (Chron. Inftit,
1. 1. ch. 13. p. 170) with great judgment and ac
curacy concludes — Novam quidem hanc menfium
Macedonicorum difpofitionem, inter alios, JoJephusy
antiquitatum judaicarum auftor , Jemper obfervat.
The table annex'd is completed (as we fhall fee
prefently) by an obfervation of Timocharis, rer
corded by Ptolemy in his almegift- by the affif
tance of which, and thofe words of Jojephus,
tv K$in tv Hhm jtaflsraiTo?, the Sun being in aries, the
Jewijh, the Macedonian, the attic lunar ; and alfo
the Nabonaffarean 466, as fix'd and afcertain'd by
* Ptolemy, together with the Julian, are reduc'd
to the Scripture aftronomical, both folar and lu?
nar, year, as ufed and applied after the Exodus,

(»9)

*

End of
the lunar month. 2
Neomania.

The Julian.
folar.

n ^ 2s*s\ <% 0 <i Q js^ -^

The Nabonaffa-
rean folar 466,
5 firft months.

1

The months of
the attic lunar
year.

.3.5 * * « § j h 5 « ™ <
S © w m. S « 2 C C u < s

The months of
the Macedonian
lunar year.

5 S. 5 3. ¦ Jo. 5 * ¦ t- £*

The months of
the Jewijh lunar
year.

1 "''
^ fc § 8 ^ S *£ J& ^ "§ -S

The adjuftment
of the months.

000 00^-000000 W W 11 ¦ 1— 1-1 M

Lunar year af
ter t^he Exodus.

OOOOO-^-OOOOOO v

Solar and lunar
year.

I^JOHffleSgeJlE**^!}*

M>

We

( 90 )
We cannot fufficiently efteem the labours of
Ptolemy. Had C. Ptolemy, the Pelufian, never
wrote, profane chronology muft ftill have lain in
a ftate of confufion and ambiguity, ufelefs and
unintelligible^ Now could we have afcertain'd
the connection of facred chronology with the pro
fane, in one fingle inftance, before the final dif-
folution ofthe Perfian monarchy by Alexander the
Great, in the 4th year of the reign of Darius
Codomannus-, we could only have noted a few
fynchronifms in the Jewijh and Chaldaan hiftory,
and in the times of the Perfian monarchy.
The foregoing obfervations may be thought
perhaps more than fufficient to correcl: the jewijh
notion ofthe Hebrew word Chodejh, and the mif-
tranflation of the Greek term Neomenia.
To proceed, fecondly, to the inveftigation of
the true meaning ojf Chodejh. Whoever is defi
rous to underftand the Mofaic computations, muft
firft endeavour, by diligence* attention, and la
bour, to obtain clear^ diftindt, and determinate
ideas of the Hebrew terms upon which thofe
computations are grounded.
It will be allow'd that every author is, and ne-
ceflarily muft be, the beft interpreter of his own
meaning. And without having recourfe to' the
greciz'd Jews, or the talmudically learned, we
have from the Hebrew bible itfelf, 3 certain rules,
in what determinate fenfe we are to interpret
Chodejh or Chodafhim, either in the lingular or
in the plural number. Rule

(9i )
Rule I.
Whenever an ordinal number, as the 2d, the
7th, the 10th, or the like, goes before Chodejh,
it then denotes one of the twelve months of the
lunar year, and the ordinal number exprefies the
diftance from the cardinal point ; before the Exo
dus, from the autumnal jequinox ; and at and af
ter the Exodus from the vernal.
Example.
Gen. ch. 8. ver. 4. And the ark refied in the
yth month (from the autumnal asquinox) on the
lyth day ofthe month, upon the mountains -of
Ararat. Lev it, ch. 23. ver. 34. Speak unto the chil
dren of Ifrael, faying, the 1 ph day of this yth
month (from the vernal aequinox) Jhall be thefeaft
of tabernacles. Rule II.
, Whenever Chodejh ftands by itfelf abfolutely,
without any ordinal number going before it, or
without either the emphatic or demonftrative
Ha prefix'd ; in this fituation, it conftantly de
notes the beginning of a month, without the ne
ceffity of fpecifying any. Juft in the fame man
ner, as in the Roman ftile, the Calends ftand dif
tinguifhed from the feveral months of the year,
though included in them. M 2 Ex-

(92)
Example.
Numb. ch. 28. ver. 11. And in the begin
nings of your months, (Heb. Berojhei chodjheicem)
ye Jhall offer a burnt offering unto the Lord.
Ver. 14. This is the burnt offering of every
month throughout the year. Heb. Zath gnolath—
Chodejh, bechodjho, lechodjhei hafhanah.
The force of Rule II. is entirely loft here in
the Englifh tranflation : but if we compare the
words ver. 1 1 . with thofe in the latter part of
the 14th verfe, in the Hebrew text together, we
fhall plainly perceive, that Chodejh, ver. 14. abfo-,
lutely put, is fynonymous with Rojh Chodajhim,
ver. 11. And the latter part of the' 14th verfe,
being literally render'd, would run thus. This is
the burnt offering, Chodejh, in the beginning of
your months, Bechodjho, in its month, i. e. in
every fucceffive month, Lechodjhei hafhanah,'
throughout all the months of the year.
1 Sam. ch. 20. ver. 5. And David Jaid unto
Jonathan, behold to-morrow is — Chodefh — the be
ginning of a month, and Ijhould not fail to fit
with the king at meat.—^—
We affuredly know from this text, that David.
fpake thus unto Jonathan, on the 30th day of
fome one month.
The Greek verfion interprets Chodejh in this
palace, by the attic term n^w/*, and the Englifh
tranflation renders it new Moon.
2 K. ch. 4. ver. 23. And he (the hufhand)
faid unto ihe Shunamite his wife, wherefore wilt
thou

(93)
thou go unto the man of God to day? Loa Chodejh,
it is not the beginning of a month, and fo no
feftival. Grec. nso/*«w*, Englifh tranflation new
Moon. Rule III.
When Chodefh occurs with the emphatic Ha
prefix'd, either explicitly or implicitly, with a prae-
pofition which excludes it, (as the initial letter
n Cheth, is indagefhable) and without the ordinal,
it then denotes Rifhon, i. <\ the ift month ofthe
ecclefiaftical lunar year, as it was transfer'd by the
divine authority and command, from libra to
aries, from the autumnal to the vernal sequinox.
Example.
Exod.ch. 12. ver. 2. Ha Chodejh hazzeh, &c.
This month fhall be, &c. — This is the ftandard
emphatic text.
Exod. ch. 12. ver. 5. And it Jhall be, when
the Lord Jhall bring thee into the land of the Ca-
naanites — which he fware unfo thy fathers to give
thee, — that thoujhalt keep this fervice,— Be ha cho
dejh hazzeh, i. e. in this very month, emphati
cally. ,
PJal. 81. ver. 4. Blow up the trumpet Be ha
Chodejh, baccejeh lejom chaggenu.
After this third rule occured to me, had I
been required to tranflate this Hebrew text in
to Greek, without regard to elegance of phrafe,
I fhould, under its direction, have done it in the
following manner.

( 94 )
Pf. 81 . <v.\. "2,a.Kwl<ra,Ti iv ru (imi ffetKniyyi,
Clangite in illo ipjo menfe Buccind,
In numerato (ftatuto) diefefii nofiri.
Blow up the trumpet in the month (Abib)
In the numbred (appointed) day of our feaft.
In the firft month of the alter'd lunar year
(Berifhon) on the 15 th day of the month* (the
numbred (appointed) day of the feaft) on the ift
day of the feaft of unleavened bread, on the felf
fame day it came to pafs, that all the hofts ofthe
Lord went out of the land of Egypt.
Blow up the trumpet in the month (Abib)
on the 15 th day of the month, that memorable,
that illuftrious day, in which,- — ver. y. I eajed
his Jhoulder from the burden, and his hands were
delivered '(by a miraculous paffage through the red
fea, Heb. Tagnabornah) from the Egyptian fer-
vile tafks, faith the Lord.
Exod. ch. 13. ver. 3. And Mofes faid unto
the people, Zacor haijom hazzeh, remember this
day, in which ye came out from Egypt, out ofthe
houfe oj bondage.- — Ver. 4. This day came ye out,
in the month Abib, or of ripening, when the
barley was ripe for the harveft ; whereby Mofes
afcei'tains the vernal aequinoctial feafon, though
not in technical, yet in terms equivalent to
them. It is hardly poflible not to perceive, that this is
a memorial pathetic PJdlm, comprifing a great part

(95)
part of the hiftory and of the chronology of fhe
Exodus. And yet, that helleniftical Alexandrian Jew,
whoever he was, that tranflated the 4th verfe of
this Pfalm into Greek, (though he was able to
write eaamch*;/ with elegance enough) has betray 'd
a great ignorance of the hiftory, and of one of the
moft important and the moft memorable tranfacli-
ons of the God of Ifrael with his people ; and,
through this miftaken tranflation, would for ever
bar up all accefs to the fenfe of a moft incompara
ble and divine Pfalm : Nor is it at all to be won-
der'd at, that the whole body of expofitors, tranf
lators, and critics, who regarded it fo far as to
adhere to it, have, one after another, ftumbled
and fallen.
Pf. 81 . •ver. 4. Greek verfion. Sct\Tia,a.Ti tv Neo/wi£ saXTiyyi
Ec sveypa vy.i§a, sojtjk vpav.
Blow up the trumpet on the ift day of the
month,
In the illuftrious day of our feaft.
Ver. 5. This day ordained he unto Jofeph (and
all Ifrael) for a teftimony, Heb. Betzeetho, & Gr.
Ec Tip i^ihBuv O.VT0V iK yfxr AiyVVTV.
Here the Alexandrian Jew, without attending
to the inconfiftency and direct contradiction to the
hiftory, connects the ift day of the month
(Ivsojw/*) with the day of the Exodus ; whereas
.Mj/w expreffly relates, that it came to pafs on the

(96)
15th, and on the appointed day of the feaft of
unleavened 'bread.
Junius & Tremellius were no mean Hebrai-
cians, yet they found this Hebrew text, a Gor-
dian knot which they could not diflblve. For
having render'd the former part, Clangite in No-
vilunio Buccina, by the mifguidance of the attic
term Nm/khw*, they were not able to proceed^
any farther; but after much hefitation and per
plexity, they at laft hammer'd out this labour'd
paraphrafe, Stativis quibufque feriis, diebus feftis
nofiris, which ^exprefies the fenfe neither of the*
Hebrew nor of the Greek.
Coverdale was bewilder'd in the fame labyrinth,
and inftead of a tranflation, gives us alfo a para
phrafe : " Blow up the trumpet in the new Moon,
even in the appointed time, upon our folemn
feaft day."
Bifhop Patrick feems to have framed both the
argument bf the PJalm, and his paraphrafe of the
4th yerfe, upon the term n««/*«««, in conjunction
with the Hebrew word Shopher, without confi
dering, that David had introduced into the fer
vice of the tabernacle a great variety of mufic
both vocal and inftrumental. There are 3 mufi-
cal inftruments mention'd in the beginning of'
this Pfalm, viz. Toph, Cinnur, and Nebel, be
fore Shopher, , (a trumpet) which is but one out
of four. Here I refer the reader to the comments
themfelves, and the argument of PJal. LXXXf,
which is too prolix to tranfcribe. Bu-

(97)
- Buchanan's poetical verfion is in the whole an
excellent paraphrafe ; but the aeutenefs of his wit
did not preferve him from fplitting againft the
common rock.
If he himfelf drew up and prefix'd the title or
argument, there is this threefold inconfiftency in
the proceeding, i. The title refers the feaft fpo
ken of, ver. 4. to the feaft of tabernacles, which
was always celebrated on the 1 5th day of the 7th
month. 2. The interpretation of the 4th verfe
refers it to the Calends, or the ift day ofthe month.
3 . The fubfequent paraphrafe refers to the fevere
affliction of the JEgyptian bondage, and their
deliverance out of it, which evidently happened
(as we have feen) at the feaft of unleavened bread.
I fhall clofe thefe neceffary remarks with part
of a marginal note in the preface to vol. 3. of
Mr. Shuckford's hiftorical connection, p. 20.
from whence it will farther appear what difficul
ties (occafion'd by the miftranflation into Greek)
have attended all attempts to unfold the fenfe of
the 4th verfe of the 8 ift Pfalm.
Mr. Shuckford had been fhewing from p. 1 6.
(and has clearly fhewn) that to an antient Ifraelite,
Month and Moon had no agreement with each
other, — that in the Hebrew, Jareach or Lebanah
are the words which fignify the Moon, and Cho
dejh is fhe word for month — That in the Hebrew
bible, there is no one text, either in the books of
Mofes, or in any of the books of the old tefta
ment, which can intimate the IJraelites to have
obferv'd the day of the new Moon, in any of
N their

(98)
their feftivals. To illuftrate this, the PJalmifi,
fays he, 'directs to blow up the trumpet, -not as
'we render it in the new Moon, nor as the LXX.
E» nm/w/j, but Ba Chodejh, upon the month day.
Here he fets down the following marginal note.
" The latter part of the verfe is thought by
*' fome writers to intimate fomething contrary to
" what I am offering : blow up the trumpet, fays
" the PJalmifi, on the month day, after which
" follows, Baccejeh lejom chaggenu. The word
" Cejeh, fay they, is derived from the verb Ca-
" Jah to cover, fo that Baccejeh may fignify at
" the covering, or when the Moon is' in con-
" junction with the Stin, covered as it were, fo
" as to give no light. Thus thefe writers think
<{ this verfe to intimate the new Moon to have
^' been a folefhn feftival..
" But I would obferve the expreflion thus taken
c< is fo Angular, unlike any thing to be met with
" in any other place of Scripture, notwithftand-
u ing the frequent mention, of the feftival here
" intended, that I fhould think we cannot fafely
*l build upon it.
• " Others derive the word Cefeh from Cafas, to
^,e number Out ; and accordingly render Baccejeh
ce upon the appointed day ; Dut were this the
" fenfe ofthe place, the word would perhapshave
" been written, not Baccejeh, but Baccefea. See
" Prov. vii. 21.
" The reader may fee what has been offer'd
" upon this text in Scalig. de Emendat. Temp.
" 1. 3. f>. 153. ' Cleric, comment, in he. and will
" after

( 99 )
" after all find the paffage to be obfcure, at moft
" but doubtfully explain'd by thofe who have
" wrote upon it."
I have laid down 3 diftindt rules, all collected
from .the Hebrew bible, for the interpretation of
Chodejh : I have confirm'd the truth and propriety
of each of them by example's. Now Mr. Shuck*
ford has refer'd the former part of the 4th verfe
to rule II, whereas it falls under rule III. For
Ba Chodejh, is Be ha Chodejh, not on the month
day, but in the month Abib, emphatically; and
the latter part of the verfe, Baccejeh lejom chag-
genu, points out the day.
A literal tranflation of thefe Hebrew words into
Englijh would run thus.-^-In the numeration or
in the number of the day of our feaft, viz. of
unleavened bread. In the fame kind of phrafe,
Afiftotle calls time, a^^ov mywriae, the number of
motion, i. e. a motion number'd. So here, in
the numeration, or in the number of the day, is
the fame as .in the number'd or appointed day ;
which intimates too, that they had a regular and
well known calendar.
We wiU now fhew the number of days in a
month, we read, Gen. 29. 14. that Jacob ftay'd
with Laban (Chodejh Jamim) a month of days,
or a whole month J hut we cannot collect from
this text, how many days the Mofaic Chodejh con
tains. We can learn this only from Mojes's ac
count of the flood, Gen. ch. 7. and from hence
learned writers have fo frequently and fo fully
proved it to be a civil or political fyftem of 30
N 2, days,

( 100 )
days, that I might have aflumed it as an acknow-
leged and well known truth, if I had not thought
it proper to obferve (to thofe who may not have
confider'd it) in what a very peculiar and lingular
manner, the author of the Pentateuch explains his
terms, and inftructs his readers.
It would be in vain for the moft cultivated ge
nius to emulate the accuracy, concifenefs, and
judgment of the Mofaic ftile. It demands and it
merits the clofeft attention of our minds. We no
where meet, for inftance, with an exprefs decla
ration, that a month contains 30 days; no, Mo-
Jes interweaves this, and feveral other points, not
neceffary to be mention'd here, into the particji- -
lars of his hiftorical narration, with a judgment
vaftly fuperior to an exprefs declaration, or pre
cife definition, which he altogether avoids.
The waters, fays Mofes, ch. 7. ver. 24. pre
vailed upon the Earth, or continued to rife 1 50
days-, and after the end of the 159 days, the waters
abated. Ch. 8. ver. 4. And the ark refied in the yth
month, on the xyth day of the month, upon the
mountains of Ararat.
Mofes had before related, ch. 7. ver. 1 1 . that
Noah went into the ark, and the flood began on
the 17th day ofthe 2d month ; he here defcribes
the continuation of the rife of the waters, in a
feries of 1 50 expanded days, both as a circum
ftance of the deluge, and as a medium of proof
in the calculation ; and he immediately reduces
thefe 1 50 expanded days to the ftate of a regular calen-

( ioi )
calendar, to give us to underftand that we might
expect one. But inftead of. defining the month,
he gives us both a divifor and a dividend, fo that
we cannot poffibly miftake the quotient : for from
7th m. 17th d. fubftract 2d m. 17th d. the re
mainder fhews that 5 months of the continuation ,
of the deluge were completed on the day before
the ark refted. So that 5 is the divifor, 150 the
dividend, and 3 o (the number of days in a month)
the quotient. 5) *5° (3°- .'
We fhall find, as we proceed, this number 30
claiming a place amongft the 7 radicals, and to be
of eminent and fignal ufe in the integral calculations.
In this hiftorical, and at the fame time, argu
mentative manner, does Mofes inform us by what
kind of month he computes. I might proceed
through the reft ofthe months, but the number
of their days will appear in the confideration of
Shanah, year, whofe form and aftronomical quan
tity we proceed to examine.
I fKall not begin my explication of that moft
diftiriguifh'd term Shanah, by amufing the rea
der with the various hypothefes, and difcordant
opinions, which, from time to time, have been
offered to the public concerning it j every known
form of year, excepting the true one, having
been affigned for it : but fhall endeavour, by gra
dual fteps, to make it appear, that it is applied,
by Mofes in his chronology, to the year of the
Sun, and to the year of the Moon ; and that the
effential diftinction, between thefe two ihcom-
men-

( 102 )
menfurate years, was eftablifh'd by the creator —
in the beginning.
But here it muft be noted, that although the
Moon has a proper orbit of its own, and a pro
per motion in that orbit, to qualify it, Lehair
gnalhaaretz, Gen. j. 15. yet the motions ofthe
Moon were not appointed for, npr have they any
fhare in the menfurations of time ; no, not of its
own year ; no more than the librations of its orb,
in the perimeter of its orbit. The days which
conftitute the quantity of its annual periods (which
are fometimes 354, and fometimes 355, by a
fecret law, not obvious to be underftood and exr
plain'd) are, and neceffarily muft be, meafured
by the diurnal motion : and although the fiated
Jacra of the antient people of God were conr
ilantly obferved on the months and days of the
lunar year; yet were thofe days to be computed,
and their fabbaths celebrated by a divine com
mand, Megnereb gnad Gnereb, from evening to
evening, or from the time of Sun-fetting to the
time of Sunrfetting, as on the aequinodtial day.
The diftindtion of years was primarily confti-
tuted by the diftance of the firft appearance of
the Moon's enlightned orb, from the Mojaic Te
kupha ; which, diftance is technically called the
epadt, and is ftill preferv'd, though not indeed;
immutably, by the original number 15, yet by li
mited variations returning in periodic times.
It may be required of me, perhaps, to fhew
by a particular illuftration, what I would be un
derftood to , mea^, £ By limited variations re
turn-

( io3 )

«c

turning in periodic times." The epadts, it is
well* known, are various and changeable: but
though the fame epadt cannot form the difference
between two fucceffiveyears, yet it has a regular
periodic return. To exemplify this, I have chofe
the firft four years of the world, or the patriarchal
Tefraeteris (which exhibits the moft perfect Sun
and Moon aftronomy) and have, fubjoined a table
of the returns of the fame pofitions — nearly ;
which are characteriz'd by the correfponding years
of the reign of Tiberius Cajar, at the diftance
from each other, of, more than 4000 folar revo
lutions. My choice was directed to thefe latter
(fori Was not confin'd to them) as being the 4
evangelical years, and if extended to the vernal
sequinoX following, they will comprehend the
whole times of the gofpel, from the firft preach!-
ing of John the Baptifi, to the crucifixion of ouir
Saviour.

¦1 3'.'

The> aftroHomical pofitions of the firft 4
lunar years, to the firft 4. folar.

Table III.

-,.$,:) *¦

,

AM.o.

A. Miii.

A. M. 2.

A. M. 3.

A. M. 4. 1

© O
-C.I5

354 O n
339 * z6

©
343 0 22
4<-354<7

0
80.35403 347 c l8

G ©
352 O 14
12C354C ;

A

( i°4 )
A periodic return ofthe fame pofitions — near
ly ; in the 15th, 16th, 17th, and 18th years of
the reign of Tiberius Cafar, reduced to the au
tumnal aequinox ; which is neceffary to be ob
ferv'd; becaufe that which becomes, by this a-
ftronomical reduction, the latter end of the 18th,
is, in the canon of Ptolemy, the beginning ofthe
19th, A. D. 32.. A. J. P. 4745.
Table IV.

14th
year.

15th year

1 6th year.

17th year.

1 8 th year.

O
C15

© ©
354 O 12
339 c 27

342 O 23
3ff354«8

© 7O354O4 346 K 19

-A. ©
351 O 14:
11*354*-

Now I am to prove, that the contents of thefe
two tables reprefent and exprefs the true form of
the Mofaic, which is an exact tranfcripr. of the
celeftial, year ; primarily conftrudted by the creator
of the luminaries, and with divine wifdom adapt
ed both to our civil and religious ufes j as will be
abundantly feen in its full explication.
Thefe pofitions of the lunar years to the folar,
the integral days of the one to the integral days
of the other, and their exact commenfuration to
an indivifible point (ftill inviolably preferving the
aftronomical diftindtion of years) are as much above
the reach of man's invention, as the Sun and the
Moon are above the power of man's formation.
The

( "5>
The double radix or epoch ofthe Moon's year,
and its obvious effects, viz. a twofold computa
tion, from full Moon (o) to full Moon (o),
and from new Moon (c) to new Moon (f),
(the one being the facred and ecclefiaftical, and
the other the civil and hiftorical, year, whilft the
Sun by its diurnal and annual revolutions mea
sures the duration of all things) cannot efcape our
notice, nor fail to engage a fuitable attention.
Has philofophy difcovered it ? Has fcience ever
taught it ?'Can the invented rules of art attain to
it ? Without fome previous knowlege of the ori
ginal characters, and the partition of the aequi
nodtial Nucthemeron into 4 equidiflant quadrants,
a more abftrufe problem, and of more difficult
folution, cannot be readily propofed. It is certain,
that fcience has hitherto declin'd the attempt;
difcouraged, it may be, by the intricate ratio of
the epadts. This feeming intricacy proceeds from
two caufes, viz.
Firft, from the admitting artificial fractions
into the calculus, and from the artificial divifions
of the ecliptic and the aequator. Hence it is infered,
that the Sun meafures by its mean diurnal motion,
59 h. 8 m. fo it does according to the rule of Three
appealed to in this- cafe, upon a miftaken hypo-
thefis, and a falfe foundation. For neither the
book of nature, nor the book of revelation, in-
ftruct us to calculate by fuch inadequate methods.
What was it milled men to cramp the Sun's annual
courfe within fuch unnatural limits, but the an-
O tient

( io6 )
tient imperfect year of 360 days ? Why not di
vide the ecliptic and the aequator into 365 degrees,
and one fourth, (with its due correction) accord
ing to Mofes and nature ?
Secondly, another manifeft caufe of this feem-
ing intricate ratio of the epacts is owing to the
ftated method of calculating fynods^ dichotomies,
and oppofitions. Thefe are conftantly fet down
in our common almanacks, under the title and de
nomination ofthe 4 quarters of the Moon ; and
we are hereby given to underftand, that the aftro
nomers are now able to correct the mean motion,
and to equate the anomalies of the Moon ; an
improvement in fcience, which the Greeks, their
predeceffors in aftronomy, could never arrive to.
Thus appears the depth of fcience in the epheme-
rides, and we cannot but admire the fpec;ulative
theory, without any poffible application either to
civil or religious ufes.
On the contrary, the original pofition and cha
racters authorize me to fay, and enable me to
fhew, that God placed the full Moon and (chaotic)
new Moon, in the central points of two interfedt-
ing circles ; to which centers they annually return,
under the diredtion of proportional laws and deter
minate variations, a table of which will be given.
In fadt therefore we have two models of Sun and
Moon aftronomy, tranfmitted to us ; the one by
Mofes, and the other by the Greeks; and if we trace
them to their refpedtive origins, the one will termi
nate in divine revelation, and the other in an am
biguous

( io7 )
biguous refponfe of the oracle of Delphos, concern
ing which we may fpeak hereafter.
As truth generates truth, and one genuine dif
covery readily opens the way for many more, fo
if we argue (as we ought to do) from the fun
damental principle, — Haju lejhanim — .we cannot
overlook a diftindtion of years ; and where muft
we reafonably fearch for this diftindtion of years,
but in the terms and ftile of facred chronology ?
Mofes introduces and ftates the chronology of
the begnning of the deluge in this peculiar ante
diluvian ftile.
Gen. ch. 7. ver. 11. In the fix hundredth year
©/"Noah'* life, in the 2d month, on the lyth day
of the month, on the fame day, the Jountains of
the great deep were broken up, and the windows
(Gr. cataracts) of Heaven were opened.
It is a circumftance worthy of remark, that
when Mofes has laid down his principles, he never
repeats them; but leaves it to the attention, un-
derftanding, and judgment of the reader, to col
lect, apply, and conclude from them.
Inftead of an open declaration, for inftance,
that he meafures by the folar years, and com
putes by the months and days of the lunar, he
gives us the year of a patriarch to exprefs the
one, and the month and day ofthe month to denote
the other.
Under the guidance of this Mofaic principle,
we fhall prove, that Noah was in the ark part of
two folar, and part of two lunar, years.
O 2. The

( io8 )
The two folar- years are diftingui'fh'd by the
numbers 600 and 601, Gen. ch. 7. ver. 11. and
ch. 8. ver. 13.
The two lunar years are thus pointed out :
Noah went into the ark on the 17th day of the
2d month of that lunar year, which was concur
rent with the folar year of his life 600. And he re
ceived the divine command to come out of the ark,
Gen. ch. 8. ver. 14, 15. On the 27th day of thg
2d month of that lunar year, which was concur
rent with the folar year of his life 601.
It will be granted without any confiderable op
pofition, that here is a high degree of probability,
and that the terms and ftile made ufe of by Mofes
do plainly authorize and juftify the application of
the fundamental principle— Haju lejhanim.
For here is evidently upon this principle, two
folar years, following one another in immediate
fucceffion; and here is as evidently, upon the
fame principle, the 17th day of the 2d month
of one lunar year, and the 27th day of the 2d
month of another lunar year, following likewife
in immediate fucceffion ; but the principal point,
of all, and which may be called conclufive, de
pends 'entirely upon the proof of that part of Prop,
IV. which fets forth,
That in the year of Noah 600, in which. the
deluge began and ended, there was a coincidence
of the lunar year with the folar ; and that the
epadt, in the conclufion of the year was 11, and
is fairly deducible from the Mojaic account.

( I09 )
I am therefore to prove, not only that Mojes
meafures the ages of the patriarchs by the years
of the Sun, and computes by the months and
days of the years ofthe Moon ; but more particu
larly, that he has clearly afcertain'd in his hiftori
cal narration the aftronomy of the deluge, and
with great accuracy and exaetnefs determin'd the
very pofition of the lunar year to the folar, which
muft neceffarily be known from the epadt.
If I do not make this appear in a clear, full, and
fatisfadtory manner, all that may be advanced be
fide in this fcheme will be of little or no avail.
And the tables I. II. given above, muft be
faid to owe their origin and exiftence in a great
meafure to the uncertainty of hypothefis.
There needs no additional proof to what has
been already offer'd, that the Mofaic computa
tions and chronology commence at the autumnal
aequinox : and both the primitive folar and lunar
year had but one and the fame cardinal point,
from the creation to the Exodus ; when an alte
ration was made, in the beginning of the ecclefi
aftical and hiftorical, the facred and civil, lunar
year, by the interpofition and authority of the di
vine legiflator : Exod. 12. i, 2. But the begin
ning of the measuring folar, and the aftronomy
of the lunar, year, continued in their original ftate j
as will be prov'd in its place.
I fay then, that the year of Noah's life 600
begins and ends with the Sun's ingrefs to libra,
and runs parallel with its correfponding folar re
volution, A. M. 1656.
' T . The

( no)
The firft .period of the Mofaic account extends
from the beginning of the civil and hiftorical lunar
year (calculated from new Moon (t) to new
Moon (c) ) to the beginning of the flood; and
includes the fpace of 46 days, equal to one thirty-,
day month, and 16 days over, exclufive of the
17th day. of the 2d month, in which Noah en-
fer'd into the ark. p. 124T5, table.
II. Ch. 7. ver. 4. I will caufe it to rain upon
the Earth 40 days and 40 nights.
Ver. 12. And the rain was upon the Earth 140
days and 40 nights.
Ch.' 8. ver. 2. And the rain from Heaven was
refrained. •*
Ch. 7. ver. 24. And the waters prevailed upon
the Earth 150 days. \
The impetuous violence of the falling rains, for
40 Nucthemerons inclufive, together with the
breaking up of the fountains of (Tehom) the
great deep, foon caufed the ark to be lifted up
above the Earth, (ver. 17.) and to float upon the
furface of the waters; (ver. 18.) which prevail
ed, fays .Mofes, meod meod, in an exceflive degree,
until all the high hills which were under the whole
Heaven were covered.
Ver. 20. Fifteen cubits upwards did the waters
prevail, or were kept in a rifing ftate,; Vaijecuffu,
haherim, when or after the mountains were co^
vered. Poftquam operti fuerunt monies illi Jun,
£? Tremell. This

( III )
This 2d period of 150 days is divided into two
parts, and has, agreeably thereto, two diftindt
terminations. ,
1. The uninterrupted 40 days rain; which,
being added to the foregoing 46, make 86 ; fo
that the rain from Heaven was reftrained, on the
26th day of the 3d equalmonth ofthe lunar year,
in a continued reckoning from the beginning of it.
p. 124-5, table.
2. The 1 10 days rifing of the waters, after the
ceafing of the rains ; for the 40 days rain are in
cluded in the 1 50, (ch. 7. ver, 24.) and muft be
fubftradted from them. Thefe no days, being
added to the foregoing 86, make 196 ; confe-
quently the waters were abated, (ch. 8. ver. 3.)
or ceafed to rife any higher on the 16th day ofthe
7th equal month of the lunar year, exclufive of
the day on which the ark refted, which was the
17th ofthe fame month. Ch. 8. ver. 4. p. 124-5,
table. III. Ch. 8. ver. 5. And the waters decreafed
continually until the 10th month: in the 10th
month, on the ifiday ofthe month, were the tops of
the mountains feen.
This 3d period of the Mofaic account fupplies us
with 74 days, towards the completion of the lu
nar year, and leads us forward from the 1 6th day
of the 7th to the 30th, or laft day of the 9th
equal

( H2 )
equal month. For 74 4. 1 96=^70; and 9+30
=270. p. 124-5, taDle: V
IV. Ch. 8. ver. 6. And it came to pafs at the
end of 40 days, that Noah opened the^ window of
the ark which he had made.
: Ver. 7. And he fent forth a raven which went
fprth to and fro, until the waters were dried up
from off the Earth.
In this 4th period of his narration Mofes changes
his ftile, from the chronological to the hiftorical;
perhaps, to notify to us the difference ; for they*
each of them occur in the Scriptures ; or perhaps^
to avoid the frequent needlefs repetition of the
month and day of the month.
We have gained from this period 40 days more
towards the completion of the lunar year ; thefe
being added to 270, make 310 days ; and they
terminate on the 1 oth day of- the 1 1 th equal
month ; Mofes therefore fent out the raven on the
1 ith day of the nth month.
V. Ch. 8. ver. 8. Alfo he fent forth a dove
from him, to fee if the waters were abated from off
the face of the ground.
Ver. 9. But the dove found no reft for the file
of her foot, andjhe returned unto him into the ark:
for the waters were on the face ofthe whole Earth t
Then he put forth his hand and took her, and pulled
her in unto him into the ark. Ver.

( "3 )"
Ver., io. And he ftayed yet other 7 days, and
again he fent forth the dove out of the ark.
Ver. 1 1 . And the dove came in to him in the
evening, and, lo ! in her mouth was an olive- leaf
pluck' d off: fo Noah knew that the waters were
abated from off' the Earth.
Ver. 12. And he ft ay' d yet other 7 days, and
fent forth the dove ; which returned not again to
him any more.
It is evident from thefe words, in the begin
ning ofthe 10th verfe — he flay' d yet other 7 days
- — that Noah waited a whole week, i. e. . from the
1 1 th day of the 1 1 th month inclufive, to the 1 7th
day of the fame month inclufive, for the return
of the raven ; but being difappointed in his ex
pectations, for the raven went forth to and fro,
until the waters were dried up from off the Earth
ver. 6. he fent out the dove the firft time, on the
1 8th day of the 1 ith month ; which, finding no
reft for the Joh of her foot, returned to him into
the ark, on the fame 18 th day.
Another week being ended, immediately fol
lowing that in which he waited for the return of
the raven— for hefiay'dyet, other 7 days, fays the
text, ver. 10. he fent out the dove the 2d time^
on the 25th day of the nth month. For 18+
7=25, and 25 — ii=:i4=;7+7.
On the evening of the 25th day of the nth
month, the dove came unto him, and lo I in her
mouth an olive-leaf pluck' d off. And he fiay'd
yet other 7 days, and fent out. the dove the 3d
P and

(n4)
and laft time (for fhe returned not again unto him
any more) on the 2d day of the 12th month.
For 254-7=32 — 30=2.
We have now collected 1 1 equal months, and
2 days over, which amount in the whole to 33a
days, and the laft period of the account is clearly
Connected with the firft, and that with the be
ginning of the year ; but of what year, is a pro
blem, which has never yet received (fince the
knowlege' of it has been loft) a fatisfactory folu-
tion. Mofes having brought us regularly down to the
2d day of, the 12th month, we are prefently per-
plex'd with a feeming interruption of the calen
dar ; and in this feeming interruption lies all the
fuppofed difficulty : and it muft be acknowleg'd,
that this difficulty would have become infupera-
ble, if Mojes had not continued his narration to
the 27th day of the 2d month, (Gen. ch. 8. ver.
14.) ofthe next fucceffive lunar year ; and as Noah
went into the ark on the 17th day of the 2d
month of the lunar year, immediately preceding ;
had he been order'd to come out either one day
fooner, or one day later, than is related by Mo
jes ; this difference of only one day, (fuch was
the then pofition of the Sun and Moon in the Hea
vens) would have proved an effectual bar to our
difcovery of the epadt, and together with it, of
the aftronomy of the year.
Before I apply my felf to confider the remaining
periods of the hiftory and chronology, we may
remember, that the laft particular, mention'd by
Mofes,

("*)
Mofes, was Noah's fending out the dove, on the
2d day of the 12th month, with this remark fub-
joined, viz. which returned not again to him any
more. But do not thefe words imply Noah's ex
pectations of its return ? Here a nice and material
queftion occurs, viz. Can we determine without
any hypothefis, or arbitrary affumption, how ma
ny days precifely Noah waited for the return ofthe
dove, after he had fent it out the 3d time ? For
in the anfwer to this queftion, we fhall meet with
the folution of the problem. Now, I fay, if we
fteadily adhere to the principles laid down, the
queftion may be eafily anfwer'd, and the pro
blem asreadily folv'd. The principles laid down
were, that Mofes meafures by the year of the Sun,
which is of 365 day9 4- -4 ; and computes by the
months and days of the year ofthe Moon,, which
is of 3 54 or 355 days.. But here the Mofaic nar
ration opportunely fteps in to our aid, and deter
mines the quantity of the then current lunar year,
and confequently, the precife number of days
Noah waited for the return of the dove, fent out
the laft time ; as I fhall make evident to the rea
der, if he will take along with him the following
Axioms. . Axiom I.
When the lunar year is connected with the fo
lar, and carried along together with it, by a true
aftronomical computation, amidft the various
< pofitions of the Moon to the Sun at the autumnal
JequinoX; it muft needs happen fometimes, that
P 2 the

( ii6)
the laft day of the lunar year will fall on the laft
day of the folar. This for want of a more proper
term, I beg to call a commenfuration ; i. e. end
ing together. When this happens, then of courfe
the ift day of the following lunar year will fall
upon the ift day of the folar. This I call a co
incidence of the lunar year with the folar, /. e. a
beginning together. Axiom II.
Whenever there happens a co- incidence of the (
lunar year with the folar, and the quantity ofthe
current lunar year is given, the epadt at the end of
the year is alfo given. For 365—3 54= 1 1 . and
365— 355=IG-
On the contrary, if the given epadt be either
1 1 or 10, we may with certainty infer a co- inci
dence, and the quantity of the lunar year. For
365—11=354, and 365—10=355.
Axiom III.
The epadt can never enter within the cardinal
limits of that folar year, with which the current
lunar year is connected ; but, being added to the
conclufion of the preceding lunar year, meafures
aftronomically the diftance from thence to the be
ginning of the fubfequent folar.
Axiom IV.
As Mofes 'ftates the chronology of the deluge, in
fuch an authoritative ftile, we muft conclude from
thence, that thofe, to whom he primarily wrote; were

( "7 )
were well acquainted with the aftronomical ca
lendar, and fix'd laws of computation ; and, that
they ftood not in need of precife definitions, and
more particular explications. And,
If we will carry along with us the principles of
the Pentateuch, and argue and conclude from
them, we can no more miftake the diflinftion of
years than they could, nor the curious laws of their
connection. And as we live in the aftronomical
age, we cannot be fuppofed to be ignorant, that
the folar year contains at leaft 365 days, and the
lunar year 354 and 355. By the affiftance of
this fmall degree of previous knowlege, we fhall
foon be convinced, that Mofes has not left the
calendar of the year of the deluge, in the ftate and
condition of an imperfect fragment, but, on the
contrary, that any additional circumftance would
have been needlefs and fuperfluous.
Thus much may fuffice as preparatory to the fo-
lution of the queftion, viz. How many days pre-
cifely Noah waited for the dove, fent out the 3d
time? We are certified from the accounts of Mofes,
that the whole fpace of Noah's abode in the ark
is bounded by the 17th day of the 2d month of
one year, and by the 27th day of the 2d month
of the next year following ; and as 1 m. 1 6 d.
(p. 1 24- 5, table) were lapfed before the entrance, fo
1 m. 27 d. were reckoned before he received the
command to go out. We have then 30+16
days on the one fide, and 30 4- 27 days on the
other : throw off the 30 on both fides, and
there

< n8 )
there will remain, 1 6 days and 27 days j but 2 7 —
16=11. Now, I fay, that this differential number n,
(though we fhall fhew a more proper deduction of
it hereafter) cannot be proved to be the true aftro-
Jiomical epadt, upon any other terms and condi
tions, than that of Noah's continuing in the ark
365 days, or a complete folar year, neither one
day more, nor one day lefs ; including the day
he went in, and the day he was commanded to
go out.
From 354fubftradt 46, (the number of days
which preceded the flood) (p. 124-5, table) remains
308. But 308457=365, and, 365—11=354,
the quantity (as may be proved) of the current lu
nar year.
Though the foregoing deduction of the epadt
1 1 is true, yet I am obliged to take notke that it
is not accurately made in all its circumftances : and
I fhall take occafion not only to enlarge, but to
fet it in a different light ; my chief defign at pre
fent being only to fhew, that fince the epadt was
1 1, (and it will clearly appear that this was the
epadt at the end of the year of Noah's life 600)
we may with certainty infer (by Axiom II.) the
co-incidence of the luminaries, and the quantity
of that lunar year, by the months and days of
which Mofes has hitherto computed.
From thefe premifes we are inftrudted to give a
determinate anfwer to the queftion propofed in
the following manner : Noah fent out the' raven
on the 1 ith day of the 1 ith month, each contain ing

( JI9 )
ing 30 days ; 3 10 days Were therefore completed
in a continued reckoning from the beginning of
the year, or the autumnal aequinodtial new Moon
evening. The complement of the year is 44 days ;
for 3 54 — 310=44. Thefe 44 days are divided
by the narration into two equal partitions ; for
332—310=22, and 354 — 332=22. Confe-
quently, as 22 d. or 3 weeks and 1 day, exadtly
meafure the diftance from the nth day of the
1 ith month, to the 2d day of the 12th; on the
former of which, Noah fent out the raven, and
and on the latter the dove, the 3d and laft time;
fo likewife, 22 d. or 3 weeks and 1 day exactly
meafure the diftance from the 2d day of the 12th
month (exclufive) to the end of the current lunar
year, or the autumnal aequinodtial new Moon
evening. But the dove returning not on that day,
Noah gave over all farther expectations, and Mo
fes thus proceeds in his narration.
VI. Gen. eh. 8. ver. 13. And it came topajs,
in the fix hundreth and firft year, in the firft month,
the firft day of the month, the waters were dried up
from off the Earth : and Noah removed the cover
ing of the ark, and looked, and behold, the face of
the ground was dry.
Mofes, in the unalterable ftile of his chronology,
firft gives us the age of a patriarch to direct us
to the year of the Sun ; and then the month and
day of the month, to direct us to the year of the
Moon.
He

( 120 )
He that reads this important text in the original
Hebrew will foon perceive it to be a key of fo-
lution *• and at leaft a ftrong confirmation, if not
an undeniable proof, that I have lightly interpre
ted and properly applied that original divine law,'
let them be for years.
When Mofes has occafion to defcribe any inter
mediate month, he conftantly introduces an ordi
nal number to determine its fituation in the ca
lendar, and then fpecifies the day. E. g.
In the id month, the lyth day ofthe month —
in the 10th month, on the ift day oj the month.
But when one lunar year had finifhed its revo
lution, and he was going to adjuft his chronology
to the beginning of another, we find a remarkable
variation in his ftile, which neither the Greek ver
fion, nor the Englijh tranflation convey to us.
Gr. Tu 'TTfaTX, iVTTfUTlf T* [AyiVOf.
Englifh tranflation, " In the ift month, on the
i ft day ofthe month."
In thefe verfions, jointly confider'd, there is no
vifible difference between this and his ufual me
thod of determining any of the intermediate
months, whilft in the Hebrew text, there is an
evident diftindtion, and a very material peculia
rity. For inftead of faying, as in other inftances,
Be echad, Be echad le Chodejh— there is fubftituted
in the room of the ordinal number, Echad, the'
appropriated term Rijhon, and he writes thus, Be
ha Rijhon, Be echad le Chodejh.
Berijhon differs little more than in termination
from the firft word ofthe Pentateuch, Berejhith. And

( at )
And as that is rightly interpreted by St. Baftl^
E» a.?xv 7v *<*T* ™ x?ovov — hi the beginning of time ;
fo this latter may with equal propriety be inter
preted — 'Ee «f ¦%» Tf KaTa. tov ina.uTov, in (he head or
beginning of the lunar year. And in truth, if
we rightly weigh and take a more clofe view of
this Mojaic term Rijhon, we fhall find it to vary
more in Jound than in fenfe, from the Jewijh Rojh
hafhanah. .
We fhall have occafion to fpeak again of Rijhon,
when we come to treat of the change of the be
ginning of the lunar year, and of its being tranf-
fer'd from one cardinal point to another.
When we read thefe words, Be ha Rijhon, Be
echad le ChodeJh? can we only confider them as
the language of one tranfmitting to future ages, a
traditional objervation, (" The beft they were able
,c to make,") of the Moon's vifibility ?
I muft not omit to obferve in this place, that
when Mofes is fetling the chronology of the be
ginning of the deluge, he expreffes himfelf thus,
viz. In the fix hundredth year of Noah'5 life. —
But when that lunar year was ended, which was
concurrent with the folar year of Noah's life 600,
and he is going to calculate the beginning of the
next, or of that lunar year which was connected
with the next fucceeding folar year 601, (whofe
epadt, "or limited number of days of its ift month,
fell within the cardinal limits of the year 600)
he only fays — in the fix hundredth and firft year —
and drops the following words — of Noah's life.
a. 1

( 122 )
I know it may be eafily faid, that this is only
an ellipfis, which is frequently left to befupplied
by the underftanding of the reader. But I here
beg leave to reply, that had Mofes explicitly wrote,
in the fix hundredth and firft year of Noah's life,
thefe additional words would have created great
difficulties in his chronology. For the folar year
bf Noah's life 60 1 is bounded on both fides by
the cardinal points, and Noah could not be faid
to have enter 'd into it, in any confifte'ney with
Mofes 's aftronomical law of reduction, before all
fhe days of the epadt, which come before the
aequinox, 'had been meafured.
But here it may be urg'd perhaps, by way of
objection, that this only changes one difficulty
for another. For is it not equally improper and
inconfiftent tomentibn the fix hundredth and firft
year, before it commenced ; as the fix hundredth
and firft year of NoahV life, before he had en
ter 'd upon it.
But in anfwer to this, I beg the favour of the
reader to return back to table. III. and p. 163. A.
M. 3. where he may perceive the new MoOn
epadt to be 7 ; but although the 7 days of this
epadt are comprehended within the extreme points.
of A. M. 2. yet are they evidently a part of that
lunar year, 347 days of which fall within the li
mits of. A. M. 3. which is the folar year next fol
lowing, and parallel with the 3d year of Addm%
life. Now if any event had fallen in the beginning
bfthis lunar year of fufficient importance to have had

( 133 )
had its chronology fix'd by the pen of Mofes, he
would not have wrote— in the 3d year of Adam's
life, but thus---in the 3d year, in the ift month;
on the ift day of the month. — And we fhould
have been certified by this form of expreffion,
that 'that lunar year which was concurrent with
A. M. 2.' was ended ; and that he was now cal
culating the beginning of another, or of that lunar
year which was connected with A.M. 3. or the
next folar year in immediate fucceffion.
From hence we learn, that every folar year is to
be looked upon in two different views. (1) As
meafuring the correfpondiog year of the life of a
Patriarch. (2) As following another in imme
diate fucceffion, without confidering t it as fuch a
meafure. It is all one in point of chronology, if we fub-
ftitute the year of the world 1657, inftead ofthe
year 6,91. Mofes^iym us the latter to inform us
of his aftronomical law of reduction ; and to let
us know, that his tables are founded upon thefe
two laws, viz.
I. That the years ofthe Patriarchs run paral?
lei with the years of the world.
JI. That every current year is the true folar.
The above obfervation, I apprehend, is no
trivial criticifrh, or fpeculative refinement, but
a necefjary diftindtion which requires, our atten
tion.
!QU vii;

( 1*4 )
VII. Gen. ch. 8. ver. 14, 15, 16. In the id
month, the 2yth day ofthe month,— God fpake un
to Noah Jaying*, go forth ofthe ark.'  •
, I fhall only make this one fhort remark upon
this laft period, viz. Mofes here clofes the hifto
ry of the deluge, its chronology, and its aftrono
my ; which he has left in fuch a ftate of perfec
tion, that no theories, tables, or calculations ;
that neithef the depths of fcience, nor the moft
elaborate rules of art, can make any improvements
upon it. This is much to fay, but it is much
more to prove it.
I fhall nowdigeft into order, and fet in one en
tire view, all the particulars of Mofes 's narration,
which we have hitherto been examining,
The folar year of Noah'.r life> 6oq.
M. D. months and days of the lunar year.
M. D. Gen. ch. 7.
** r t « ¦
-oV- °
¦§sll. 16 46 days before the flood.
£ CH. 17 Ver. 11. Noah enters the ark.
a- III. 26 40 ver. .i;2. Rains ceafe.
jj j VII. 16 no -The Waters continue rifing
' 404^110=150 days.
VII, 17 Gen, ch'. d; ver.^ The ark refts,
;; ." III.

IV.

( i25 )
M. D.
196 Brought over.
(IX. 30 74 The waters decreafe.
III. s X. 1 Ch. 8. v. 5. The tops of the moun-
( tains feen.
rXI. 10 40 Noah waits before he fent the
the raven.
XI. n 1 ver. 7. The raven fent out.
XI. 17 Noah waits' for the return of the
raven.
XI. 1 8 7 The dove fent out the firft time.
XI. 25 7 ver. 10. The fecond time.
XIJ. 2 7 ver. 12. The third and laft
V * time,
SumTot.332. •*

7%e folar year of Noah'j life, 601
M. D. months and days of the lunar year.
M. D. Gen.ch.S.
I. 30 ver. 13.
II. 27 ver. 14.

Sum Tot. $y.

We have here the collected number of 332
days, under the year of Noah's life 600, and of
57.

( i^6)
^y days, under the year of < Noah's lifer 60 1.
Should it be afk'd in what manner we are to rea
fon upon them, how we are to apply them, and'
.what to, conclude from them, my answer is, that
it has been already determin'd upon the principles
-of the Pentateuch, that they are the months and
days of two diftindt lunar years ; and that Mofes
meafures by the folar, and inftructs us rightly to
compute by the lunar, year.
Was it poffible, upon this occafion, /to call in
and confult an antient Greek, a J?w, and a Turk,
all acquainted, in their way, with the lunar com
putation ; as foon as they fhould be inform 'd, that
a certain event was hiftorjcally related to have
come to pafs on the 332ddayof a lunar year,
they would, without hefitation, affign for it,s
complement 22 days, the fpace which Noah
waited for the return of the dove, fent out the
third and laft, time. But the Turk would endea
vour toknow, whether it was of 354 or of 3 55
days ; if the former, he would fay, 22 days muft
be added ; if the latter, 23 ; whilft the Athmian
and the, Jew would be filent in this particular.
They would be equally furpriz'd, that the 3 3 2d
day of a lunar year fhould be calculated to- be the
2d day of the 12th month, and, would jointly
infift upon it, that it muft neceffarily be the. 7th,
becaufe 7422=29. They would unanimoufly
agree, that Mofes was certainly no aftronomer,
becaufe he had betray'd fuch a grofs and total ig;
ndjance of the menftrual revolutions of the Moon,,
v and

( I27 )
'arid was an entire ftranger to Its periods and
fynods. From thefe 332 days, and their complement
22, as Mofes has brought down the account to the
2d day of the 12th month, we are clearly and
fully inform'd, not only ofthe number of the days
in a month, but alfo in what manner the Antedi
luvians computed and adjufted the months of the
lunar year. For,
M. D. D. D.
To 1 1 + 2. and to, 330 4- 2. and to, 332.
Add 22. 22. 22.

Wehave,n424. 330+24. 354-
From thefe feveral refults, We affuredly know,
that the patriarchal lunar year, digefted into a ca
lendar, was compounded of 1 1 thirty-day months,
whilft the 1 2th confifted of 24 days, and fome
times of 25. For 354— 330=24, and 355—
330=25. It is matter of fome furprize, how it came to
pafs, that all, who have hitherto made the enqui
ry, fhould agree in concluding, that Mojes has
left the calendar of the deluge in a precarious,
uncertain, and imperfect ftate. Should the rea
fon be nicely examined into, it might be alledg'd,
perhaps, that it is owing to this, viz. becaufe
Mofes has not exprefly related, that Noah fent
out the dove, the 3d and laft time, at the di
ftance of 22 days precifelyj from the autumnal aequi-

( 128 )
Kquinoctial Moon's vifibility. But fhould this
be alleged as the ground of the uncertainty, muft
it not be immediately removed, as foon as we"
come to confider that Mofes primarily addrefs'd
his chronology to thofe who were well vers'd in
the aftronomical calendar, and habitually exer-
cis'd in the ftated laws and rules of its calcula
tions ?
Suppofe fome Englifh hiftorian had related a
very memorable event to have happen'd, A. D.
1656. Feb. 2d, would the Englifh reader, who
was familiariz'd to the Julian calendar, and con
ftantly reckon'd the times by its months and
days, have ftood in need of fuch a minute expli
cit remark as this, viz.
N. B. February is the 2d month in the Julian
calendar, and in every common year has 28 days,
but in a biffextile, or at the end of every 4th year
of 366 days, it has 29.
Would not the Englifh reader, I fay, have
looked upon fuch an explicit remark as this, ra
ther as an affront to his underftanding, than a ne
ceffary information, and have thought the hifto
rian an injudicious and circumftantial trifler ?
It may not be alio w'd as yet perhaps, that thefe
are parallel cafes, but the farther we proceed the
more we fhall be convinc'd that they are.
We may reafonably imagine, that much of the
primitive knowlege, and many antient traditional
dogmata, fubfifted amongft the Hebrews and the If.

( J29 )
¦IJraetites, in the times when Mojes wrote ; which
are entirely loft to -us. And confequently, we
have no other light to guide our fteps, and direct
our purfuits after original truths, but the princi
ples, data, and terms, &c which are recorded
in the Pentateuch. And indeed, if we rightly
eftimate their number and their value, we have no
great caufe to complain. r
But here perhaps an opponent may arife, and
zealoufly allege againft all that has been offer'd
in fupport of a diftindtion of years, the contrary
Jentiment of archbifhop UJher. And it is poflible
that fuch an opponent might argue thus.
Have we not equal reafon from Mofes' s account
to complete thefe 332 days into a folar year, (as
the judgment ofthe learned archbifhop of Armagh
led him to conclude) as into a lunar year ?
To which I would reply,
Have we not equal reafon from Mofes 's account
to complete them into a lunar year, as into a
folar ?
He would appeal to the authority of the arch
bifhop, and I would appeal to Mofes's funda
mental principle — Haju Jejhanim— Let them be
for years.
Will any one engage to prove, that I have
mifinterpreted the , Hebrew text, and mifapplied
the principle ? If not,— -then where fhall we find
an arbitrator ?, And who will undertake to mode
rate the difpute, between the authority of arch
bifhop TJfhery and the writer of the Pentateuch ?
.{ R But

( 13° )
But in order to fhew a due deference and re
gard to the decifion and judgment of the truly
great and learned Primate, I will refolve thefe 332
days into their equal months-, and digeft them
into two diftindt columns,' and then we fhall fee
what advantage a defender .of the folar hypothefis
will be able to gain.

The months and days df

The months and days of

the folar year.

the lunar year.

I. 30 30

I. 30 30 ¦•"-'<»•*"&

II. 30 60

II. 30 60

III. 30 / 90

III. 30 90

IV. 30 120

IV. 30 120

V. 30 150

V. 30 150

VL 30 180

VI. 30 180

VII. 30 210

VII. 30 Y210

VIII. 30 240

VIII. 30 240

IX. 30 270

IX. 30 270

X. 30 300

X. 30 300

XI. 30 330

XI. 30 330

XII. 2 332
* *

XII. 2 332
* *

Upon the firft view of this diftribution of the
months it might be fairly faid, is it not evident to
fenfe, that 3 3 days (according to the prelate's deter
mination) are the complement of the folar year ?
True: but is it not as evident to fenfe, that
22 days (according to a contrary determination)
are alfo the complement of the lunar year ? We

are

( I3i )
are ftill therefore lipon an equality, nor is there
any advantage gained.
Had this been a real and not an imaginary
confeft, it muft, I think, have been entertaining,
and perhaps, furprifing to thofe who could not
fee as yet beyond the veil.
But to put a flop to unneceffary amufements,
I will be bold to fay, -it is impoffible for the moft
fubtile, aiid the acuteft reafoner, by any^ methods
of arguing, to fuperfedethe certainty of that fun
damental principle of the Pentateuch, (by whofe
fole influence, as by a faithful polar ftar, I have
all along directed my courfe) and that, for this
fpecial reafon, becaufe this equal diftribution of
months and days has a real foundation in nature ;
it is the immediate refult of a true aftronomical co
incidence of the lunar year with the folar, at the
time of the deluge. By virtue of this co-incidence;,
the months and days of the folar year (by which
Mofes only meafures, but never computes) lie con
cealed- under the months and days of the lunar:
and as the months contain 3 o days refpectively,
they muft needs be exactly commenfurate to each
other. This is called by the mathematicians
Epharmofis or adaptation, and we may fee it exem
plified in the 4th Prop, of Eucl. elements.
Hence it comes to pafs, and we cannot fuffi-
ciently admire it, that the "1 ft day of the ift month
of the lunar year was alfo the ift day of the ift
month of the folar.
And the 17th day of the 2d month of the lu
nar year, (by which Mojes computes Noah's en-
R 2 trance

( 132 )
trance1 into the ark) was alfo the 17th day of the
2d month of the folar. To pafs by the interme
diate co-incidencies, I fhall only add, that,
The 2d day of the 1 2th month of the lunar
year (on which/ as Mofes relates,, Noah fent out
the dove, the^dand laft time) was alfo the 2d
day ofthe 12th month of the folar.
' Now we' begin to draw near to a point; the
fcene is opening, and that feemingly inacceffible
truth (qua a Jeculis in puteo latuit) is ready to
difplay itfelf, by a moft eafy and obvious calcu
lation. For as 33 days are the complement of
the folar year, and 22 of the lunar; thefe com-
plemental days ; (by means of the co-incidence,
which will be demonftrated, to be true) muft ne
ceffarily include the true aftronomical epadt^ and
it is the difference ofthe two additional numbers;
fo that the whole calculus is no more than fimple
fubftraction, viz. 33 — 22=11. the epadt.
* We may properly; enlarge it thus, 332433=
365, and 332422=354. And 365-354=11.
the epadt as before.
- Let it be carefully noted, that this laft calcula
tion, eafy and fimple as it is, not only gives the
epadt, but places it in its true natural fituation,
at the end of the year of Noah's life 6od.
Again, 365— 1 1=354— 354=0. the index of
commenfuration. If thefe things are fo ; then furely it may be
faid, that thofe reafonings and decifions (afcribe
them to whom you will) muft be thought Jome-
what deficient ; which overlooking the lunar year, en-

( !33 I
entirely loft the, lunar epadt, and, hr fure confe
quence of that, the aftronomy of the. Pentateuch.
The following fentiment and refolution is as
juftifiable in chronology, as in natural philo
fophy. i . . .- . , /'.'•'' '" , ' i --
Nullius addiftus, Jurare in verba Magifiri.
The precife number of days which Noah ftay'd
in the ark, are the? moft important circumftance
of the chronology of the deluge, and the cer
tainty of the deduction entirely' depends upon
them. Longinus thought fit to characterize the Jewijh
legiflator with this tit\e-—,>sTuyiiwAn?,-;:a no or
dinary man; and cites thefe words of -the Penta
teuch ,ytvto-Qa <?*>; it, iyivw, to illuftrate the true fub-
lime; and yet Mofes, ^without any ftudied or
naments of fpeech, or affectation of language, jn
the moft natural, fimplicity of a: plain hifiorical
narration, tranfrnks to thefe latter times, I will
add, to the moft remote and diftant ages to come,
not only the uniform, beautiful, . and moft admi
rable contexture, but alfo the. moft exact aftrono
my of the antediluvian calendar; and patriarchal
year. Nay, he with the fame unaffected fimplw
city records the laws of calculation in his prin
ciples, data and terms.
For my own part, when I reads and confider
the fecrets and the wonders of ,th^, narration, it
feems to me impoffible for any one, except the
epicurean deift, to doubt of the divine fuperin-
tendence

( '34 )
tehdence with refpect to Mofes ; and a provi
dential predetermination with refpedt :to Noah.
Had Noah abode in the ark one day more, or
one day lefs, than as the time now ftands- punctu
ally limited, we could not have recovered from
the hiftory of the deluge the original celeftial
year. - - '¦¦'¦¦ .'--.*,.•. .
. How far we may be able to philosophize upon
Noah's flood, as to its natural caufes, and its na
tural effects, I do not know ; I can only tell^ that
from Mofes's account, we have a plenteous promp-
tuary and fund of ufeful knowlege and inftruC-
tions. ¦'
If we will be at the pains to examine in what
manner archbifhop UJher reckoned the time of
Noah's continuance in the-ark, We fhall foon per*
ceive, that his miftake is not entirely owing to
the error of a principle, as to a partial confide
ration. The following- extract from his Chronologic
Jacra, (ch. 3 . p. 1 6 . ) will evidence his hypothefis,
and the ground of the miftake.
" Illud igitur immotum maneat, quod fpiritu
" Janfto tam luculenter hdbemus expreffum, Anno
"600, Vita Noia, Menfe2, die \y diluvium cce-
" plffe;, Anno 601 menfe 1 diei fuperficiem terra
" aquis liber at am, Gf menje 2 die 27 iellurem
". plan? arefaftam effe: & confequenter integrum
" Annum (uide excurrentibus diebus nihil dica-
" mus) Noam in area exegiffe.'\
The

(135)
The reader may be pleafed to obferve, that the
following calculus proceeds upon the folar, (j. e.
archbifhop UJher's) hypothefis.
3654-57 (folar days) =422 — 46 (days, which
lapfed before the flood) =3 y6 — 365= 1 1 . This
remainder the archbifhop calls excurrent days, or
which ., exceeded the meafure of the folar year.
But in truth, they are the days of the epadt, and,
by a mistaken hypothefis, have been reckoned
twice over ; firft, , in the additional number 3 3 ,
(which includes them as the epadt in its true
place, at the end of the year 600, as was noted
above) and again in the number ^y ; which are
days of the lunar year, and not of the folar. From
57 lunar days, fubftradt 11, the remainder 46,
gives the correfponding month, and day of the
month, of the folar year 60 1.
Noah then was order'd to come out of the ark,
on the 1 6 th day of the 2d month ofthe folaryear
601 ; yet we exprefly read, Gen. ch. 8. ver. 14.
In the 2d month, the 2yth day of the month, God
J'pake unto Noah, faying, go forth ofthe ark.
Therefore Mofes meafures by the years of the
Sun, but computes by the months and days ofthe
year of the Moon.
Should any doubts ftill remain upon the reader's
mind, as to the certainty of this diftindtion of
years (which I fo ftrongly plead for, and aim to
eftablifh) I am in hopes, that what I am going
farther to add, will entirely diffipate them, and
fet every point in a clear, and in its proper light. /
From

C '#>)¦
From the ift day of the -ift month (inclufive)
of the year of Noah's life 6oO^ to the 27th day of
the 2d month (inclufive) of the year of his life 601,
in which he was commanded. by God to go forth
of the ark, there had paffed one entire folar year;
and part of another; and alfo (through the co
incidence) one entire lunar year had paffed, • with
part of another, whether Mofes computed by its
months and days or not. But fhould it be con
cluded that he did not, then I afk, how will it
be accounted for ? If I am found capable of ad-
jufting from the ftile of, Mofes's chronology, and
the circumftances of his narration, the very fame
pofition of this lunar year to the given folar, as
the aftronomer will find by a backward computa
tion to that year.
I would beg the favour of the candid reader's*
attention to the following part *>f the deduction,
which will approve itfelf to be in the conclufion,
one of the moft perfect exemplars of aftronomical
chronology, that^was ever delivered to the workl. v
When the God of nature, the creator of the lu
minaries, vouchfafes himfelf to determine (and
incites his amanuenfis to record) the times and
feafons, can the div|ne computation fail to awaken
our attention ?
My enquiries muft ftill proceed upon the ori
ginal principle of the twofoldyear, and the argu
ment in its favour is obvious and concife. Mo
fes, in the introdudtion .to his Pentateuch, opens
his hiftory with the mutual offices and fettled or
dinations of the two great luminaries. Now here
Mojes

( J37 )
Mofes either lays down a fundamental principle as
a directory, or he does not. If he does not, all
enquiries of this kind muft needs be as vain as
groundlefs. If he does, why may we not pre
sume with confidence, upon his application of it ?
* Should any one object againft my reading the
text thus — In the fix hundredth (folar) year of
Noah's life, in the 2d month, the 17th day of the
month, ofthe (lunar year)— what methods would
he take to convidt me of error ? I will try to argue
for him, and fee what may be urg'd.
Firft, in one entire folar year which had paffed,
there are 365 days, and 57 given towards another,
which may be fet down thus,

600.

A.

601.

D.

D.

365-

57-

But I fhould reply, that in one entire lunar year
which had alfo paffed, there are 3 54 days, and ^y
given towards another, which, according to my di
rectory, I fhould fet down in this diftindt manner.
' rtS- • -hi;
A. 600. A. 601.

Solar year
Lunar year

365 —
354<"

46.
46.

--•Secondly, 365—46=31-9, and 3I9+57=376;
From hence it might be infer'd, that Noah was
in the ark a whole folar year, and 1 1 days over.
But not to continue thefe arguings any farther,
I think I may fafely fay, that they are not of fuf-
S"^ • ficient

(138)
ficient force to overthrow, or fo much as weaken
thofe foundations on^ which I hope to raife a com
pact and firm fuperftructure.
As to the precife number of days, in which
Noah was confin'd to the ark, my directory in-
ftrudts me to collect, ftate, and determine them
in a different manner, and the calculation muft
be framed to correfpond with the diftindtion of
years. But here we muft remember the co-inci
dence and its effedts. For,
As 46 days of the lunar year, fo likewife an
equal number of the folar, muft needs have been
meafured before Noah enter'd into the ark. This
fuggeftion being fufficient, I fhall proceed to the
calculation, and number the feveral fteps.
(0 3544-57=4J I- Thefe 411 days mea
fured the entire fpace from the beginning of the
year 600, to the laft day of Noah's continuance in
the ark.
(2) 57—11=46, and 365446=411. The
folar days, by means of the co-incidence, muft
neceffarily be equal to the lunar, and we fee here
that they are fo.
(3) 411 (lunar days)— 46=365. Thefe ^6^
days limit the time of Noah's confinement, with
out excefs or defect.
(4) 411 (folar days) —46=365, as before.
Although Noah was in the ark 365 days, or the
quantity of a folar year, yet was it not a diftindt
folar year, following in a regular fucceffion, but
is compounded of the parts of two folar, and of
the

( T39 )
the Parts of two lunar years. We muft therefore
feparate and determine thefe parts refpedtively. I
fay then, *
(5) 354— 46=3°8> and 3o$+$y=36s, as
before. (6) 365~46=3I9> and 365—319=46. Then
319446=365, as before. Set the feveral parts
orderly down in the following manner.
A. 600. A. 601.

Solar year 319
Lunar year 3 08 c

.4 467=365. The days of
4- ^y y Noah's confinement.

From this difpofition, even fenfe may judge,
that Noah was confin'd to the ark, 319 days ofthe
folar year of his life 600, and of the concurrent
lunar year 308. To thefe we muft add 46 days
of the folar year of his life 60 1 , and of the con
current lunar year 57, and #e have the whole
fpace on both fides.
(7) 319 — 308=11, the epadt, in its proper
place, at the end of the year;
Thus much may ferve to introduce the princi
pal points to be proved, which may be juftly
reckoned amongft the depths of genuine facred
chronology, and have lain hid for ages. Nor is
it an ordinary fatisfadtion to be affured, that they
are all capable of a proper folution.
I was follicitous fome .pages paft to make it
feem probable, that Noah waited for the return
of the dpve fent out on the 2d day of the 12th
month, 2 a days precifely, or to the end of the
S 2 cur-

( 140 )
current lunar year : and I might have render'd,it
more probable by varying and enlarging the ar
gument. For the recorded number of days of the
firft lunar year are 332, and the recorded number
of days of Noah's confinement may be thus ob- ;
tained; viz. 332 — 46=286457=343, which
is the number fought. Set thefe two numbers
down together with the well knbwn quantities '
of a common lunar and of a civil folar year, in
one line. 332, 3.43* 354> 365- .[
From this fituation of thefe numbers, we may
readily perceive, >
Firft, that 22 days are the complement of 332
into a lunar year, and of 343 into a folar, or the
time of Noch's abode in the ark.
Secondly, that they follow one another in arith
metical progreffion, continually enereafing by 1 1,
and that the laft of them in order is the epadt,
in its natural fituation at the end of the year.
But having made a farther progrefs, and in
fome meafure opened the fcene, inftead of calcu
lating probabilities, and fearching for arguments
to confirm them, I fhall now exert my endeavours
to remove far off from the reader's mind, all
thoughts and'apprehehfibhs of uncertainty and in
terruption; and here I fcruple not to affert, and
fhall apply rhyfelf to prove, that if Mojes had not
related any one circumftance of the deluge, be
fides the year, month, and day of Noah's entrance
into the ark, and going out of it, he" would by
this

< *4* )
thisfiile alone have render'd both the calendar
and the aftronomy of the year, abfolutely perfect
and complete; excepting only the neceffity of
knowing the quantity of Chodejh : he would, by
thisfiile alone, have accurately fettled and deter
min'd thefe 3 things, (i) ,The co-incidence of
the lunar year with the folar. (2) The limited
number of days contained in the epadt. And,
(3) in confequence of that, the quantity of the
lunar year, immediately preceding. Nay, I durft
go a ftep farther, and fay, that when God com
manded Noah to go forth of the ark, in the fix
hundredth and firft year, in the 2d month, the 27th
day of the month, he, at the Jame time, expref-
ly determin'd, and Mojes by the Jame terms, ex-
prefly recorded (as he had before ftated the time
of his entrance) the then pofition of the Sun and
Moon in the Heavens.
-i In order to illuftrate the truth,, and evince the
certainty of this unexpected and amazing propo
fition, 1 fhall beg leave to borrow the ftile and
terms of Mojes' s chronology, (for hiftorical cir
cumftances and facts are not indifpenfibly ne
ceffary) and transfer them from the year of Noah's
life 600 and 601, to the years of our Lord (ac
cording to the vulgar account) 1066 and 1067,
which comprehend the firft year of the reign of
Willicm the Conqueror-;
> According to the Englifh chronicle, William
the Conqueror -began to reign Oftober 14, A. D.
1066, and he reigned, by the accounts of hifto
ry, 20 years, 10 months, and 26 days. Thefe odd

( 142 )
odd months and odd days may be very pertinent,
and have their ufe in a chronicle bound to hifto
rical verity ; but they are fo far from being effen-
tially neceffary, that they cannot be admitted into
a canon, adapted to the purpofes of aftronomical
chronology. Witnefs Ptolemy's canon of kings,
(whofe infallibility depends upon calculated eclip-
fes) but much more and above all, Mofes's tables
ofthe genealogies of the patriarchs, (which the
more the reader examines, the more he will ad
mire) both before and after the flood, ever con-
fifting, each, of them of integral years.
Rejecting therefore Oftober 14, A. D. 1066,
we will carry back the beginning of his reign to
the beginning of the year, and make the years of
his reign, and of the reigns of all the Jucceeding-
kings and queens fince the conquefi, run parallel with.
their correfponding Julian ; having received my
chiefeft inftrudtions from the uniform aftronomi
cal law of Mofes's canon of patriarchs.
To fhew that we are not pinn'd down to thisi
the table of kings, &c . fubjoined, may be confi-r
dered, if we are fo difpofed under a twofold re
duction ; viz. Firft, to the Julian calendar, as
it is by its author extended from January 1, to
December 3 1 . Secondly, to the fame, as it may
be calculated from the Mofaic cardinal point, to
the fame cardinal point again : of which re
duction the characters of the Sun's ingrefs to
libra, placed in each of the extremes of A. M.
~5°7'?— » are a fenfible. indication. A

( H3 )
A TABLE of the kings and queens fince the co'rtqueft,
the years of whofe reigns are made to run parallel not
with the Julian, as it lies extended from January i to
December 31, but, as it may be computed, from the Sun's
lngxtii to. libra, and its return to the fame point again.

Names of kingsl Years
and queens, of reign
1 O

Anni^Lr. Ang.

A. M.
-ru -n.
©5°73©

A. D.
I066:£r

William I.
William II.
Henry I.
Stephen.

21:0- 35 19

2I:£b 34
69 88

50945107
5142 5161 •

IO87
1 100
"351154

Henry II.
Richard I.
John. Henry III.

35 1017
56

123 *33
150
206

51965206 5223
5279

1 189
1199 12161272

Edward I.
Edward II.
Edward III.
Richard II.

3520 5° 22

241 261 3Ir 333

53H533453845406

r3°7i327 *377J399

Henry IV.
Henry V.
Henry VI.
Edward IV. V.

9
3922

347
356 395
4J7

5420 5429 54685490

14*314221 46 1
1483

Richard IK.
Henry VII.
Henry VIII.
Edward VI.

2
2438 6

419443481 487

549255165554 556o

1485 1509
*547 *553

JViary I.
Elizabeth.James I.
Charles I.

¦ 5
45
'22 24

492 537559 583

55^5
5610 5^325656

1558160316251649

Abafileutus I.

, II

594

5667

1660

Charles II.
James II.
Wil.III.M.II.
Ann.

25 4
13
12

619623636
648

5692
56965709 5722

16851689
17021714 _

George I.
George II.
Current

J3
23 24

661684 685

5734 57575758

1727=2: 1750O 1751©

Should

Should a proper authority give a fandtion' td
this aftronomical reduction^ noted in the table by
its fymbols, and re-eftablifh the antient original
laws of meafuring by the years of the Sun, and
of computing by the months and days ofthe years.
of the Moon, we fhould foon be fenfible of the
benefit. Then- our accounts would be no more
perplex'd with the civil precejfions of the aequi-
noxes, nor fhould we ever hear again ofthe lunar
anticipations. . For neither the one nor the other
have a juft foundation in nature, but owe their
origin, and all their hypothetical and delufive
powers to an erroneous computation : but this
reduction being admitted, and thefe laws reftorerf
and applied, no poflible miftake could arife, no
after error be ever able to infinuate itfelf into our
chronology ; no, not in the multiplied fucceffions
of revolving ages.
Not to be too follicitous about matters which
fall not withfn my province, fince the year of the=
Moon may be applied, ad libitum, to the year of
the Sun, (to any of its cardinal points) I fhall
make choice of the former redudtion of the firft
year of the reign of William the conqueror, to il
luftrate the truth, and evidence the certainty of
my propofition. Becaufe, by this reduction, we
fhall meet with the fame pofition of the lunar year,
with refpect to the Julian folar, taken in its pro
per fituation and extent, from January 1 to De
cember 3 1 ; as Mojes has determin'd by his ftile,
and recorded in the year of Noah's life 600, with
refpect to the tropical folar, extended from libra to

( H5 )
to libra. And I was the .more inclined to chufs
this reduction, becaufe as thefe two diftindt lunar
years differ in their quantities, and their attend
ing epacts; fo this difference will occafion fome
variation in the ftile of Mofes's chronology, and
enable me to exprefs and manifeft the quantities
of each by that variation ; which muft make the
illuftration and the proof more clear and full.
In the clofe of the foregoing paragraph, I la
bour'd under the difficulty (and it may often be
my cafe) of finding out proper words, in order
to prevent my meaning from being mifapprehend*
ed, where fo nice a point is depending, as that, of
the fecret and almoffc imperceptible efficacy of
Mofes's fiile in chronology, undeniably is*
I would not he thought to infinuatej that it is
in the nature of a calculus to difcOver and fix the
pofitions of the luminaries in general, or in a given
year ; this is fo far from being the truths that on
>the contrary, vit is peculiarly adapted, (in his ac
count of the deluge) nay, I may fay, it is entire
ly appropriated, to a year of co-incidence, and to
the then pofition, which was but one, amongft
many, ofthe Sun and Moon in the Heavens.
, I hope it Will not be thought a trouble to re
turn to and confider the 13th verfe of the 8th
chapter; And it came to pafs in the fix hundredth and
firft year, in the tft month, the ift day of -the
month, the waters were dried up from off the
Earth: and Noah removed the covering of the
X . ..:¦!.... ¦¦ arh

( 14$ 5
ark, and looked, and behold the face of the ground
was dry.
Now is it not natural to fuppofe, that Noah,
and thofe who Were in the ark with him, might
be fufficiently tired with fuch a long and tedious
confinement, and were all as impatient as a
fhipwreck'd mariner, to fet their feet again upon
dry land ? And admitting the furface of the Earth
not to be quite fo firm and folid, as in procefs of
time it might and would be, yet they would have
been releafed from their prifon, and enjoy'd their
much wifh'd for liberty; yet notwithftanding
this, Noah did not conduct them out, in the. iff
month, on the ift day ofthe month, when he looked j
and behold the waters were dried up from off (the
face of) the ground : but he patiently continued
in the ark, to the 57th day following, and waited
for the command of God himfelf.
Ver. 14. In the 2d month, the 2yth day of the
month, Godjpake unto Noah, Jay ing, go forth of
the ark.
When God fpeaks, we have infinite rea^n to
expect perfedtion.
This important text is the key which unlocks
the whole fecret, and whilft it difplays the won
ders, it conveys to the mind, at the fame time,,
an affecting and lively fenfe, ofthe univerfal bene
fit of a divine revelation.
God inclined Noah to refide patiently in the ark
until this day, this very day, for fpecial reafons ;
viz. that by this means, Mojes, his amanuenfis,
might tranfmit to future ages the aftronomy of
that

( H7 )
that deftroying year, in which the Earth, mifera-
bly defaced and torn by an infupportable deluge,
was almoft if not altogether reduc'd to the origi
nal Tohu and Bohu. And this, firft, as a heaven
ly atteftation, as an undeniable, becaufe demon-
ftrable proof of the reality and certainty of the
fadt : fecondly, with a gracious intention to in-
ftrudt ages to come, in the clear knowlege of the
perfect, caeleftial year, and of its unerring (tho'
plain and fimple) laws of calculation.
This point then is fettled, that Mofes's ftile in
chronology ferves not as a calculus to difcover
and determine, but as a fore and faithful index, to
point out to us, what was the pofition of the lumi
naries at the beginning and end of that memorable
year, of which he has given us fuch a large ac
count, fuch a circumftantial hiftorical narration.
There is no neceffity at prefent for the multi
plying of queftions, or' making a follicitous en
quiry, how or in what manner, by what principles
and laws, Mofes might attain to the knov/lege of
fuch an exadt aftronomy ; all that the propofition
requires, or that lies upon me to make appear, in
a fafi&fadtory manner, is only this ; viz. that by
his very terms and ftile, he has actually, exp:eflly,
and precifely fiated and determin'd the true quan
tity of the epadt, and of the finifh'd lunar year,
together with the co-incidence and the com
menfuration. Thus then I enter upon the illuf-
tration and the proof.
(i) In the beginning of A. M. 1655, or the
year next before the flood, the lunar computa-
T 2 ' tion

( i4« )
tion ended on thei ith day of the ill month of
the tropical year. But 1.1+354=365, therer
fore, in the conclufion of the old world, A. M,
1655, the laft day of the lunar year, fell upon
the laft complete day of the tropical folar, which
is; as I have called it, a commenfuration.
(2) So likewife, in the fame manner, in the
beginning, of A.D. 1065, the year next before
the reign of William I. the lunar computation
ended on the nth day of the ift month of the
Julian year ; but January 1 1 4-3 54=365, there
fore, A. D. 1065, the laft day ofthe lunar year
fell on December 3 1, or the laft day of the Julian^
and there was again a commenfuration.
But as a corincidence muft neceffarily follow a
commenfuration, therefore, in courfe, in the
year of Noah's life 600, which runs parallel with
A.M. 1656, the ift day ofthe ift month ofthe
lunar year fell upon the ift day of the ift month
of the tropical folar; the lunar year was of 3 54
days, and the epadt 1 1 — by the terms and ftile of
Mofes's chronology, in his account of the deluge,
as fhewn, p. 1 37.
So likewife, in the fame manner, in the' ift
year of the reign of William I. which runs parallel
with A. D. 1066, the ift day of the lunar year
fell upon the calends of January, the 1 ft day of
the Julian ; this lunar yeai* was of 355 days, and
the epadt 10 ; which particulars are precifely ftated
find determin'd by a Juitable variation, in the
terms and ftile made ufe of by Mojes, in his ac
count pf the deluge. I ,. Thefe

C *49 )
Thefe peculiar aftronomical characters, arifing
from the application, of the lunar year to the Ju-,
lian, remarkably diftinguifh the ift Julian year.
of the Englifh vera ; efpecially if we add the ift
day of the week, on which the calends of Janu
ary happen'd that year.
We will now make tables of thefe feveral pofi
tions,' in' the fame manner as above, and then
fubjoin the Mofaic terms and ftile, and point out
particularly how they exprefs and record the aftro
nomy.

A. M. 1655
A.N. 599

A.M. 1656 600

A. M. 1657 601

— 365
¦ 0ii<T354f

^ 365 354* TI

46 46

A. D. 1065

A.D. 1066

A. D. 1,067

Jan.,. 365
"C.354C

' 365 ,
355< 10

4,6
[46

Under thefe tables we will recite ,
The terms andfiile of. Mofes'j chronology.
I. A. M. 1656. Gen. ch. y. ver. n. In the
fix hundredth year of Noah's life, in the 2d
month, on the 17th day ofthe month.
2. A. M. 1657. Gen. ch. 8. ver. 13. In the
fix hundredth and ift year of Noah's life, in the
gd month, on the 27th day of the month, 3'.

( ISO )
3. A.D. 1066. In the ift year of the reign
of 'William I. in the 2d month, oh the 17th day*
ofthe month.
4. A. D. 1067. In the 2d year ofthe reign
of William I. in the 2d month, on the 26th day
of the month.
Some remarks here may be neceffary, and will
not be, I hope, unacceptable to the reader. When
we take a view of thefe tables, we may perceive
that the year of Noah's life 600 is connected
with A. M. 1656.
(1) It is very obfervable, and all who have
read the bible muft needs have obferv'd it, that
the year of the world never once occurs, whether
weconfult the original Hebrew, or the Greek ver4
fion, or the Samaritan Pentateuch, . or Jofephut\
now this is no negligent omiffion, but was pur-
pofely defigned to manifeft to us the noble aftro
nomical law of the facred canon, 5757 revolu
tions of the Sun were completed laft autumnal
jequinox, A.D. 1750, of thefe 3471 4- were
paffed at the eftablifhment of Cyrus the Perfian's
univerfal monarchy, including that fpace of
time, in which the Jews returned from Babylon-
-to Jerujalem. For every one of thefe, there is
^n affighable and correfponding year, either of a
patriarch, or of a limited period, or of a judge,
or of the reign of a king of Judah, or of Ifrael, '
or of the Babylonifh captivity. And though all
may not confidently acquiefce in this determina
tion, upon tht account of fome imagin'd difficul ties

( 151 )
ties which have been raifed ; yet, whatever pre-
judicate opinion may fuggeft, it will moft furely
be found in the refult, a demonftrable cer
tainty. (2) In the year of the world 1656, extended
from libra to libra, the connected lunar year (as may
be feen in the table) was of 3 54 days, and the
epadt of 1 1 . In a juft aftronomical agreement
here (as I fhall prefently fhew) the terms and ftile
of Mojes's chronology compute the 27th day of
the 2d month ; for 1 1+46=57 — 30=27.
(3) In the Julian year of our Lord 1066,
which is extended from January 1 to December
31, the connected lunar year was of 355 days,
and the fubfequent epadt of 10. In a juft aftro
nomical agreement hereto, the terms and ftile of
¦Mojes's chronology, compute by a fuitable varia
tion, only the 26th day of the 2d month; for
104-46=56 — 30=26.
Thus far may be admitted as an illuftration,
but it may be afk'd where is the proof?
I have alleged above, and am bound to fup
port or retract it, that if Mojes had related no one
circumftance of the deluge, befide the year,
month, and day of Noah's ingrejs and egrefs, he
would have render'd thereby both the calendar,
and the aftronomy of the year abfolutely perfect
and compleat, excepting only the previous know
lege how many days are contained in the Hebrew
Chodejh. How ftrange and unpromifing foever this alle
gation may be thought at the firft view, as foon as'

C *s* 1 .
as Mojes's fundamental principles and data Cofftd
to be rightly underftood and confider'd, its truth
will immediately fhine, as indifputably clear as
the truth of an axiom. .
The fundamental principle is this, viz.
Prop. 3d, That Mofes meafures by the years
ofthe Sun, and computes by the months and days
of the years of the Moon.
This principle is a fure directory to a right ap*
plication of the data^
The data, in the prefent cafe^ are the 17th
day of the 2d month of one lunar year; and the
27th day of the 2d month of another, following
it in immediate fucceffion.
A lunar year muft, in nature^ confift either of
3 54 days, or of 355; never lefs than the one;
never more than the other. The number of in
tervening days, which lie between the above gi±
ven limits, muft, by the fundamental principle
and data, be juft 365. They cannot poffibly be
one day more, nor can they poffibly, be one day^
lefs. Thefe 365 days muft neceffarily include <
the quantities of both the lunar years, and both
their epacts. The ift month and 16 days, both
of the folar and the lunar year were lapfed, be-*
fore the entrance into the ark. A month has 30
days, 304-16=46.
Before we offer the rule, how to calculate the
juft quantity of the epadt, and of the connected
lunar year, "A. M. 1656, and A. D. 1066, efta*
blifhing at the fame time the co-incidence and
com*

( 153 )
commenfuration, firft, divide the days of the
folar year and of the lunar, as inftructed by the
given limits and data, in the following man
ner.

A.M. 1656. A.D. 1066.
Solar year j 46+319 I +46 I 46+319
Lunaryear J 46+308 c J +57 \ 46+309 c

+46+56

This being done, the whole of the calculus,
in both cafes, will proceed readily ; and may be
eafily underftood with a fmall degree of attention.
A.M. 1656.
1. 354 — .46=308 c lunar days, or the num
ber of days of the firft lunar year, in which Noah
continued in the ark.
2. 308 (+57 lunar days=365, the whole
fpace of his confinement, including the day in
which he was commanded to go out.
3. 365 — 46=319 folar days, or the number
of days of the folar year of his life 600, in which
Noah refided in the ark.
4. 365—319=46, the number of days of
the folar year 601.
5. 319+46=365, the entire fpace, as be
fore. 6. ^y — 46= 11, the quantity of the epadt.
7. 365 — 11=354, the quantity of the lunar
year. 8. 354 — 354—0, the index of commenfu
ration. u a;

( i54 )
A. D. 1066.
0) 355— 46=Jo9c. (2) 309c +56=365:
(3) 365— 46=3J 9- (4) 365--319=46- fa)
56 — 46=10, the quantity of the epadt. (6)
365 — 10=355, the quantity of the lunaryear.
(7) 355—355=0, index of commenfuration.
But as I have applied the lunar year to the Ju
lian, A.D. 1066, I- may be more particular
here, without running any hazard of being thought
obfcure or unintelligible. If we look into the
lowermoft table for A. D. 1067, (p. 149) we
may perceive the lunar days to be placed thus —
C 10 [ 46. Now 46+10=56. To 46radd De
cember 31, and from the fum 77, fubftradt the
compound 56, remains December 21. If we
look for December 21" in the Julian calendar, we
fhall find over againft it, in the column of cok
lected days, reckoned from the calends of Janu-
ary, 355 days. Thefe 355 are the days of < the
concurrent lunar year, and they conftituteits true
quantity; but they are alfo the collected days of
the Julian .year, which lie concealed under the
days of the lunar, being co-incident with and
commenfurate to them, Mojes's fundamental
principle then — Haju lejhanim — is no deluiive
guide ; it is far from being chargeable with an
abfurdity, nor can it be impeach'd as irreducible
to pradtice.
Now fhould fome one aftronomer be difpofed
to make a calculation for the given year, A. D.:
1066,

( 155 )
1066, (though I do not know that this calcula
tion ever has been made by the tables) and not find
December 2 1 to be the day after the Moon's con
junction, (though it is neceffary to note, that De
cember 1 9 paft 6 in the evening, in the primitive
account, is December 20) then it muft beallow'd,
that I have not added any degree of proof to the
illuftration. It is poflible that the reader may by this time
be in fome meafure reconciled to the truth and
certainty of my 3d propofition — That Mojes
meafures by the years of the Sun, but computes
by the months and days of the years of the
Moon.- And may I not be permitted to indulge a fan*
ther hope, that he finds himfelf fomewhat en-
ciin'd to admit,
. That Mofes's hiftorical narration of the circum
ftances, procefs, and conclufion of the deluge, is
extremely curious, and is, in fact, the key, where
by we may open many, if not moft, ofthe fecrets
of the antient and original computation of times,
according to the Hebrew text.
Thefe laft words, — according to the Hebrew
text,— are here ernphatical, fince the fepfuagint
verfion reads, ch. 7. ver. 1 1 . erroneoufly and .
corruptly, EpJVit x.o-iui*£irr*pM<>ti i> e. the 27th
inftead of the 17th day of the month. Now I
doubt not to fay, againft the moft critical acumen,
that had there been found no other difference, but
this one, between the chronology of the feptua-
gint verfion, and that of the original Hebrew, this
U 2 - one

( 156)
me difference alone is of fuch importance,
that it would have kept the aftronomy of the
Pentateuch in an irretrievable ftate. x Should any
one apprehend that this affertion may be confuted,
I could wifh to fee the arguments.
The particular difcoveries arifing from the Mo-
J'aic hiftory of the deluge are, (i) The number
of days in a primitive month. (2) The manner
of computing and adjufting;the months of the lu
nar year. (3) The manner of computing and
adjufting the months of the folar year. (4) The
law of their connection, which our aftronomers
have not taught us. (5) The quality of the
Moon (c) which conftitutes the head or begin
ning ofthe Scripture lunar year.
The two firft of thefe have been confider'd
and ftated already : proceed we then to the 3d.11
Bifhop StUlingfleet in his Origines Jacraj (1. ,1.
ch. 6.) from an obfervation of Diodorus Siculus,
refolves the confufion and ambiguity of heathen
chronology, into two caufes.
Firft, Their not having any certain parapeg- .
' mata or epocha, from whence to deduce a true •
accountrof times.
Secondly, The uncertain and various form of
their years.- ¦- tv.
But is not this the prefent ftate of the^cafe?
Have either the Jews or the Chrifiians (with the
¦Hebrew bible in their hands) any allowed grounds to

( *S7 )
to boaft of what Diodorus Siculus calls — ru?*rnyf*«
ms-Tivoptfav ? Is their epocha from the creation, or
their ara mundi, fuch a one ? Then, I afk, who
has demonftrated its certainty ? The Chrifiians,
we know, have rejected the Jewijh aera, whilft
the Jews continue to reckon the feveral periods of
the world's age from it.
The jewijh asra from the creation terminates
A. J. P. 953, whilft Scaliger cbufes 764. Arch
bifhop Ufher 710, Mr. Bedford yob. Upon which
of thefe diffentient hypothefis may we infallibly
depend ?
Qua, quibus anteferam? Qua prima exordiajumamf
Secondly, The uncertain and various form of
their years.
We may argue here, as we did before, with
refpect to the different and difcordant opinons
concerning the world's asra, or epocha, from the
creation : fince we fhall fcarcely find any two
Chriftian writers agreeing in their fentiments
about the Scripture years ; nay, pages might be
.filled with a recital of the particulars of their dif-
agreement. Had the great Stillingfleet, when he wrote his
Originesjacra, been required to determine the
quantity, and delineate theyor»z,of the patriarchal
year, there is reafon to think, he would have re
fer'd the querift, for the folution of his quaery,
to archbifhop UJher 's annals. And had the learn
ing and judgment of the primate been confulted on

( 158 )
on this head, would he not have refer'd him to
the /Egyptians for its form, and to the Romans for
\ts, quantity? lam led to think that he would,
by the following paffage^ in the preface to hi&
annals. -: ->
," Primorum patrum, veterumque Mgyptiorum
" & Hebraorum annus, , ejufdem cum Juliano
" quant it at is fuiffe reperitur, fed ex menfibus \2
" equalibus, dierum 3 o conftans (Hebraos enim ante
" Babylonicam \captivitatern " lunaribus menfibus
"fuiffe ujos, probari non pot eft) dierum epagome-
" non 5, & quarto quoque anno 6, ad 12 menfis
" finem, adjeftd appendicula."
Imake no doubt but that archbifhop Ufher;.
following the thread of the Mofaic narration,
traced out the fprimitive calendar to the 2d day
ofthe 1 2th month; but when he had gone
thusfar, finding no more circumftances related,
which might direct him to compleat it, yethow^-
ever perceiving, that the collected number of 332
days evidently included 1 1 thirty-day months, and
the Mgypto-Julian year, as it feems occurring to
his thoughts ; he to 332 added, (hypothetical-
ly); 28 days, which made them 360, or 12 equal
months, of 30 days a-piece : to thefe .360 days,
he added the 5 well known Epagomenai, which
> made them 365 : to thefe he continued to add
6 hours, which made them 3654, and compleat-
ed the Julian year. Thus finding himfelf in the-
end poffefs'd of a civil folar year, the neareft' to
the, true' one, that ever was or poffibly can be
ob-

( 159 )
obtained, he refted in the conclufion and enquir
ed no farther. ,
Thefe feem to me to have been the feveral fteps
of archbifhop UJheFs reafonings and determina
tion, both of the form and of the quantity of the
Scripture folar year, as may be plainly gathered
from the above cited paffage in his preface.
According1 to this determination then Methufa
lah lived 969 JEgypto-Julian years ; but the au
thor ofthe Pentateuch died 1426 Mofaic Shanim
or tropical years, before the firft fix'd /Egyptian
year was reckoned.
The JEgypto-Julian year, bears the fame date
with the Alexandrian sera of the Aftiac victory,
An. Mr. Nabonaff 719, Aug. 29. Nor can it
be proved from authentic teftimony, that the fo
lar year, in that form and in that quantity, was
ever in civil ufe before that time, in any one na
tion. But, defering farther difcourfe concerning the
quantity of the primitive folar year, how does it
appear that Mofes gives a fandtion to the archbi-
fhap's determination of its form, or the manner
of computing and adjufting its months? For
where are the Mojdi'c principles and the Mofaic
hiftorical data to be feen in the feveral fteps of the
proceeding ? Thefe muft ftill be collected from
the limited time of Noah's continuance in the
ark. It has been made fufficiently plain and clear al
ready, that Noah ftay'd in the ark 3 19 days ofthe folar

( x6o)
folar year of his life 600 ; and 46 days of the folar
year of his life 601. Now then,

M.

D.

D.

Ifto

10+

19

300+19

3i9

We add,

1 +

16

30+16

46

Wefhall have 11+35 33°+35 365
Again, Noah was in the ark 308 days of one'
lunar year, and 57 days of another j therefore,
M. D. D.
Ifto 10+8 300+8 , 308
We add, 1+27 , 30+27 57
We fhall again have 1 1 +35 3304-35 365
We conclude then, from both deductions taken
jointly (I refer here to that ofthe lunar year, as ftated
p. 127.) that the manner in which the antedilu
vians computed and adjufted the months, both of
the folar and of the lunar year, was as follows.
M. D. D.
Solar p u+35 33°4-35 3^5
The patriarchal >year
LunarJ^ n+24 330+24 354
11 n 11
The epadt at the end ofthe deluge.

( »6i )
I will now offer a calculation 'grounded upoa
Mofaic data, which will confirm archbiihop
UJher's conclufion, excepting the quadrants, which
will be confider'd_ hereafter.
From the ift day ofthe ift month ofthe folar
year of Noah's life 600, to the day in which he
received the divine command to eome out of the
ark, there paffed 411 days, both folar and lunar $
therefore, M. D. D. D.
If from 134-21 390+21 41 1
We fubftradt 1 + 16 30+16 46

We fhall have 12+ 5 360+ 5 365
But this is much more antient than the JEgypto-
Julian year.
We have now obtained from Mofes thefe 3
numbers, 354, 360, 365. The firft is the quan
tity of a lunar year, the 3d of the folar, exclufive
of the quadrant, and the 2d is a mean proportion
between the quantities of both.
To 365 add 1, or the autumnal aequinodtial
day, then the 4 following cafes will include all
the variety of the epacts, in a year of co-incidence*
z ce *. , c I ?including the
1. 354, 36o, S66,6+6^i2^quino(|ialday;
2. 355, 36°, 365. 54-5= i°> excluding.
3- 354-, 360, 365, 6+5=1 1, excluding.
•4- 355:360,366,5+6=11, including*
X The

( 162 )
The co-incidence of the 'lunar year with the
folar, the exact commenfuration of the days of
the one to the days of the other, confequent
thereupon; and the mean proportion 360, admit
of the following partitions.
Solar ) ^330+24 +6+5
Days of the Syeat.)
Lunar J , O30+24C+6+5
It is evident to fight, that in a year of co-inci
dence, the 24th and laft day of the 12th month
of the lunar year falls upon the 24th day of the
1 2th month of the folar. 330+24 folar days=
354; borrow 6 days from the lunar epadt, and
add them to thefe 354 folar days, and we fhall
have 360, or the 12 equal months of the folar
year. Now, I fay, that the 5 remaining days
are the. complement of 365 folar days, and alfo
of the epadt.
I thought it the more neceffary to make this
obfervation, becaufe it is evident in fact, that
the fbns of Noah in general, when they came to
be difperfed, loft all knowlege of the aftronomy
of the year ; and retained no more of the antient
and original computation, than thefe 360 'days,
or the 1 2 equal months of the folar year.
And when in after ages, they by fome means
.recovered the 5 remaining days, they added them
to the 360, as the complement of the folar year,
(in which they Were miftaken almoft a .whole
quadrant) but they were not capable of confi
dering

( 163 )
dering them as the complement alfo of the lunar
epadt; nor has its primitive application and ufe
been reftored by all the improvements and inven
tions of fcience. And yet the mythologic fable
reprefents Hermes as playing , at dice with the
Moon, and winning from her, the 72d part of
360 days ; which plainly implies, as \t feems to
me, fome imperfedt tradi donal notion of the lunar
year. This propofition I offer, as an hypothefis
of the origin of this very antient year of 360,
which has been productive of fo various and un-
fatisfying folutions.
There is no neceffity to recapitulate the parti
culars, which have been hitherto ftated, and, in
fome meafure explain'd ; but it • may be neceffary
to remember and carry along in our minds, that
Mojes's aftronomy proceeds altogether upon a di
ftindtion of years, and that thefe two diftindt
years had at the time ofthe deluge {the co-inci
dence proves this) one and the fame common
epocha, and that their refpedtive annual periods
commenc'd at the fame cardinal point ; and that
this cardinal point was the autumnal equinox.
Thus, in the more remote and primitive ages,
ftood Rifhon (Gen. ch. 8. ver. 13.) the ift month,
as it were, the head of the lunar year.
But when Mojes, Levit. ch. 23. takes occafion
to treat of, and is enumerating to the IJraelites,
all the folemn affembly days and appointed feafts
of the Lord throughout the ecclefiaftical lunar
year, we then receive a different inftrudtion : we
are plainly and openly inform'd, that the epocha
„ X 2 , are

( i64 )
are become as diftindt as the two years them
felves; and are fo disjoined the one from the
other, that the 15th day ofthe 7th month ofthe
lunar year might, and • fometimes adtually did
fall, Tekuphath hafhanah, on the cardinal point
of thfe folar. From 7 m. 1 5th day, fubftract 1 5,
the remaining fix compleat Chodajhim meafure
the determinate diftance of Rijhon from itsantienf
original fituation. And if that antient original
fituation was at the autumnal aequinox, it muft
have been transfer'd, the aftronomer will fay, to
the vernal ; Ej- k?i&> tk hx/k jutO^-raTo?, the Sun be-r
ing in aries, fays Jofephus. Hence the annual
courfes of the two great luminaries mutually in-
terfedted each other in the circle of the year. And
thefe numbers thus placed to each other, 1 5, 1 80,
15, exprefs the limited and invariable diftance
between the feaft of tabernacles, and the ift day
ofthe feaft of unleavened bread, from the times
of Mojes, down to the times of Nehemiah.
Although it does not appear, that the Patri
archs, the Hebrews, the IJraelites, or even Jews,
before the times of Alexander, had any knowlege
of the divifion of the ecliptic into two unequal
fegments, at the aequinodtial points, nor were
able to afcertain the Sun's ingrefs to aries ; yef
fuch was the original aftronomy, and fuch the
conftruction, both of their alter'd and unalter'd
year (as we fhall fee from the following tables,
and fhall be more fully inform'd by the calculations) that

( i65)
that the IJraelites could not fail of keeping their
paffover on the 14th day of the month Abib, or
at the vernal aequinox.
The alteration of the beginning of the facred
year, and the transferring of Rijhon to the oppo-
fite cardinal point, is fuch a remarkable tranfac-
tion, fuch an unufual proceeding, its like not be
ing to be met with amongft the nations, that Mo
fes has in a particular manner inform'd us, when
it was done, by whom, and for what ends and
purpofes ; viz. to be a permanent ftanding me
morial of great bleffings and very fignal mercies
at that time received ; alfo, a prediction and
type of greater bleffings and more fignal mercies
to come.
He introduces his relation with fuch an awful
folerhnity, that we in a moment perceive it was
no conftitution of the elders, no private inftitute
of his own, but was commanded and immediate
ly executed by the interpofition of the fupreme
legiflator "himfelf, by the fole authority ofthe God
of nature, and framer of the caeleftial year.
Exodi ch. 1. ver. 1. The Lord fpake unto
Mojes and Aaron in the land of JEgypt, faying,
Ver. 2. Ha Chodejh hazzeh Rojh Chodajhim,
Rijhon hua lacem lechodjhei hajhanah.
Septuagint verfion. o pm vm vpiv «?%« pnvw,
•p^aTH &?iv (zscu) up''" w T"s fulfil' th eviavTu.
This month fhall be unto you the' beginning
of months, it fhall be unto you (Rijhon) the ift
month (Hajhanah.) of the (lunar and ifacred)
' The

( 166 )
The alteration of the beginning of the year
took place from this day forward, and both Mo*
j'es and the prophets punctually compute the
times by it ; and even the exil'd difpers'd Jews
begin their facred year to this day from the ver
nal aequinox : and fhould a reafon be demanded
of them, they are able to plead divine authority,
and the exprefs command of God himfelf for the
antient ufage. For,
PJal. 8 1 . ver. 4. This was a fidtute oj the
God ofjfrael, and a law ofthe God of Jacob.
Ver. 5. This he ordained unto Jofeph, (and all
the 1 2 tribes of Ifrael) for a teftimony— through
out their generations, by an ordinance for ever.
The hiftory of the Pentateuch abounds in the
recital of events and facts, extraordinary in their
nature, important in their confequences, and de-
monftrably true.
The chronology of the Exodus, like the Mo
faic year, was never yet, as I know of, collected
and proved from the Hebrew text, and yet it is a
demonftration worthy of the facred record's, and
highly becoming the author of the Pentateuch,
but I fhall not anticipate it here.
The reader is now thoroughly prepared and
qualify'd, not only to perqfe, but to underftand
the following fchemes, both of the alter'd and
unalter'd Scripture year ; nor will he ftand in need
of an index to point out to him the Angular im
portance of the appropriated term1 Rijhon— Be-
rifhon, be echad lechodejh. .Gen. 8. xiii. And

( 167 )
And perhaps, when he takes • a review of the
emphatic text above, and ferioufly weighs and
confiders it in its whole tendency and defign, he
may become fenfible, that when God fpeaks, and
Mofes records, we are fure to be inftrudted in
points, which not only concern more immediate
ly the IJraelites ; but remotely in the before-ap
pointed feafon, the Gentiles alfo, and the whole
race of mankind. I.
The aftronomical pofition of the lunar year to
the folar at the deluge, when they jointly began
their annual periods from the autumnal aequinox j
which Mojes has left upon record, as a moft per
fect ftandard and exemplar of the antediluvian
calendar^ and patriarchal year.

Chodjhei

( 168 )

*

Chodjhei IfLaJhanahi

Rijhon

s£=

L 30 30

©
II. 30 60 »
III. 30 90
IV. 30 120
V. 30 150
VI. 30 180
Abib
Y
©
VII. 5 0 2IO HaChodefh hazzeh lacem
TrTTT ^ Rojfi cbodafbim. Exod.
VIII. 30 240 12-A
IX. 30 270
X. 30 300
XI. 30 330
Lunar \
>year XII. 24 354 <r A.M. 1656. V.
Solar <
XII. 35 365^ N. 600.
.<- ©
II. *
Chodjhei Hajhanaht
:£= I. 3O 3O VII. 30 30
©II. 30 60 VIII.3O 60
III. 30 90 IX. 30 90
IV. 30 120 X. 30 120
V. 30 150 XI. 30 150
VI. 30 180 XII. 30 180
Abib V VII. 30 2IO I. 30 $q Rifhm hua ta-
© VIII.3O 240 II. 30 60 %; tjla*
IX. 30 27O III. 30 90 nah, Exod.'
X. 30 300 IV: 30 120 I2,2,
XI. 30 330 V. 30 150
hnar?year.XII-24 3 54 « VI. 24 174C
Solar57 XII. 35 36j^A.M. 1656.
0 I
( i69 )
I will take it for granted that the curious and
inquifitive reader has view'd with fome attention
thefe two fchemes of the Scripture year in its dif
ferent ftates, before and after the Exodus. If he
has, it cannot have efcaped his notice, that Rijhon
is placed at the autumnal aequinox in the firft,
and over againft Abib, or at the vernal aequinox,
in the fecond. Now if it be admitted, or can
be proved, that thefe adjuftments are true, then
the aftronomical fituation of all the intermediate
months muft follow of courfe.
By the joint affiftance of thefe fchemes, and
the 39th verfe of Levit. ch. 23, and the 16th
verfe of Exod. ch. 23, and the 2 2d verfe of Exod.
ch.24-; I (hall be able to eftablifh that fundamen
tal principle, from which I have hitherto argued,
and upon which I have confidently proceeded, be
yond all grounds of doubt, or even a fufpicion of
uncertainty. Take fcheme II, in which the
months of the unalter'd folar, and the alter'd lu
nar year, are fet down collaterally.
Now I fay, that the autumnal aequinodtial
point of the ecliptic is diftant in nature, from the
winter folftitial, 89 d. fome odd hours, and odd
minutes ; the epocha of the folar year, and alfo of
the lunar, before the Exodus was 0 ; confe-
quently, the laft day of the 3d month (the fum
of whofe days=9o) of both years, muft neceffa
rily fall in a year of co-incidence, upon the day
of the winter folftice. Whilft the laft day of the
9th collateral month of the alter'd lunaryear,
Y re-

( i7° )
reckon'd from Abib, or ©, would be co- incident
with the fame folftitial point. Now let us con-
fult the prophet Jeremiah, (who lived many
hundred years after the Exodus) and fee what ac
count he gives ofthe alter'd year.
Jer. ch. 36. ver. 9. And it came to pafs, in
the §tb year of Jeohiakim, the Jon ' of Jofiah king
of Judah, in the 9th month, that they proclaimed
a faft unto the Lord. -
Ver. 10. Then read Baruch in the book, the
words of Jeremiah, in the houfe of the Lord.
Ver. 16. And all the princes faid unto Ba
ruch, we will furely tell the king of all thefe
words. Ver. 22. Now the king Jat, in the winter
houfe, in the 9th month, anft there was afire on
the hearth burning before him.
Here an opponent might plead, that the pro
phet might as juftly be fuppofed (fince nothing
appears to the contrary) to compute by the 9th
month of the folar year, reckon'd from the vernal
aequinox, as from the 9th month of the lunar,
beginning from the fame cardinal, which only
infers a change in the epocha of -both, and why
fhould we not infer it ?
My reply to the objection is this : The prophets
are but commentators upon the law ; Mofes fixes
the ^ ftandardj and they conftantly follow its di
rections. But it is undeniably certain, the legi
slator enjoins the IJraelites to obferve the feaft of
tabernacles, and the feaft of ingathering, upon
r the

( W )
the 15th day of the 7th month of the alter'd lu
nar year, Tekuphath hajhanah, in the revolution
of the folar. And if we eaft but our eye over
table II, we fhall fee the 7th month of the alter'd
lunar year, over againft the original cardinal point
of the unalter'd folar. This argument is clear

r b

and decretory; and I need not fearch for any
more inftances. -
Therefore, Mofes and the prophets, both be
fore and after the Exodus, compute by the months
and days of the lunar year, but never by the
months and days of the folar.
Having now finifh'd my account of Chodejh and
Shanah, I -fhall proceed to fhew that the antient
people of God had not only a regular and well
known calendar in the reigns of David and Solo
mon, but fomewhat more than this, viz. that
the fame form of year, the fame uniform ftile of
chronology, and the fame invariable law of com
putation is continued ' without interruption,
throughout the Hebrew Scriptures.
Nehemiah returned to the Perfian court in the
^id'yeaVof.Artaxerxes'Longimanus ; and in that
very year the certainty of the old teftament hifto-'
ry end's"; nor can it be determin'd, but by con
jecture, in what year, either Nehemiah, iheTir-
Jhatha, or ' Maiachi, who was the laft of all in
the fucceffion of prophets, died. Lower down
than thefe times then we cannot come.
It is a fentjment of Sir J. Marfioam's, alia
chronologic fuit antje Babyhnicam captivitatem,
alia poft reditum — If by the words, poft reditum,
Y 2 this

' . ( i72 )
this learned writer would be underftood to mean,
immediately after the return, I am obliged to dif-
fent from him, becaufe I fhall undertake to prove
the contrary from the Scriptures. And what rea
fon can there be to infer and conclude a different
law of computation, where there is no effential
difference in the terms and ftile ofthe chronology,
nor any variation from Mofes's original ftan-
dard? It may be faid perhaps, that Ezra and, Nehe
miah, both of them, annex political names; viz.
Nifan, Tifri, Adar, &c. to their months, which
they borrowed from the Chaldeans in their capti
vity, and doubtlefs, together with them, their me
thod of computing times. But the' reafon alleg'd
here can be of no weight, becaufe, although in
Solomon's reign, they had before this introduc'd
political names to their months (3 only of which
are tranfmitted to us, viz. Zif, Ethanim, But)
yet are they ever explain'd and determin'd in both
cafes by ordinal numbers, and by this means,
reduc'd to the genuine Mofaic ftile. The truth
of this will plainly appear in the following ex
amples, to which more might have been added,
had not thefe been fufficient to evince, that one
uniform and invariable ftile of chronology, one
well known law of computation, runs through the
Hebrew Scriptures, from the 600th year (and up
wards) of Noah's life, to the 3 2d year of Artax-
crxes Longimanus king of Perfia.
Thofe who may chance to read the following
proofs will think it no fmall matter of wonder, that

( *71 )
that this part of the Scripture account has not been
more attentively confider'd and regarded.
The Mofaic original flandard.
Gen. ch. y. ver. 1 1. In the fix hundredth (fo
lar) year of Noah's life, in the 2d month (of the
lunar year, from the autumnal aequinox) the fame
day, were all the fountains of the great deep
broken up. 
Thefiile of Mofes'* chronology continu'd.
(1) 1 K. ch. 6. ver. 1. In the 4th (folar) year
of Solomon's reign over Ifrael, in (the month
Zif, which is) the 2d month, on the 2d day of
the month, (2 Chr. ch. 3. ver. 2.) (of the alter'd
lunar year, from the vernal aequinox) he began to
build the houfe of the Lord.
(2) 1 K. ch. 6. ver. 38. In the nth (folar)
year of Solomon's reign, in (the month Bui, Which
is) the 8th month (of the alter'd lunar year, from
the vernal aequinox) was the houfe finifh'd.
(3) 1 K. ch, 8. ver. 2. * In the 12th (folar)
year of Solomon's reign, all the men of Ifrael af
fembled , themfelves unto, king Solomon, at the
feaft (of tabernacles) in (the month Ethanim,
which is) the 7th month, * on the 15th day of
the month, (of the alter'd lunar year, from the
vernal aequinox) Levit. ch. 23. ver. 34.
(4) 2 K. ch. 25. ver. 8, 9. In the nth (fo7
lar) year of king Zedekiah, (which is the 1 9th
year

( *74 )
year of Nebuchadnezzar king of Babylon) in the
5th month, the 7th day of the month, (of the
alter'd lunar year, from the vernal aequinox) came
Nebuzarad'dn captain of the guards, a fervant of
the king of Babylon, unto Jerufalem.
(5) Jer- ch- 52- ver- 13- * ^n l^e Irtk (f°^ar)
year of king Zedekiah, in the 5th month, the
iothday ofthe month, (of the alter'd lunar year,
from the ' vernal aequinox) he (Nebuzaradan)
burnt the houfe ofthe Lord, and the king's houfe,
and all the. houfes of Jerufalem, and all the houfes
of the great men burnt he with fire.
(6) 2 'K- ch. 25. ver. 27. And it came to
pafs, in the 37th (folar) year of the captivity of
Jehoiachin, 'king of Judah, in the .12th month,
the 2ythdayof fhe month, (of the alter'd lunar year,
from the vernal sequinox) that Evil-Merodac king
of Babylon, in the year that he began to reign,
did lift up the head of Jehoiachin king of Judah
out of prifon."
(7) Ezek. "ch. 24. ver. 12. In the 9th (folar)
year of king Jehoiachin 's captivity, in the 10th
month, the ibth day of the month, (of the al
ter'd lunar year,' from the vernal aequinox) the
word ofthe Lord came unto me, faying, ver. 2.
Son of man, write thee the name of the day,
even of this'fafne day, the king, of Babylon let
himfelf againfi4, Jerufalem, this Jame day.
(8) Haggai, ch. 1. ver. 1. In the 2d (folar)
year of Darius (Hyftajpes king of Perfia) in the
6th month, the' ift day., of the month, (of the
alter'd

( 175 )
alter'd lunar year, from the vernal aequinox) came
the word of the Lord, by Haggai the prophet,
unto Zerubbabel.
(9) Zechar.ch. 1. ver. 7. In the 2d (folar) year
of Darius (Hyftajpes king of Perfia) in (the
month Shebat, which is) the nth month, the
24th day ofthe month, (of the alter'd lunar year,
from the vernal aequinox) came the word of the
Lord unto Zechariah,
(10) Zechar. ch. 7. ver 1. And it came to
pafs, in the 4th (folar) year of Darius (Hyftajpes
king of Perfia) in (the month Chifieu, which is)
the 9th month, the 4th day of the month, (of
the alter'd lunar year, from the vernal aequinox)
that the word of the Lord came unto Zecha
riah. (11) Efiher ch. 3 . ver. 7. In the 1 2th (folar)
year of king Ahajuerus (i. e. Artaxerxes Longi-
manus) in (the month Nifan, which is) the ift
month (Berijhon) they eaft pur, that is, the lot,
before Human, from day to day, and from month
to month, to the 12th month, that is the month
Adar. (12) Ezra,ch.6-. ver. 15. In the 6th (folar)
year of the reign of Darius (Hyftajpes king of
Perfia) in the month Adar, (which is the 1 2th
month) Efiher, ch. 3. ver. 13. On the 3d day of
the month, (of the alter'd lunar year, from the
vernal; aequinox) the houfe ofthe Lord was fi-
nifhed. (13) Ezra, ch. y. ver. 8, 9. In the 7th (folar)
year (of Artaxerxes Longimanus the king of Per fia)

C 176 )
fia) in the 5th month, on the ift day of the
month, (of the alter'd lunar year, from the ver
nal aequinox) Ezra the fcribe, came unto Jeru
falem, according to the good hand of his God
upon him.
(14) Ezra, ch. 10: ver. 16, 17. They fat
down, in the 1 ft day of the 1 otlynonth, (ofthe
alter'd lunar year, from the vernal aequinox) to
examine the matter; ver-. iy. And -they made an
end with all the men that had taken ftrange wives, v
on the ift day ofthe ift month (Berijhon,<3)
(15) Nehem. ch. 8. ver. 2. * In the 21ft
(folar) year (of Artaxerxes Longimanus king of,
Perfia *)¦ — in the 7th month, on the 1 ft day of
the month, (of the alter'd lunar year, from the*
vernal aequinox) Ezra the prieft brought the law
before the congregation— and, ver. 13. He read
therein. Can any one carefully perufe and weigh all
thefe texts, to which many more might have been
added, collected from tne Hebrew bible, and en
tertain a doubt, whether the ftile of Mofes's chro
nology, and determinate law of computing times,
be continued without any effential alteration down
to the age in which Nehemiah lived, and to the
2d great monarchy, or not ? It is poflible indeed,
that fome feeming difficulties may occur to the mind
in the reading of them ; but this is not at all to
be wonder'd at, nor will it be mifinterpreted to
my prejudice, fhould I freely fay, that the whole
fcheme

( *77)
fcheme of facred chronology has not hitherto been
rightly explain'd, or thoroughly underftood.
There is one feeming difficulty (amongft others
perhaps) which may probably perplex the rea
der's apprehenfion, and rife up, as an objection, in
fome fuch form as this, viz.
How can we reconcile to the writings of the
prophets, what has been advanc'd and afferted,
concerning the alter'd lunar year, and the unal-
ter'd folar, feeing it muft needs be admitted,
from the whole tenour of the above cited texts,
either that the epocha of both years was tranf-
fer'd to the oppofite cardinal point at one and
the fame time ; or that the facred writers, one
and all, who have given any characters and nota
tions of time after the Exodus, meafure as well
as compute by the months and days of the lunar
year, exclufive of the folar ; and fince it is undeni
ably certain, that, in all the colledted inftances,
they ftill reckon the years of the reigns of the
kings of Judah, of the Babylonijh captivity, of
the reigns of the kings of Perfia, (the fame may
be faid of the years of the judges, of the 40 years
in the wiidernefs, and alfo of the lives of Mojes
and Aaron) from the vernal aequinox, and never
once from the autumnal ?
My reply to the apprehended difficulty is this :
The miraculous deliverance of the children of If
rael from their /Egyptian bondage and flavery
by the mighty hand and ftretched-out arm ofthe
God of their fathers was an event and tranfaction
of fufficient importance to be the foundation of a
Z new

( 178 )
new aera ; and this too, the aera ofthe Jewijh po
lity, which from hence dates its rife, and derives,
its origin. This polity fubfifted 1 565 folar revo
lutions, before it was finally fubverted.by the Ro
mans. It began and it ended at the vernal aequi
nox, and at the feaft of the paffover ; though the
iemple indeed was not' reduc'd to aflies till fome
time after, i. e. on the ipth day of the Macedo
nian month Lous, as Jojephus relates, 1. 5.ch. 11.
De. Bell. Jud.
From this miraculous eftablifhment of the
Jewijh polity, and the commencement of its cor-
refponding aera, we infer a twofold application of
the folar year ; the one hiftorical, adapted to the
aera ; the other in ftridt propriety, aftronomical,
both as to calculation and meafure.
My reafons for the certainty of this diftindtion,
or twofold application of the folar year, are thefe
two ; although one has been mention'd, and the
other hinted at already.
( 1 ) After the Exodus, God, by the hand of
Mofes, commands the' children of Ifrael to ob-
ferve the feaft of tabernacles on the 15th day of
the 7th month of the facred and ecclefiaftical
lunar year, commencing at the vernal aequinox,
Tekuphath hajhanah, in the revolution of the (fo
lar) year. Therefore the autumnal aequinox, or
the original Mojaic cardinal point, was ftill the >
aftronomical epocha of the fix'd and unalter'd
folar year. (2) The

( x79 )
(2) The Hebrews, IJraelites, and antient Jews,
were acquainted with no aftronomical characters at
the vernal aequinox.
They could not determine the Sun's ingrefs to
aries (as we fpeak) with that exaetnefs and certain:-
ty as they could into libra.
Npr is it any-where commanded, thou fhalt
obferve the feaft of unleavened bread on the 15th,
day of the ift month, Tekuphath hajhanah, in
the revolution of the year. Again farther, they have
no calculations, much lefs did they make any ob
fervations of the Moon's vifibility at the paffover,
in the beginning of the month.,
If we deliberately view fcheme II, of the al
ter'd lunar year, we can reckon no more than 174
days from aries to libra, in the firft fix months of
it : , at this cardinal point only, we find the aftro
nomical character of ;the Moon's phafis. In 1 74
days there are included 5 equal months ; 5x30
= 150. But in every primitive lunar year there
are contained 1 1 equal months, which amount to
330 days. But 330 — 150=180. And juft fo
many days intervene between the autumnal aequi
nox and Rijhon invariably.
My Scripture directory, in this.adjuftment of
themonths, is taken from N°, 6. 2 K- ch. 25.
ver. 27. where we are inform'd,, that Evil-Mero^
dach, king of Babylon, in, the year he began to
reign, lifted up the head of. Jehoiachin, the cap
tive king of Judah* out of prifon, in the 12th
Z> 2 month,

( z8o ) /
month, on the 27th day bf the month, of the
alter'd lunar year, from the vernal aequinox.
Now if from the quantity of a primitive lunar
year we fubftradt 1 1 equal months, or 330 days,
there can remain no more than 24, or 25 days at
the moft, for the 12th month, but here are 27.
Confequently, the 1 2th 'month of the alter'd lu
nar year muft neceffarily confift of 30 days, and
by fcheme II, fo it does.
I have been labouring to prove,, that the Pa
triarchs, the Hebrews, the IJraelites, and the
antient Jews, obferved one and the fame method
of computation.
Ant i qui & recentiores Judai — is a diftinctipn
to be met with in the writings of the learned. .
And this diftindtion is well .grounded, and ne
ceffary to be kept up. But the queftion is, in
what point of time are we to fearch for its epo**
cha ? It is to be wifh'd, that thofe, who made
the obfervation and admitted it, had fix'd the
hiftorical date of its commencement. But as I
do not find this to have been done, my own pri
vate judgment leads me to refer it to the times of
Alexander, about the year ante A.*D. 331 ; be
caufe the Jews, being then difpers'd through the
Grecian colonies, and living under the govern
ment of the JEgypto-Macedonian, and Syro-Ma-
cedonian kings, foon became graeciz'd or helle-
niz'd in their language, manners, and ufages j
and learned from their conquerors to compute by
unequal months, to which the very conftruction
of the primitive aftronomical calendar muft needs
• have

.

( i8i )
have kept them, as it might feem entire ftran-
gers. The fon of Sirach, Jojephus, and Philo- Ju-
daus, are all of them antient writers ; and yet they
muft all be reckon'd amongft the latter Jews.
We cannot but take notice of the fenfible diffe
rence between the interpretation of the Pfalmifi
and the fon of Sirach, of Gen. i. 14. Haju lao
thoth ulemognadim. They both have refpect to
this text; the one in the genuine ftile of an anr
tient Hebrew, the other in the exotic language of
a latter Jew.
The PJalmifi writes, Pf. 104. 19. God has
appointed the Moon — Lemognadim (/. e. for the
regulation and determination of the periodic re
turns of folemn affembly days, which were ever
obferved on the months and days of the facred and
ecclefiaftical lunaryear) without referring to, or
including, the fenfe of the preceding words —
Laothoth. But the author of Ecclefiafticus, vers'd in the
Greek tranflation, plainly refers to, and includes
this miftaken interpretation of Laothoth — a«
2s;uift!jfl-«/i«o*so?Ti)f. From the Moon is the fign of
thefeaft. Then it follows, Eccluf. 43. wr. 7.
The month is called after her name. But neither
was the Moon a fign of the feaft (of the paffover)
to an antient Jew ; nor is Chodejh denominated
from Jareach or Lebanah ; nor is there a Hebrew
text to parallel this.
As to the fori of Sirach, at may be juftly re
marked, that though he has retained and record ed

( 182 )
ed much of the oeeonomical, political, and reli
gious wifdom of the old Jewijh church, yet has
he no where difcover'd any the leaft knowlege
ofthe old He/brew method of computing times. ;
It does not fall within the compafs of my pre
fent defign to enlarge upon this fubjedt ; but from
what has been offer'd, , I may venture to -ap
peal to any impartial and candid enquirer, whe
ther the above citations from Philo, (who was
contemporary with Jojephus) together with -the
calculation of Ptolemy, be not a clear and ~\ fuffi
cient proof, that the Jews, before, at, and after;
the burning, of the 2d temple (how long after I
cannot fay) began their facred year, mito, <™mJVj,
the evening next after the Moon's conjunction
•with the Sun, according to mean motion, and as
inftructed by the Greeks : nor can it be collected
from the aforementioned authors, nor from Eu-
febius, who wrote in the former part of the 4th
century, nor from Rabbi Hillel's aftronomical
year, which was publifh'd about the middle of it,
A. D. 358, that the Jews made any obfervations
of the Moon's' vifibility. ; .
Whether this conclufion be admitted or not
by thofe who aire qualified to criticize, and to fit
as judges upon antient and different accounts ; yet
ftill it is neceffary to preferve a diftindtion, of pe
riods and intervals, and to have due regard to the
refpedtive ufages and cuftoms which are related in
each of them.
,»The ift period then or interval, which merits
our notice, commences with the primitive ages and

( i«3 )
arid origin of time : and if we terminate it in the
3 ad year of Artaxerxes Longimanus, where the
old teftament hiftory ends, it will contain at leaft
an uninterrupted fefies of 3575 years ; but I
would rather extend it to the conclufion of "the
Perfian monarchy, which fubfifted after this 1 o 1
years. The principle fcope and intention of my
fcheme limits my refearches to this interval.
The 2d period or interval I fuppofe to extend
from the conquefts of Alexander, when the Jews
were firft difpers'd amongft the Greeks, down to
the end of the 4th century; how much farther
downwards I cannot fay ; nor do I undertake to
fix the beginning or ending of the 3d period ; I
can only obferve, that the Babylonijh Talmud,
which informs us of the pradtice, made its firft ap
pearance in the beginning of the 6th century.
But now to make fome application of all this :
I fay then, as 12 months of the lunar year and
12 fynodic lunar months are amongft the cha-
radteriftic differences between the computations
of the antient, and of the latter Jews (which
has been obferved before ;) fo is the beginning of
the month on the evening next after the fynod,
calculated by the mean motion, more gracorum ;
and the method of fettling it from the evening of
the Mopn's firft appearance after its conjunction
with the Sun, determin'd by obfervation, toge
ther with the numeral denomination of a 13 th
month (no trace or footftep of which is to be
found either in the Scriptures, or in- Jojephus, or
in Philo ) though their computation was lunar) to
which

C 184 )
which we may add, the fuperftitious tranflation
of Feria: thefe, I fay, are amongft the cha-
radteriftic differences between the computations of
the, latter Jews, and of thofe whom for diftindtion
fake, I, call Rabbins and Talmudifis.
Confequently, as the Julian year cannot be
reckon'd backwards beyond the times of its firft
inftitution by Julius Cafar, without being confi-
der'd as proleptical ; fo neither can that method
of fettling the beginning of the lunar months,
which obtained amongft the Jews in the 2d pe
riod, be reckon'd backwards as a Jewifh com
putation beyond the times of Alexander, with
out being confider'd likewife as proleptical : Nor
laftly, can we extend the talmudical year back
wards to the times of the 2d temple, without en
tirely fuperfeding or fhewing a total difregard to
the teftimony of the moft approved writers of
that age, who treat of thefe points.
It muft be thought ftrange and unaccountable,
that the Talmud and Maimonides fhould fo confi
dently refer the whole affair of adjufting the be
ginning of the facred year, and of determining its
quantity, to the Sanhedrim or great confiftory at
Jerufalem ; that they fhould fo punctually relate
their fitting the whole 30th day of the month,
in a room called Bethjazek, belonging to the
great or outward court of the temple, to take evi
dence of the Moon's firft appearance, and ftridtly
examine the witneffes about the circumftances of
it, when Jofephus, who lived whilft the 2d tem
ple was ftanding, was an eye witnefs of its de-
ftruction,

( **S)
ftrudtion, and wrote not long after it, fhould re
cord nothing like it, or give the leaft intimation
of any fuch cuftom ; nay, Philo his contempo
rary attefts the direct contrary, and refers the
whole to calculation, after the manner of the
Greeks. Thefe things are . too difficult for me
either to reconcile or to comprehend.
Mr. Whifton, in his fhort view of the harmo
ny of the '4 gofpels p. 196, inferts a fcholium,
the former part of which I fhall here tranfcribe,
and leave the reader to judge, how far it may be
thought to confirm the above, diftindtion of ages
and cuftoms.
Scholium. " It muft here be obferv'd, that
il I fay nothing ofthe delaying the month Nifan
ct upon the latenefs of the fpring, and feveral
cc other occafions which, the Jewijh writers fpeak
" of in aftertimes, no more than I do of the
" tranflation of their feafts from one day in the
" week to another, upon fome trifling reafons
" alleged by them alfo. And I Jake no notice
" of thefe things, becaufe they all appear to me
" to be of a later date, and not to have been
" ufed in the times of our Saviour. The rules
" I here go by are the very fame that we find
" in Philo, in Jojephus, and in the other certain'
" remains of that and the foregoing ages ; while
" the other, which we meet with in the later
" Jewijh authors, can by no means prove any
tf jiich antiquity."
If there are any who can implicitly credit the
farrago of the Mijhnah, and the tales of its volu-
A a minous

C 186 )
minous Gemara, I am under no neceffity to make
myfelf an opponent ; fince there is no room to
make it a queftion, whether the authority of the
Pentateuch, and the authority of the Talmudy
are built upon diftindt foundations. For my own
part, I profefs myfelf to give the preference to
the writings of Mofes and the prophets before
all the Tannaim and mifhnical doctors, collective
ly taken. I am forry I cannot conclude this argument,
or even lay the foundations of my fcheme, with
out difcovering a very wide difagreement in fen-
timent, from feveral authors of confiderable
note. I meet with the following , extract from the
writings of the learned Sir J. Marjham. — Mihi
nondum efi compertum quis fuerit , intercalationis
fecundi Adar author, quo tempore caperit. — It is
plain from this paffage, that Sir J. Marjham,
after all his enquiries, found himfelf incapable of
fixing the beginning of the 3d period.
¦  Ludunt operam chronologi qui veterum
Hebraorum tempora ad cyclicas rationes reducunt.
Veteres (viz. Hebrai) non ex Jcripto, non ex com-
puto, Jed ex obfervatione Neomenias Juas notabant.
Tempora quo vetuftiora eo incertiora. Nullum
extat in S. Uteris intercalationis vefiigium ; neque
confiat chronologiam technicam fiante primo templo
Judaisfuiffe cognitam.
Sir J. Marjham has delivered it as his fenti-
ment, that the antient Hebrews — Ex obfervatione
Neomenias Juas notabant— -Bu): he fays this wholly and

( i«7 )
and folely upon the authority of the Talmud and
Maimonides ; for as to Scripture, exprefs tefti
mony there is none.
Dr. Prideaux has entertain'd the fame notions,
and has fallen, I fhall not fcruple to fay, into the
fame miftake, as appears from the following
paffages in the preface to his hiftorical connection,
vol. I.
Antiently the form of the year, which they '{the.
Hebrews and IJraelites) made life of, was wholly
inartificial. For it was not Jettled by any aftrono
mical rules or calculations, but was made up of
lunar -months, fet out by the phafis or appearance
of the Moon. ' When they Jaw the new Moon, then
they began their months, which Jometimes confifted
of 29 days, and fometimes of 30, according as the
new MOon did fooner or later appear, p. 5.
P. 8. — In their intercalated years there was
another month added after Adar, which they called
Veadar ; or the 2 d Adar, and then their year con
fifted of 13 months. 
P. 10. Thefe having been the forms of the
Jewifh year, that is, the inartificial form, ujed
by the antients in the land of Canaan, and the ar
tificial and afironomical jorm now in ufe among
the moderns.  &c. ;
The Reverend Mr. Bedford muft be allpwed
to have employ'd much time and pains on the
fubject of the Scripture chronology, and he afferts,
without the leaft doubt or hefitation about its truth
and certainty, that " The computation of lunar
A a 2 " months

( i88 )
" months began from the creation." p. 24.
fedt.5. " It is evident, fays he in the beginning of the
fame feet ion, that the computation of months at
firft was made by lunar months, which began upon
the evening, when the new Moon did firft appear."
p. 24. fedt. 5.
ic And thus, from the beginning, the month in
Hebrew was called (Jareach) the Moon, or (Cho
dejh) the renovation of light. And the accent,
which fomewhat refembles ajemicircle is called Ja
reach ben fomo. The. Moon a day old, or the
Moon newly begun." Sect. 5. p. 24.
Sect. 1,5. p. 27. ~lt The method therefore ob
ferved by the antient Patriarchs was this : they be^
gan their year with a new Moon— For this pur
pofe they took the beft obfervations they were ca
pable of." 
Sect. 6. p. 24. It is evident, that for the de-?
termining the beginnings of fome months a due care
was taken in the rejpeftive evenings to ' obferve,
whether the Moon was vifible or. not, and report
the fame to Juch who had a power to fix the
months. This was done in Greece to the Epo?o/, or
magiftrates at Athens, and in the land oj Canaan,
to the Sanhedrim at Jerufalem.
This method was certainly ufed in the old world
until the time of Mofes— at the autumnal aequiT
nox ; and after that, by the Jews, at the ver- '
nal. P. 24.
This wes their method until their famous aftro
nomical year was fettled by Rabbi Hillel.  This

( ?89)
This method which they (viz. the Patriarchs,
Hebrews, Ifraelites, antient Jews, and latter
Jews) ufed is exaftly defcribed by the Talmud and
Maimonides. p. 24.
It would be needlefs to tranfcribe any more,
becaufe it is already too evident to be either de
nied or concealed, that when Mr. Bedford wrote
this, he might be juftly faid to have fet at
the feet oft* Maimonides, and not at the feet of
Mofes. It were to be wifh'd that,
Chap. II.
Of the antient method of computing years
and months, p. 23. had not been admitted into
a learned and elaborate treatife of the Scripture
chronology. But here I muft except Sect. 19.
p. 29. which contains a ufeful and demonftrable
truth ; which will prove, in the iffue, an infalli
ble teft and criterion of the genuinenefs and au
thenticity of the Hebrew text, and of the abfolute
certainty of its chronological notations ; its diftindt
epochs and periods.
Mr. Marjhal in his chronological treatife upon
Daniel's 70 weeks chap. V. has given a fum-
mary, chiefly from Mr. Selden, of all that may
feem neceffary to be faid further concerning that
form of year, which is defcrib'd in the Talmud ;
which Mr. Marjhal allows to be a Jewijh year,
but by no means the antient Scripture year, made
ufe pf all along by the facred writers ; much lefs
that,

( *9° )
that, by which the years of Daniel's prophecy of
the 70 weeks are to be reckon'd. This is the
main and fole point, which the whole fcope and
force of his argument is intended to prove, as may
be plainly feen from the enfuing account, which I
fhall give in his own words.
P. 243, 244, 245. " That the form of year,
" made ufe of by the Jewijh Sanhedrin for the
" regulating of their feftivals, fhould have been
"the year of reckoning intended in this prophe-
" cy, it is in no wife likely for the following rea-
" fons.
" Firft, it is no Scripture year. For it con-
" fifted VarioUfly fometimes of 12 months, fome-
" times of 13 months, by the intercalation ofthe
" Jewijh Veadar, or 2d Adar. But of this Vea-
" dar, or 2d Adar in the Jewifii year, we have
" not throughout the Scriptures fo much as one
" fingle mention of it, either by name, or as a
*c 13 th month. Whereas we have 12 months
" byname, and 12 months alfo in order ofnum-
" ber, as the ift, and 2d, and 3d, and fo on to
" the 1 2 th, but never beyond that to the bring-
•c ing in ¦ of a 13 th, any where in the Scrip-
" tures.
" Secondly, It was ever of moft uncertain ac-
" count, as being merely artificial and arbitrary,
" as it depended purely Upon the determination
" of the Sanhedrin. The people knew nothing
" at all about the year current, whether it would
" be a year confifting only of 12 months, or
" otherwife of 13 months, till they of the San-
, " hedrin

c(

(c

( J9i >
hedrin had made public declaration of it. And
this we are told was not ufually done till to
wards the end bf the year. It was,
" Thirdly, A year very uncertain alfo as to its
rife and origin. For who can tell how, or
when it was firft invented ? Nor is it lefs uncer
tain, " Fourthly, As to its continuation. For who
can tell us, of a certainty, how long it was in
ufe among the Jews ?
" Fifthly, 'Tis fo as in itfelf, fo alfo as, to any
real ufe that it could be of to the people, how
ever we are told by the learned Mr. Selden, that
it was the year in civil ufe among the Jews.
" He hath told us this indeed upon the teftimony
" of both the Talmuds, and upon the teftimony
" alfo of Maimonides from them : and yet he
" himfelf has made this moft improbable by his
" own moft juft obfervation of the manifeft diffi-
" culties and uncertainty neceffarily arifing from
" accounting by fuch a form of year.
" But however fetting afide this, methinks
" had it been a year commonly known and in or-
" dinary ufe among the Jews, it fhould have
" been fo in Scripture times; if not in all, at
*' leaft in fome or other of them. And then con-
$c fequently in an intercalary year, we fhould
" have there read of an additional month, known
" by the name either ofthe month Veadar, or the
ct 2d Adar, or otherwife by a numeral denomina-
" tion of a 13th month. " For

( 192 )
" For it is much that whereas, as I before ob-
" ferved, in the holy Scriptures we have men-
" tion made ever and anon of 12 months by their"
" refpedtive names, or in numeral order fo many
" months fpoken of with their hiftorical events
<c for which they are remark'd, that however no-
" thing at all fhould have happen'd through the
" whole courfe of facred hiftory, to the making
" famous alfo a month Veadar, or a 13th month,
" as well as thofe other 12, of which there is
" mention made under a twofold denomination
" as above."
I can readily agree with the very learned chro-
nologift, Mr. Marjhal, that the Jewijh talmudi-
cal year is not an exact exemplar of that, by
which Mojes and the prophets meafured the times
and regulated the feftivals ; yet I cannot admit
his inference and conclufion, which he fo ftrong
ly urges, and fo zealoufly infifts upon in the pages
immediately following, 245, 246, 247.
<e And fo far as Scipture is our light here, not
" this, but the antient Jewijh year, or the Scrip-
" tureyear of 36o,days muft have been the -civil
" year, or the year in ordinary ufe among God's
" people. -
" For, it is in no wife probable, that in the re-
" gulating of king Solomon's officers (1 K. iv. 7.)
" who made provifion for the king's houfhold,
" each man his month in the year, or of thofe 12
" -captains ( 1 Chron. xxvii. 1.) which went in
" and out before the king, month by month,
" throughout all the months in the year, any re-
" gard

( *93 )
" gard fhould have been had to that irregular
tc form of Jewijh year, as it differently confifted
" now of 12, now of 13 months : for had a
" Veader been here to be provided for, as in an
" intercalary year, it muft have been then in the
" cafes before us. 12 officers of the houfhold,
" and 12 captains, each man his month, had not
" been fufficient for the number of months in fuch
" intercalary year.
" — But upon the foundation of Scripture
" months, of 30 days to a month, and of 12
" fuch months conftituting the Jewijh ordinary,
" or common year, the regulation was moft rea-
<c dily adjufted, the monthly fucceffion of officers
" doubtlefs had their refpedtive falaries by the
" fame known and ordinary Scripture year, con-
" fitting now in Solomon's time, as antiently and
" from the beginning, among God's people, of
" 12 equal months of 30 days, and of 12 times
" 30, or 360 days.
" — Upon the whole then, as thus before
" and after the captivity, we have evident foot-
" fteps of a year of 360 days, as a known and
" common form, of year among the Jews, what
" hinders in the prophecy before us given to that
" people, that the year of reckoning intended in*
" it fhould not have been this very Jewijh year,
*c even as a Jewijh form of year, as the fame
tc was, as I have fhewn, undoubtedly their cn-
" tient Scripture year."
Mr. Marfhal has labour'd hard to prevent the
reader from miftaking the Jewijh 13 -month
B b year

( J94 )
year for the true antient Scripture year ; he con
tends that it was. an irregular form of year, and
could not be in ordinary and common ufe, as it
was fo difficult and uncertain in its application 5
yet it muft be faid, that he has mended the mat
ter but very little, and is likely to make a very
infufficient compenfation, whilft he aims to fub-
ftitute in its ftead the imperfect mutilated folar
year of 3 60 days : for 3 60 days can never be made
to meafure the Mofaic Shanah, or a true folar re
volution. Mr. Marjhal' 's hypothefis, and my 3d propofi*
tion are here fet in an irreconcileable ftate of op
pofition to each other ; and my whole fcheme
feems to ftand as yet unfupported by any concur
ring teftimony. It muft make its way and efta-
blifh itfelf, as it can, amidft an endlefs variety of
hypothefes and opinions.
However, notwithftanding this great contra
riety and uncertainty of conjectures (for nothing '
more than conjecture has been hitherto offer'd as
I know of) fome eminent writers of this age
have by their juft and pertinent reafonings, def-
cants, and obfervations, brought us to the verge
of truth. But as foon as they have made the leaft
efforts to reduce this theory and fpeculation to
practice, then ignotum nefeio quid, fome fecret
and in furmoun table difficulties have immediately
interpofed themfelves, and put a flop to all fur
ther progrefs.
Mr. Shuckford, when he firft enter'd upon the
difficult undertaking of connecting facred and pro fane

( 195 )
fane hiftory, adopted a notion advanced by Mr.
Whifton in his theory bf the Earth, and is the bar
fis of his anti-mofaical hypothefis, viz. That the
antediluvian civil year was both folar and lunar
(fo far he is in the right, and will be countenanced
by the Pentateuch) and that each of them con
tained juft 360 days, and were exactly commen-
furate to each other ; that at the flood the hea
vens underwent fome change (by the defcent and
impulfe of a comet, fays Mr. Wifton) and thereby
the folar and the lunar year were lengthned in the
fame proportion to each other, as we now find
them to have ; that long after the deluge, nei
ther the Jews nor any other nation had any no
tion of the years containing any more than 360
days : but when he came to treat of the inftitu-
tions of Mojes's law, and to confider the Jet Jea-
Jons for the conftant and regular obfervance of" its
feafts, his judgment led him to correct, and his
ingenuity to retract the error.
Mr. Shuckjord is the only author I can find,
that ever attempted to frame a fcheme or draught
of the Mofaic year, and he attempts it by the an
nual circulation of the fabbaths. But as he pro
ceeded upon a miftaken hypothefis (being miffed
by Jofephus's wrong interpretation of the Hebrew
text) the refult was, as he candidly acknowleges,
that he could not fatisfy himfelf. However, it
being almoft impoffible for a perfon of his difcern-
ment and penetration to overlook the theory, fo
he reafons extremely well upon it, as will appear
B b 2 from

( 196 )
from the following paffages in his preface to
vol. 3.
" If the IJraelites, when they came into Ca-
" naan, had not been inftructed to compute fuch
" a number of days to a year, as might come
" very nigh to the true meafure of it, they could
" not long have continued to keep their Jet feafts
" in their proper feafons. The heathen nations
" had as yet no notion of the years containing
,c more than 360 days. But fuch a year falling
" fhort 5 days, and almoft a quarter of a day,
ct of a true folar revolution, it muft be evident,
" that the fiated feafts of Mojes's law, if they
" had been obferved in a courfe of fuch years,
cc would have returned 5 days, and almoft a
" a quarter of a day, fooner than the true Jeajon
«' of the year, for obferving them, could have
" returned with them; and this in a very few
" years muft have brought them into a great
" confufion. — p. 2.
" Mofes lived almoft 40 years after his giving
cC the lfraelites thefe inftitutions ; and if all this
" while 360 days had been computed to be sa
" a year, it is evident that the feafts of the law
" would by this time have gone backwards al-
" moft 210 days from what was the real Jeajon of
" the year, at which they were at firft appointed.
" But we find, that when the lfraelites came
" into Canaan, and were to keep the paffover
" there on the 14th day of the month Abib,
" — The corn was ripe in the fields — Jordan
" was in that flow over all its banks, which that
" river

( l97 )
" river was annually remarkable for, all the time
" of harveft — fo that the paffover, and confe-
" quently the other feaftsj fell this year at about
" the times to which Mofes at firft fiated them :
" and therejore the IJraelites muft have had fome
" method to adjuft the computed year to the true
" meafures of a real one. — p. 3.
" But by what particular method the antient
" lfraelites regulated their year, may perhaps be
" difficult to be afcertain'd." — .p. 4.
Mr. Shuckford concludes the whole of thefe
reafonings (whether upon juft and good grounds,
or otherwife, may appear in time) with the fame
fentiment that Dr. Prideaux has exprefs'd in his
aforecited preface, viz. " That antiently the
*' form of year, which the Hebrews and lfraelites
" made ufe of in the land of Canaan, was wholly
" inartificial ; for it was. not fettled by any aftro-
" nomical rules or calculations." What is here
fuggefted may be plainly and clearly colledted
from the 12th, 13th, and 14th pages ofthe
fame preface to Mr. Shuckfprd's 3d volurne.
P. 12.  " In order to fix their times right,
" they were in the firft place to obferve the
" month Abib, the harveft month, to appoint
" the beginning of that to its true feafon ; and
". this they might do in the following manner.
" When they found at the end of the year-^-that
" the harveft was not fo forward as to befit to be
": begun in about 16 days, they might then add
fo many days to the end of their year, as might
be requifite. This, I think, might be the
" me

te

<(

( 198)
method, in which the antient lfraelites adjufted
their year to the feafons. We may obferve of
" this method 6f adjufting the year, that it is
,c eafy and obvious ; no depths of human fcience,
" or fkill in aftronomy, are requifite for the pro-
" ceeding according to it : the lfraelites could
" only want once in about 20 years to lift up
" their eyes, and to look into their fields, and to
" confider before they proclaimed the beginning
" of their month Abib, whether, or how much
" they wanted of being white to harveft ; and this,
" with the obferving, their fabbaths as above re-
" lated, would furnifh them with a year fully
" anfwering all the purpofes of their religiori or
" civil life : and this method being thus capable
" of anfwering all purpofes, without leading
"' them to a neceffity of fixing aequinoxes, efti-
" mating the motions of the heavenly bodies — I
" am the more apt to think, that this was the
" method which God was pleafed by the hand of
" Mojes to fuggeft to them."
There is a very near affinity between what is
here offered to the reader by Mr. Shuckford, and
the above cited remark of Sir J. Marjham,
" Neque conflat chronologiam Technicam flante
" primo templo Judais fuiffe cognitam."
Although Dr. Prideaux has given fuch a parti
cular account of the Jewijh year from the Talmud,
and has miftakenly applied the practice of the
lateft times, and in the 3d period, to the antient
IJraelites in the land of Canaan ; yet no one mo
dern writer has traced with a more juft exaetnefs the

( 199 )
the out-lines of the Mofaic computation, than he
has done, whilft he has made no attempt to fill
them up, or to frame a calendar. In the ioth
page of this fame preface, fpeaking of an addi
tional month in order to keep the beginning of
the lunar year, as near to the cardinal limits of
the folar, as fuch intercalation could effect it
(fpeaking ftill rabbinically) he reafons in the fol
lowing juft manner upon the precife bouridaries,
and the pundtually determin'd feafons of the facred
and ecclefiaftical Scripture year.
" They were forced, fays he, to eaft in ano-
" ther month, fometimes in the 3d year, and
" fometimes in the 2d, for the fake of their fefti-
" vais. For their feaft of the paffover (the ift
," day of which was always fix'd to the middle
" of their month Nijan) being to be celebrated
" by their eating of the pafchal lamb, and the
" offering up, of the wave fheaf, as the firft fruits
" of their barley harveft', and their feaft of pen-
" tecoft, which was kept the 1 5th day after the
" 16th of Nifan," — (fays Dr. Prideaux, upon the
authority of Jofephus, but the Hebrew text ex
prefsly fays, Mimmochorath Haffabbat, e craj-
tino ipfius Jabbati, on the morrow after the
(feventh day) fabbath, in the paffover week,
which was the day in which the wave fheaf
was offered) " being to be celebrated by the of-
" fering of the two wave loaves, as the firft fruits
" of their wheat harveft ; and their feaft of ta-
<c bernacles, which was always begun on the 1 ,5th
" of Tifri, being fix'd to the time of their inga-
" thering

( 200 )
" thering of all the fruits of the Earth. The
<c paffover could not be obferv'd till the lambs
" were grown fit to be eaten, and the barley fit
" to be reaped ; nor the pentecoft till the wheat
" was ripe; nor the feaft of tabernacles,, 'till the
" ingatherings of the vineyard and olive-yard were
" over. And therefore thefe feftivals being fix-
" ed to thefe Jet Jeafons of the year," — here I will'
beg leave to fubjoin — by the immediate appoint
ment bf God ; Rijhon, the head, the beginning,
the ift month of the facred lunar year, muft,
and ever did fall (under certain determinate varia
tions) on the divinely appointed feafons of the
true folar.
Can we poffibly read and lay together thefe
things, as ftated in Dr. Prideaux's own words,
without making it a juft matter of wonder and fur-
prife to find the whole of this evident aftronomi
cal theory funk and loft in a (fuppofed) rude, un
certain, and inartificial adjuftment of that very
year, which has the fingular privilege of claiming
the creator himfelf for its author and inftitufor,
and is, we may be fure, as perfect as infinite wif-
dom thought fit to make it. .
Mr. Whifton, from a remote diftant view, and
a fort of apprehenfion of an aftronomy in the He
brew bible, expreffes himfelf thus in his fhort
view, &c. p. 17. " There is good reafon to doubt,
*' whether in the days of Jeroboam f almoft any
1 ' other nation but the Jews, whowere thereinguided
" by divine revelation, knew and made ufe of a
" fixed folar year or its equivalent." When I com pare

( 201 )
pare thisfiktoourabkjkoncejfion and Jplendidinfinua-
tion,". with/feveral pofitions to be met with in
this treatife, directly oppofite to, and fubverfive
of it, I cannot but conclude that — he wrote an im
portant truth, .without attending to what he wrote,
or knowing for a certainty that it Was a truth.
That he .did not, know for a certainty that it
was.a.trutb,)imay be evidenc'd from his confus'd
antbijberpl^x'd interpretation- of propofition II,
:w»hich»we firidifet dowji at^rge,' p. 15.
I'inLt! yd e^,W.v^Oo ¦".•¦: ... -v
-\M1. •" Tbafo Jemifh^eir-, by which the facred
•5( i writers* ireckaasMthe feveral . intervals fince the
'hdsinge\l®xat tesfafwae-thhExodus out of /Egypt,
'$\w^ £ifherA1l&e frifc.jbll&ye^yor ¦ a lunar one
'^ifi>fad|j)ifte4 %w.pJ!^pBi) intercalations to, the fd-
JSi la^/^s'toIKevinia ininn(e!C.eqhivaleAtto it."
ih amarbl aiodw sr'j ni A*r r ' > V\i ¦• /-"-¦
This propofition has two faces, ©ne of which
looks towards the Pentateuch, the other towards
tfcie ^aJkarari; > for Mofefn®. (where mentions,' or
§l&e&<the leaft; hint of, ^anl intercalary month in the
-Iwainyear. £ Land ¦ we "linay) :from hence reafonabty
conclude- jtfafltheE^akutffivbiffome feCret,' and a*s
yet, unknown law in the Mofaic lunar computa
tion, which thetfrnfifioriarycon^pller of the Mi/fana
and the Talmudical dodtors were utter ftrangers to ;
and it is the ofiace.of the Scripture ehroriologift to
ufe his> endeavours toinveftigate and unfold it.
As;Mh Whifton'sicomment and jcholium an
nexed to Prop. II are very mifcellaneous, and
abound with hefitatioris,, doubts, uncertainties,
C c and

( 202 )
and reverie, I fhall not decline the trouble of
drawing up and laying before the reader a fynopfis
of their contents.
Comment. I. " This (adjuftment by proper iri-
" tercalations) is evident, becaufe their year by
,c the exprefs law of God was to be commenfu-
" rate to the feafons." II. It may be queftion'd,
" Whether the Jews ufed the lunar yeaf before
" the Babylonijh .captivity, as they have done
" fince," (viz. the time of Alexander, by lunar
months ?) Anfwer'd — " ft wants not its probabi-
f< lities, yet is it by no means certain ; and is of Jo
(l J'mall confequence either "way, we need not fpend
" time in the enquiry about it." III. " The Ju-
" Han year is fo near to the Jewijh year (whether
" it were folar or lunar) that it will fupply its
tc place, well enough, in the whole fcheme of
" facred chronology."
Scholium. I. " The Julian year meafures the
" poft-diluvian year only j for the year before the
'" deluge was of a jhorter duration, and contain-
" ed but 360 antediluviain days. Proved,
(1) " From Mr. Whifton's edition of his new
theory of the Earth.
(2) " From the Mofaic account of that year
wherein the waters were upon the Earth.
(3) " From the bifliop of Wbrcefkr's differta-
tion concerning Daniel's weeks. (4)

(C

cc

t(

(203 )
(4) ¦*« From the antiquity of this year of 3,60
" days; it being the mofi antient civil year, of
which any footfteps remain in hiftory, for a
long time after the flood.

<< tc

C{

II. " It is poflible, and not at all abfurd to
", fuppofe, that the poft-dUuvian patriarchs be-
cc.fore the Exodus us'd the fame year-, and that
Mofes alfo refers to the fame, in the hiftory of
thofe times, till the divine law interpofed.
*c But, III. It is neceffary to fpeak with cau-
" tion in the prefent cafe, Becaufe,
(1) " We have no pofitive evidence, from the
" Mofaic ftile, ofthe ufe of a different year fince
" the flood. And,
(2) ,*' Beqaufe* if the Patriarchs did ufe the
" year of 360 days, yet Mofes in his hiftory might
" reduce thofe years to that natural one — which
c? was us'd afterwards, and give us the whole
" -.period fince, the flood in the fame method of
"computation. \ .-,
-; (3) "c* .Becaufev all chronologers have hitherto
*' fuppofed the year in Mojes, before and after
" the Exgdus, to be the fame. Therefore,
IV. 'Mt is not fafe without more exprefs evi-
" dence to»difturb the fettled account of thofe
" times, but we fhall. jitppoje the- year fince the
" the deluge to be conftantly the fame. And,
V. •" Equivalent to the Julian."
C c 2 Thus

(,2p-4-)3
T\hus being come to the bottom ofthe account
byfummihg up the whole, we are>gn/5en.; to< un-1
derftand, contrary to all our hopes and expedta-'
tions, that Prop. II. both that patit. ofr it which
is Mojaic, and that which is Talmudic, muft be
difcarded, abrogated, cancel'd ;: whilft fhe'lealilri-
ed and heterogeneous fcholium; conveys juftlfd"
much inftrudtion and no more,- than what arch '-
bifhop Ujher had long before left* upon r record in
the preface to his annals, vizj^lih ,.r.v '¦= :?.
.'•.. • -d,i • ;<¦:•, ' .vVj ,.j ;t[ ,'iJI sJ-.':i "
Primorum patrumj >vehrumque3/Egyptidrum '&
Hebra'orum annus, 'ejujdem cum Juliana quantita-
tis'fuiffereperitur. -:• - ¦ ¦¦¦; *•, ^..d^V/ ^ (i.)

,-f,

¦KJf: ,*:\J

So when the mountains labdur'd ta!proclucei ¦
Some huge gigantic birth— -oufcpop'd a mc^ufe.
- > ¦ ' ' • i " ' . -***¦. mi
¦ li * ' ' ¦ ,.f. - > ,„f V ;•¦ ' » i:: j j
Iti is-a confiderable objection againft1 'Mi* Bed
ford's proceedings, that, notwithstanding the pro-*
mifing-1 title of his book, he no where fuppojfes
either any latent principles of aftrononaypin. the
Pentateuch, or -any the leaft degree of krio\iyl^ge
of it in the Patriarchs. They only (according to
his Talmudic hypothefis) fettled the beginning of
their year by an obfervation of the Moon's viabi
lity (if not obftructed by clouds, and therebyVren-
der'd uncertain) about the time of the autumnal
fequinox, as near as they could compute.
1 They were fuch proficients in the celeftial fci
ence, that they could as certainly computethe -num-

C 2°5- )
number of years by furhmers ; as , the -number oi:
da^soby- .Suri-rifipgs. . . And her very ferioufly .fug-,
geftstfO; this. (fame. -.-chapter of principles, that the
jodpini&n Gregorian -year might ferye-. (Mr. Whip
^'T.theraftronOmer, .adds -well enough} for a juft
Computation, .without, any fenfible, difference horn?.
the^egltfnipg-.of the world . f| . May ,we .not. infer
fjtbm. henee,S, that fbad itriotvb.een.for Julius Ca\
j^f?a'.aiheathew-,..fand:Pdpe Gregory ^ 3, , Adam.and.
the^mfi o£r xhie.i^vimitive Petriartihs would1 jhaye,
had:?n«jfQ,laf year ,at'rall?t!And.yet,i.,Mir. Bedford
and Mr. Whifton] bdthvof "therft, explain;,, as aftifo-?
npwfcw®iihe. iMofaJicK)8h&n@H% and >bpi-rig,;;p:fo-
GegdQdijthijjs .-far,- they unkindly..- pahn upon us the
ohfjl ^&"<^jyeaif;iriiitsftead..j,..ii,u ,h\. ¦¦.-;-¦ f< vt ,-';;
'nu^aSmgt^tMr.lBedJord'^s^ehsmei us gfdfsly.ig-
toBtanfe.vW,e,',ar€ $0 fuppo-fe him, makingrari obfer-
wsift^in.h'fycjm? two treefoj or fetting Ap two! fticks,-
direfl^oppofite to fach other^ upon a horizon-.
irf ojjejfcftiej ,-:t$< leannflfrpmnthe^projedtion of- the
fhadovVj**whether»the declination of , the.Sun was
northward or fouthward. ',
-I- have -no intention or defire fo 'depreciate
Mr. Bedford's labours, and I am, to my great
fatisfadtion, affured, that he had a full view of one
Mofaic principle* though in his calculation he
takes; no fmall pains to conceal it, for a reafon
hereafter to be.explain'd. And I may take oc-;
cafion to -make it appear, that by the affiftance
and direction of this one Mofaic principle, he was
ienabled to effectj what all his fkill in modern
aftronomy,, his ; too familiar acquaintance with rab-

( 206 )
rabbinical learning, and the trafh and trumpery
ofthe Talmud, could not have enabled him to do.
It is a circumftance to be remark'd, that arch
bifhop Ufher and Mr. Bedford have built upon
principles quite the reverfe to each other. ... The
archbifhop fuppofed that the antient I/raeHteshad
no acquaintance with the lunar year; Mr* Bed' J
ford, on the contrary, that they had no certain
knowlege of the folar.; Unite thefe contrariant
hypothefes, and add the patriarchal law of con
nection; then from this union and compofition:
will arife the true Mojaic twofold year. <¦" j
I freely profefs, that I fhould have thought it
an extreme difappointmentj had it been impoffi
ble to have difcovered, I will not fay the out
lines only, but a well-concerted fcheme of Sun
and Moon aftronomy in the Pentateuchjr and
throughout the Hebrew bible. I enter*dupon
the fubject and profecuted the enquiry with no
fmall degree of confidence^ that it was poflible to
find, in the writings of the divine legiflatoiy fuch
principles, mediums, and data, as would be in
themfelves fufficient to eftablifh and demonftrate
an uniform and moft perfedt fyftem of aftronomi-*
cal chronology.
And indeed the very ftile of Mojes's chronology
muft neceffarily tend, I think, to create fuch a fecret
perfuafion, at leaft, in the mind of every attentive
reader. E.g. — After 430 years, (in the ift month,
on the 1 5th day of the month) on the felf-fame
day it came to pafs, that all the hofts of the Lord
went out ofthe land of /Egypt, Exod. 12. But

( 207 )
But when we add to this the ftrict precepts to
obferve every inftitution of the law in its Jet and
appointed feafon, we are in the plaineft and the
flrongeft terms diredted to conclude, that,
In what proportion foever wejuppoje the Mo
faic Shanah to exceed the true meafure of a folar
revolution, in the fame proportion exadtly (mul
tiplied by a confiderable number of years) the fet
and appointed feafons muft depart from the fefti
vals. On the other hand, in what proportion foever
the Mojaic Shanah be fuppofed to fall fhort of the
true meafure of a folar revolution ; in the fame
proportion exactly the feftivals muft depart from
the fet and appointed (folar) feafons.
And yet Mofes, without making any allowance
for a fuppofed excejs on the one hand, or a Juppofed
defeft on the other, thus fixes the feafon, and
thus enjoins the regular and conftant obfervance pf
the inftitution of the paffover, and ofthe feaft of
unleavened bread attending it.
Levit. xxiii. 5. In the i^thdoy ofthe \fi month,
at even, (Heb. bin hagnarbajim, i. e. in the mid
dle diftance between noon and Sun-fetting at the
vernal equinox) is the Lord's paffover.
Ver. 6. And on tbe 1 $th day of the fame month
is thefeaft of unleavened bread unto the Lord : fe
ven days ye muft eat unleavened bread.
Exod. xiii. 4. This day came ye out in the
month Abib, i. e. of ripening, or at the vernal
aequinox, Ver.

'(:2o8<)
Ver. to. 'Thou jhalt'y -therefore keep- Ibis-tfMi-
nance l Lemognado, in it's feafon -, Mijamim Jemi*
mah. '.-,.' ' " ' - -¦'" ¦'¦>'} "< V.'. -;\-\v,
Exod. xii. 14. ^fti this day '_/&#// & nniojoh
for a memorial; vand you] Jhall keep' it a feaft uhto
the Lord throughout your generations : you Jhall
keep it a feaft by an ordinance for ever. ..<¦- .fr -
Ver'.; 1 y.- And ye Jhall objerve the feaft- bf un
leavened bread; jor in this felf-famejiday",^i>^:7
brought your armies out of the land of iEgypt t
therefore jhall; ye pbj'efcve this- day in your gsnkra-
tions, by an ordinance--' for' ever\ i.e. du^riig\ the
continuance of youf temporary ¦ polity; n ' , n yu i ,
...Now. J fay,1 if Mvjis had 'not delivered to the
IJraelites together with thefe precepts a true aftr©-
nomical calendar - ( fuppofingv tbemVto- have yno
traditionary or practical knowlege of f\iCh a one)
inftead of acting the paftof a wHfe arid divirie-fe^
giflator, he muft neceffarily have fdbjected! hiaik
felf to the juft imputation of a rigid and; Severe?
tafkmafter ; not unlike thofe ¦ /Egyptians,^ who
enjoined > the daily tafk, and exacted tlie1 con
ftant tale of bricks/ without afford ing any,. ftraw*;
At the end of the. calendar before our common
prayer book, 'we have, * - -.:i - -. • .= i*.

T'3'V' "'.iV'

A table -to find xhif\er for eveA

-v

The principal decorations and erabellifhmHnts
6f this -table- are the golden 'numbers, -or primes;
in the firft column on the left hand. . The title
prefix'd is a manifeft indication, that the authors of

( 2°9 )
of thefe pafchal (commonly called) Nicene canons
aimed at a conformity to the precepts, of Mofes^
enjoining the antient lfraelites to obferve in ite
feafon the feaft of the paffover ; and they tacitly
eftablifh'd thefe canons, as if they had been drawn
up and exprefs'd in the following authoritative
ftile, viz.
Ye fhall obferve the Chriftian Pafcha always
upon the i& Sunday after the ift (aftronomical)
full Moon, which happens either upon or next
after the vernal aequinox, viz. the 21ft of March.
Ye fhall obferve the feftival of Eafier by this
rule, and by this table, throughout your genera
tions, by an ordinance for ever.
And yet we find by experience, notwithftand-
ing the golden numbers, that the two great lumi
naries have been fo far from giving their Janftion
to thefe authoritative canons, that the Sun has
departed about 1 1 days, and the Moon above 4,
from the original pafchal limits ; from whence
we affuredly know, that they are of mere human
appointment, and not poffibly of divine inftitu
tion. Now here comes the main queftion to be
folv'd in the courfe of this enquiry, which is this;
viz. what was that form of year, that fure and
unerring rule of computation, which could ena
ble the antient lfraelites to obferve the inftitu-
tions of the law in their divinely appointed fea
fons ? And this, throughout their generations, by
an ordinance for ever ? D d And

( 210 )
And it may with good reafon be made a que
ftion ; fince the Europaan nations (however cul
tivated and improved by philofophy and fcience)
are not, as yet, poffefs'd of any fuch perfect civil
year, nor have they juft grounds to boaft of any
fuch indefectible rules of calculation ; the many
different eftimations ofthe tropical year are a fuf
ficient proof of this.
" And I think it was never pretended" (as are
the words of Dr. John Wallis, profeffor of geometry
at Oxford, in a letter to his grace the archbifhop
of Canterbury, dated Oxford, June 13, 1699)
" That the civil year ,muft needs agree (exactly
" to a minute) with the calefiial, and if never fo
t{ much affected is impoffible to be had." But,
perhaps, this may be found a too hafty and pre
cipitate conclufion.
The Julian year has meafured, fince its firft
inftitution, 1795 entire revolutions. And it re
mains to this day in the fame ftate of imperfec
tion, as it was then in, when it came out ofthe
hands of the Egyptian Sofigenes. We ftill conti
nue to reckon for 3 years fuCceffively, with the
old Egyptians and Chaldaans, 365 days precifely ;
whilft the Sun annually meafures almoft one
fourth' part of a day more : confequently, at the
end of every 3d Julian year, there is a manifeft
deficiency of near 18 hours from the Sun's courfe.
But in every 4th Julian year we compute 366
days, whilft the Sun equably meafures as before.
But the excefs of the 4th year being equal to the
defect of the 3 immediately preceding by the un- na-

( 211 )
natural aid and affiftance of a quadriennial inter
calary day, the Julian and the tropical folar re
ckoning are brought to a near equality.
And how have the aftronomers, labour'd from
age to age fince the cultivations of fcience to de
termine, if it might be, the exaft quantity of their
difference ?
Repeated obfervations, as experience has affured
us, have been found inadequate.
Sir Ifaac Newton has carried the rules of art, I
will venture to fay, as to this particular cafe, to
their Ne plus ultra, and yet it is uncertain.
Science has hitherto been contented to fubmit
to the determinations of art, and, in every calcu
lation, affumes the artificial conclufion, as a firft
principle of nature.
But if external nature be inacceffible, and turns
us over to artificial rules ; if the adequate correc
tion of the quadrant cannot be absolutely afcer
tain'd upon the principles of the Pentateuch, and
the data of infpired Mofes ; then a due adjufiment
of this primary ordination and original eftablifh-
ment of the creator muft ftill remain uncertain.
To proceed ; as Mr. Whifton by his doubting
comment and Julian Scholium has entirely fet
afide and render'd quite evanefcent that fpecious
propofition which he had laid down, as cited
above, I fhall here fupply its place by the follow
ing one.
That original antient year (of the Patriarchs,
Hebrews, lfraelites, and Jews, who lived before
the time' oi Alexander) by which the facred wri-
D d 2 ters

( 212 )
ters reckoned the feveral intervals from the firft
point of time to the 3 2d year ofthe reign of Ar-
taxerxes Longi manus king of Perfia, was the true1
folar year ; with which the twofold lunar ye'ar
(both ecclefiaftical and civil) was conftantly con-
mefted, and carried all along together with it, by
the laws of an extremely curious and mofi exaft
aftronomy. This is my account, in general, of the Mojaic
twofold year.
Before I enter upon the direct proof of this
propofition, and its feveral parts, I think it pro
per and neceffary to take notice of xsmi *5 **'?<"»
times and Jeafons, two very frequent and impor-,-
tant diftinctions in the terms of facred chrono
logy. The, word jeajon, in our language, is equivo
cal ; and without fome particular remarks ^and
obfervations may be apt to miflead the concep
tions of a mere Englifh reader.
Xf oca/, times, are meafured by the annual revo
lutions of the Sun, which muft neceffarily include
and diftinguifh the 4 feafons, viz. autumn, win
ter, fpring, and fummer. But thofe 4 feafons of
the folar yeaf are not called by the Greeks, **(?<»,
but co*>&t-
The PJalmifi compares a good man to a tree
planted by the water fide, which fhall bring forth
its fruit in its Jeajon. Here one vers'd in the
Scripture computation and careful application of
its terms, if an Hebraician, would not expect to
read in the original text, Lemognado, but Beg-
nitto j

( 2I3 )
nifto; which ftand as diftinguifh'd from each
other in the Hebrew language, as «a;?cu and »?«
in the Greek : and , both of them more fo, than
times and feafons, according to the vulgar accep
tation in the Englifh.
In the 14th verfe of the ift chapter of Genefis
we read in our tranflation, and God Jaid, let them
be for figns and for feafons, and for days and
years. Here the original word mogdanim, and
the Greek verfion, k*h>os, have no immediate refe
rence in their primary fignificatiQn to the 4 jolar
jeajbns, which are included in the following word
Shanim-, but in this, and in other texts, they, in
their fcriptural ufe and application, exprefs the fa
cred and ecclefiaftical feafons, pinn'd down indeed
to the folar ; they principally, if not conftantly,
denote folemn affembly days — holy convocations
—fet conventions, or fiata Jacra; nor are they
computed and adjufted by the annual revolutions
of the Sun, but by the months and days of the
year ofthe Moon.
God has appointed, fays the PJalmifi, the
Moon, Heb. Lemognadim, Gr. w x.a.1^, i. e. for
facred, folemn, ecclefiaftical feafons, periodically
returning. St. Paul calls the year of Chrifi's Nativity,
wAMf apa, T* x?0'^' trie fnllnefs of time, Gal. iv. .4.
But, ox.a/fof, the feafon. of that time will be
proved to be the 1 5th day of the 7th month, or
the feaft of tabernacles ; which is the only feaft
of Modi's law, whofe celebration was folemniz'd
with an octave. The ift, typifying and fore-
fhew-

C 214 )
fhewing the day of his birth ; the laft, of his cir-
cumcifion. And I doubt not to fay, that the
Scripture aftronomical demdnftration of the birth
of the Meffiah, both as to time and feafon, will
merit an attentive examination. But before we
attempt to raife a fuperft.ru cture, we muft lay fure
foundations. When our Saviour's difciples, after hisrefurrec-
tion, propos'd this Jewijh queftion to him ; Lord,
wilt thou at this time reftore the kingdom to If
rael? They received this anfwer, It is not for you
to know, x?oV*< $ **'? Kf > times and feafons, which
the father has put in his own power.
There is a remarkable paffage in the evangelical
hiftory, which will convey to the mind a very
clear notion, I think, and a very affecting fenfe
of this fcriptural term, kai^. When the paffover
day was come, in other words, in th^ beginning
ofthe 14th day of the ift month of the facred
year, which Mojes calls Abib (vernal) and the
Evangelifts, one and all, defcribe by a periphrafis,
ftill refering us to the Mojaic pafchal canon? in
the 1 2th chapter of Exodus (which he that run
neth, while he reads, cannot but perceive ) Jej'us
fent before him two of his apoftles, Peter and John,
from Bethany to Jerufalem, faying unto them,
Go into the city unto a certain man, and fay unto
him, the mafter faith, o *«<? 0; ^ iyyo; uTi-^-Mat.
xxvi. 18. Our Englifh tranflators have render'd
it, my time is at hand ; but the word in the ori
ginal is not xjsw time ; but km^ feafon. As if
it had been faid, the before- appointed feafon of my
being

(2I5)
being'offer'd up as the true pafchal lamb is at hand ;
mypredided (Exod. xii. 6.) day (of the month)
is come ; my predicted (Exod. xii. 6.) hour (of
the day) is coming, o »*/?<>* ^ c_yy0S «Ti — Chrift
diedj fays St. Paul, Rom. v. 6. k<lt& kai^ov.
Whether this diftindtion,which I have here offer'd
to the reader, has been obferv'd and approved of
by the commentators in general, I cannot fay ;
but I am ftrongly perfuaded, that if parallel places
be confulted and laid together, it will appear to
have a juft foundation.
Being now fupplied with a fufficient flock of
principles, data, and terms, to enable me to
frame the integral calculation, I fhall with plea-
fure enter upon the proof of my 6th, 7th, and
8th propofitions, (the 5th will be confider'd,
when we come to afcertain the aftronomy, both in
the beginning and in the end ofthe year of Noah's
life 600, A-M. 1656) which no one, from what
appears, has ever yet attempted.
I could with that the intelligent reader would
not think, that a bare tranfient and curfory pe-
rufal of the Mofaic table annex'd would be
fufficient to qualify him to pafs a true judg
ment and determination concerning it ; but that
he would examine it thoroughly, with as much
care and attention, as it really deferves. I have
endeavoured to illuftrate feveral particulars by
obfervations and remarks, to which he will be
able to add, I do not doubt, others that may
have efcaped me ; and as foon as he fhall be con
vinced

( 216 ,)
vinced of its truth, certainty, and perfection j
and fhall have a clear view upon what an impreg-
nible foundation it is built, and that, like the
books of kings and_ chronicles, it is an uncommon
teft and Criterion of chrbnological fkill and acu
men, he will not regret either the time or pains,
that a due examination of it (for it muft be ftu
died) may have coft him. •
It has been the moft ufual method to make
two diftindt tables of thefe genealogies ; the one,
ofthe Patriarchs who lived before the flood ; and
the other, of thofe who lived after it ; and like-
wife to end the account at the birth of the eldeft.
fon of Terah, who was born to him, when he
was 70 years old : but as in itfelf it is one con
tinued table from JLdam to Jofeph, I have fo re
prefented it ; and, doubtlefs, it ought to be fo
exhibited j for why a divifion ? And I am fure
there is very good reafon to afk, why a mutilation
of this incomparable canon ?
Had I produced Mojes's canon of Patriarchs
(as Dr. Overal dean of St. Paul's produced Pto
lemy's canon of kings) from fome very antient
MS. which had lain buried in obfcurity and
oblivion for ages, and publifhed it together with
the demonftration, need it be doubted, whether
all the curious would have highly admired, and
have proportionably rated the genuine antedilu
vian antique.
The intrinfic value and fuperior excellency of
this Mojaic table arifes from the- perfection of
its

( 217 )
its inherent aftronomy, and the curiofity from its
high antiquity.
The moft antient ethnic epocha is that of the
fiege and the taking of Troy, which Diodorus Si-
culus and Dionyfius of Halicarnaffus agree to
place in the 408th year before the Olympiads. ¦
The firft Olympic game, after its reftoration by
Iphitus, was celebrated A. M. 3232, in the 33d
year of Uzziah or Azariah king of .Judch, at
the fummer folftice, according to this fcheme of
facred chronology. From A. M. 3232 fub
ftradt 408 years, remains A. M. 2824, the
10th year of Ja'ir. But this backward com
putation, from the 33d year of Uzziah king of
Judah, A. M. 3232, to the 10th year of Ja'ir,
A. M. 2824, will not reach the death of Jojeph, by
445 years : and when Jofeph died, the Patriarchs
had been in poffeffion of an aftronomical calendar
and computation, 2369 years. This indeed muft
be acknowleg'd to be very extraordinary, and
will not be implicitly credited, but upon fuch
evidence and proof, as will amount, without ex
ception or referve, to a mathematical certainty.
When archbifhop Ufher contemplated the ta
bles of the genealogies of the Patriarchs, both
before and after the flood ; the folidity of his
judgment would not permit him to fubfcribe to
the abfurd traditional notions of the Jews, that
the Patriarchs were all born and died at the au
tumnal equinox, on the fame month and day :
yet it led him to adopt an hypothefis unwarranted
by Mofes, viz. that the lives of the Patriarchs
E e were

(2l8 )
were (only) to be eftimated like the reigns of the
kings of England, in our chronicle ; where the
odd months and days collected and included
meafure the whole diftance fince the conqueft ;
dating the beginning of the account, Oft. 14,
A. D. 1066. And it is more than poflible, that
the learned prelate would have fmiled at the fim-
plicity of him, who fhould have fuggefted to
him, that the years of the Patriarchs run pa*
rallel with thofe of the world, without any re
gard to the particular day, either of their birth,
or of their death ; juft in like manner, as the
years of the reigns of the kings in Ptolemy'^ canon
run parallel with their correfponding Nabonaffa-
r-ean years, without any regard to the month and
day of the month, in which they began and end
ed their refpedtive reigns, and as they were re
ckoned in the annals of the feveral kingdoms.
And further, that the only effen tial difference
between Mojes's canon of Patriarchs and Ptole
my's canon of kings was this, viz. that the firft
in itfelf confider'd is truly aftronomical, becaufe
built upon an aftronomical year ; whilft the other
is not, as being founded on a civil one.
As this Mojaic table is the very bafis, and the
main fupporting pillar of the whole fabric of fa
cred chronology, we muft carefully look to foun
dations ; and be able and ready to prove, when
called upon, that the whole and every part is
rightly and duly conftrudted, according to the
original plan of Mofes,;. and in exadt conformity
to his explicit directions : for it may with fome
pretext

( 2I9 )
pretext of reafon be alleged, that according to
the table Noah was 302 years old at the birth of
Shem ; whereas, on the contrary, Mojes expref-
ly writes, Gen. v. 23. Noah was 500 years old ;
and Noah begat Shem, Ham, and Jap het.
• 'Tis certain that this text demands our fpecial
attention with refpect to Shem, by placing him
the firft inlorder; and poffibly a hafty inconfide-
rate reader might be prompted to infer priority
of birth from priority of order: but if he fhould,
he would conclude erroneoufly, and in flat con
tradiction to the Mojaic data, and circumftances
of the hiftory, as may be plainly feen by collect
ing and duly comparing them.
Ch. vii. 6. Noah was 600 years old when the
flood of waters was upon the Earth, i. e. he was
in his 600th current year, ver. 11. For Mofes
conftantly compleats the current year, when he
has occafion to mention the age of a living per
fon. Thus, Abram was y ^ years old when he
departed out of Har an. Again, Jofeph w as 30
years old when he ftood before Pharaoh. I need
not produce any more examples.
Gen. xi. ro. Thefe are the. generations of 'Shem:
Shem was .100 years old, and begat Arphaxad,
2 years after the fiood.
Now from thefe circumftances of the hiftory
we may argue as clofely and certainly as in the
mathematics. For if Noah was 600 years old at
the end of the year in which the deluge happen'd,
then at the end of 2 years after it he muft be 602 ;
therefore from 602 fubftradt the 100 contem-
E e 2 porary

( 220 )
porary years of Shem's life, remains 502 for the
age of Noah at the birth of Shem, as fet down in
the table.
Shem is placed the firft in order, .becaufe, a-
mongft other reafons, the chronology and the ge
nealogies are continued in the line of Shem, and
not in the line of Japhet or Ham.
It may likewife be urg'd by way of objection,
juft in the fame manner as in the aforemention'd
cafe of Shem, that according to the table Terah
was 130 years old at the birth of his fon Abram;
whereas, on the contrary, Mofes exprefsly writes,
Gen. xi. 26. And Terah lived 70 years, and be
gat Abram, Nahor, and Haran.
But fhould any one, by the fole guidance of
this text, again infer priority of birth from prio
rity of order, he would again conclude errone
oufly, and in direct contradiction to the circum
ftances of the hiftory, as plainly related by
Mojes. Gen. xi. 32. And the days of Terahwere<20$
years. Gen. xii. 4. Abram was y$ years old when he
departed out of Haran.
Mojes, by thefe data, has clearly, taught us to
argue and conclude in this manner. From 205
years fubftradt the 75 contemporary years of
Abram s life, the remainder 130 rightly- deter
mines the age of Terah, at the birth of A&r am.
Abram is pkced the firft in order for the fame
reafons that Shem was, becaufe the chronology and

( 221 )
and the genealogies are continued, in the line of
Abram, and not in the line of Haran or Nahor.
I am fenfible but of one objedtion more of this
nature, which can be made, and it is this. Ac
cording to the table Jacob was 9 1 years old at
the birth of his fon Jofeph. But here it may be
afk'd, where does .Mi?/^ fpecify the age of Jacob
at the birth of Jofeph? I anfwer very plainly and
clearly in the circumftances of the hiftory.
Gen. xli. 46. Jofeph was 30, years old when
he ftood before Pharaoh, and was advanced to
that high dignity. The 7 years of plenty im
mediately follow, at the end of which Jofeph was
^y years old. Upon the return of his brethren
into Egypt to buy corn, he told them, Gen. xiv.
6. For thefe two years hath the famine been in the
land ; Jofeph was now 39 years old. In this year
Jacob defcended into Egypt, and ftood before
Pharaoh, Gen. xlvii. 9. When the days of the
years of his pilgrimage were 130 years. There^
fore from 130,' fubftradt the 39 contemporary
years of Jofeph' s life, and the remainder 9 1 , right
ly determines the age of Jacob at the birth of jo
jeph, as in the table.-
Here I fhall offer a few remarks, (1) We can
not with certainty collect in what year of the life
of Jacob, any. one of his 12 fons was born, ex
cepting only Jojeph. (2) Not one of the 12 fons
of Jacob is enrolled in the lift of Patriarchs, or
admitted into the canon, but only Jofeph. (3)
Jojeph lived no years, the whole of which con-
ftitute a correfpondirig part of the world's chro
nology,

( 222 )
nology, which is peculiar to Jofeph, for it can
not be faid of any of the other Patriarchs. (4)
As thefe no years clofe the canori, the chrorio-
logy cannot be extended one year farther by the
lives of the Patriarchs, it being no where intima
ted, nor can it be gathered from hiftorical rela
tion, in what year of the life of Jojeph, either
Ephraim or 'Manaffeh was born. (5) From hence
arifes a very nice, and one of the moft difficult
demOnftratidns of the Pentateuch ; which con
fifts in the afcef-taihing in which of the 430 years
of fojourning y^/e^ died* or, which amounts to
the fame, how many years 'precifely intervened
between the death of Jojeph, and- the birth of
Mojes ; who was 80 years old when he flood be
fore Pharaoh, and demanded the difmiflionof the
lfraelites.
Archbifhop Ujher's hypothefis determines them
to 64 years, but the certainty of this determina
tion was never yet proved, nor can be, from the
aftronomical data of the Pentateuch ; which can
not be treated of properly in this place. But to
return ;
There is no fuch table td ' be met with, as the
Mofaic, but in the mofi antient facred records.
We may perceive, by a curfory view of it, that
it divides itfelf into four diftindt periods; in every
One of which the ages of the Patriarchs decreafed
proportionally, or about one half. The ift pe
riod contains 10 generations, from Adam (who
ftands at the head of all epochs, periods, and
computations) to Noah inclufive. It commences on

(.223 )
on the 4th of the Hexaemeron, at the autumnal
aequinox, and it ends at the birth of Shem (who
ftands at the head of the 2d period) A. M. 1558,
at the autumnal aequinox. During the ift period,
men generally lived between 900 and 1000 tro--
pical years.
' A table of the ages of the Patriarchs of the ift
period.

I.

2.

3-

1 Adam 130

800

93°

2 Seth 105

807

912

3 Enojh 90

815

905

4 Cainan 70

840

910

j Mehalaleel 65

830

895

6 Jared it 2

800

962

y Enoch • - 65

300

365

8 Methufalah 187

782

969

9 >Lamech 182

595

777

10 Noah 502

448

95°

-ru -n.
A. M.0 15 58 © Shem born,

. The 2d period contains 4 generations, from
Shem to; Heber inclufive. It begins at the birth.
of Shem, A.M. 1558, at the autumnal asquinqx;
and it ends at the birth of Peleg, (who ftands at
the head of the 3d period) A. M. 1757, at the
autumnal aequinox. During this 2d period, men
generally lived between 400 and 500 years. No one

( 224 )
one perfon born after A. M. 1558 is recorded
to have lived 500 years, excepting only Shem,
who reached 600 years, p8 of which he paffed
in the old world, and 502 in the new. So that
Shem lived juft as many years in the new world,
as Noah was old at his birth.
A table of the ages of the Patriarchs of the 2d
period.
1. 2. 3.
1 Shem 100 500 600
2 Arphaxad 35 403 438
3 Salah 30 403 433
4 Heber 34 430 464

199 Peleg born A. M. 0 1757 0
The 3d period contains 5 generations, from
Peleg to Terah inclufive. It begins at the birth
of Peleg, A.M. 1757, at the autumnal aequinox,
and it ends at the birth of Abram, (who ftands
at the head of the 4th period) A. M. 2008, at
the autumnal aequinox. During this 3d period,
men generally lived between 200 and 300 years.
No one perfon born after A. M. 1757 is record
ed to have lived 300 years.

( 225 )
A table of tbe ages of the Patriarchs of the $d
period.
I. 2. 3.
1 Peleg 30 209 239
2 Reu 32 207 239
3 Serug 30 200 230
4 Nahor 29 119 148
5 Terah 130 y^ 205

251 Abram born A* M. 2008 0
The 4th period contains thirteen generations,
from Abram to David, (who ftands at the head
of the 5th and laft period) exclufive. During
this 4th period, men generally lived between 100
and 200 years. It begins at the birth of Abram,
A.M. 2008, at the autumnal aequinox; and it
ends at the birth of David, A. M. 2918, at the
vernal aequinox. No one perfon born after A.
M. 2008, is recorded to have lived 200 years.
David lived 70 years, 2 Sam. v. 4. „which has
been the general ftandard of human life ever fince,
and is to this day ; though many never attain to
it, and a certain proportional number exceeds it.
No one perfon, born after A. M. 29i8> isrecord-
ed to have lived 180 years, which was the age of
Ifaac, or 1 y^ years, which was the age of Abra-*
ham at his death. F f A

' ( 226 )
A table of the ages ofthe Patriarchs of the 4th pe
riod, as far as the canon extends, containing
only 4 generations.

1

1.

2.

3-

1 Abraham

100

7.5

l75

2 Ijaac

60

120

180

3 Jacob

91

56

H7

4 J°fePh

39
290
+y*

71

no

361 A. M. 2369 0 Jofeph died.
The feveral tables of the refpedtive ages of the
Patriarchs in the 4 fucceflive periods confift,
each of them, of 3 columns; the ift of which
exhibits the ages of the Patriarchs, at the birth
of their recorded fons, in whofe line both the
chronology and the genealogies are cbntinued.
Thefe numbers collectively taken conftitute a
fucceffive uninterrupted feries of tropical years,
and thereby afcertain aftronomically the world's
age, or determinate paft duration. As for exam
ple, The ift table comprehends 10 lineal des
cents in a continued fucceffion, and the numbers
of Col. 1 . being collected into one fum produce
and exprefs 1558 folar revolutions; hence we in
fer that Shem was born A. M. 1558, at the au
tumnal

( 227 )/ * •
tumnal aequinox. If we fet them down in the
following manner, we fhall have a clear view of
the whole. A.M.
Tab. i. Col. i. 1558 Shem born, 2d period begins. .
Tab. 2. Col. 1. 199 1757 Peleghom, 3d period begins.
Tab. 3. Col. 1. 251 2008 Abram born, 4th period beg.
Tab. 4. Col. 1. 361 2369 Jofeph died.
The refpedtive numbers of the 2d column in
form us how many years the Patriarchs lived af
ter the birth of their recorded fons. Thefe in
conjunction with thofe of the ift are a fure and
ufeful directory for the drawing out a table at large,
which will, reprefent in one commodious view
the aftronomical parallelifm of the correfponding
years of the contemporary Patriarchs^ To il
luftrate this by the table ; we will take the year in
which Adam died.
Adam lived 930 years, and as the year of his
life 1 runs prallel with A. M. 1, fo the year,
in which he died, runs parallel with A. M. 930.
From 930 (col. 3.) fubftradt 130 (col. 1.) the
age of Adam at the birth of Seth, the remainder
800 (col. 2.) fhews us how many years Seth lived
contemporary with Adam. Again, from 800
fubftradt 105, the age of Seth at the birth of his
fon Enojh, the remainder 695 gives the contem
porary years of Enojh. In like manner, the fol
lowing numbers, 605, 535, 470, 308, 243,
^6 denote the contemporary years of Cat nan, Me-
halaleel, Jared, Enoch, Methufalah, and Lamech.
F f 2 All

(>228 )
All thefe years begin and end together at the au
tumnal aequinox; they are all aftronomically
commenfurate to each other, and they all run pa
rallel with A. M. 930, in which year Adam died.
See the table.
Methufalah lived 243 years with Adam, and
died in the beginning of the year of the deluge,
in the 969th current year of his life, and in the
726th year from the death of Adam ; for 969 —
243=726. If to 725 we add 930, the life of
Adam, the fum 1655 fhews the duratfej^ of the
old world, meafur'd by the lives of twwmtedilu-
vian Patriarchs : which feems incredible to us,
who live in the 5th period, in which the term of
human life is contracted into the narrow fpan of
70 or 80 years. And if Mojes had not recorded
and tranfthitted to us the aftromony of the primi
tive world, together with the precife time of its
continuance, and the longevity of the Patriarchs,
his plain hiftorical account, however true in it
felf, would not have gained credit with fome,
whilft unfupp^rted by'dem'onftration. But the
certainty arid perfedtion of primevalaftronomy
may poffibly. extort an aflent to the truth of Mojes's
narration, from thofe who are far from paying an
implicit regard to his authority, as an infpired
hiftorian. Mofes has recorded the ages of Methufalah, and
of Aaron, under fuch peculiar circumftances, as
plainly direct our thoughts to fome uniform and
eftablifh'd law of reduction.
Me-

( 22;9 )
Methujalah was 369 years old at the birth of
his grandfon Noah; the flood happen'd in the
600th current year of Noah's life,' and confer
quently, in the 969th of Methujalah. And as
Methufalah was not involy'd in the deluge, if we
fuppofe him to have died the day before it began,
or a week before it, according to the opinion of
the Jews, he could not have lived any more than
968 compleat years, one month and odd days,
reckoning from the autumnal asquinox : yet, fays
Mofes, Gen. y. zy.
All the days of Methufalah were 969 (compleat)
years. Aaron was 83 years old at the vernal aequinox,
about the time of the Exodus. Exod. vii. 7. He
died 'on mount Hor, (Numb, xxxiii. 38.) in the
40th year after the children of Ifrael were come
out of the land of Egypt, oh the ift day of the
5th month, viz. from the vernal aequinox. And
yet, fays Mofes, ver. 3 g.
Aaron was 123 (compleat) years old, when he
died 'on mount Hor.
It is undeniably certain, that Mofes compleats
the laft current year, both of Methujalah and of
Aaron's life, by a well known and determinate
law 5 the queftion is, by what law ? Here the
anfwer, I think, is obvious, viz. The indif-
penfible obligation, that the antient IJraelites were
under to obferve their feftivals in their fet and
appointed feafons, throughout their generations,
by an ordinance for ever, fully inftructs us to
conclude, that Mojes's law of redudtion was a
true

( 230 )
true aftronomical law. And thus I endeavour to
convey to the reader's mind a clear, eafy, and
familiar conception of it. Y
The flood began and ended in the 600th year
ofiVo^'slife, A. M. 1656. Thefe 600 years
of Noah (computed each of them from the au
tumnal aequinox, to the autumnal aequinox fol
lowing) carry us back to the conclufion of the
year of Lamech's life 182. Fof fo many years
old was Lamech, by Mojes's aftronomical law of
reduction, at the birth of his fon Noah, A. M.
IO56,©. Thefe 182 years of Lamech carry us back to
the conclufion of the year of Methufalah 's life 187.
For fo many years old was Methufalah by Mofes's
aftronomical law of reduction, at the birth of his
fon Lamech, A. M. 874,0.
Thefe 187 years of Methufalah carry us back
to the conclufion of the year of Enoch's life 65.
For fo many years old was Enoch, by Mojes's
aftronomical law of reduction, at the birth of his
fon Methufalah, A. M. 687,©.
Thefe 65 years of Enoch carry us back to the
conclufion ofthe year of Jared's life 162. For fo
many years old was Jared, by Mojes's aftronomical
law of reduction, at the birth of his fon Enoch,
A. M. 62*2,0. Thefe

( 231 )
Thefe 162 years of Jared carry us back to the
conclufion of the year of Mehalaleel's life 65. Few*
fo many years old was Mehalaleel, by Mojes's aftro
nomical law of reduction, at the birth of his fon

-/-u

Jared, A. M. 460,©.
Thefe 6 c; years of Mehalaleel carry us back to
the conclufion of the year of Cainan's life 70. For
fo many years old was Cainan, by Mofes's aftro
nomical law of reduction, at the birth of his fon
* ' £=
Mehalaleel, A. M. 395,©.
Thefe 70 years of Cainan carry us back to the
conclufion of the year of Enojh's life 90. For fo
many years old was Enojh, by Mofes's aftronomical
law of reduction, at the birth of his fon Cainan,
-1-
A. M. 325,©.
Thefe 90 years of 'Enojh carry us backto the con
clufion of the year of Seth's life 105. For fo many
years old was Seth, by Mofes's aftronomical law,
of reduction, at the birth of his fon Enoch, A. M.
235.®- Thefe 105 years of Seth carry us back to the
conclufion of the year of Adam's life 130. For fo
many years old Was Adam, by Mojes's aftronomi
cal law of redudlion, at the birth of his fon Seth,
-n.
A. M. 130,0.
Adam, 130—130=0.©.' Therefore, thefe
130 years of Adam's life carry us back to the
¦ 4th

C 232 )
4th of the Hexaemeron, and to the autumnal
aequinodtial day ; from which, and the 15th of
the thirty-day month of the lunar year (eftablifh'd
from the beginning) the divine chronologift dates
his computations.
From this plain account, and familiar reprefen-1-
tation (antecedent to proof) we learn with fome
degree of fatisfaction, in what a curious, exadt^
and fkilful manner, the genealogies of the Pa*
triarchs, both before and after the flood, from
the 4th of the Hexaemeron, to the end of the
year in which Jofeph died, are reduc'd to confix
tute an uninterrupted fucceffive chronology, and
the aftronomical age ofthe world:
Hence alfo it comes to pafs, that all the' chro-
nologifts, who derive their computations from the
authentic Hebrew text, have ever collected 1656
years, from the creation to the deluge inclufive ;
though they have been much divided in their fen-
timents and conjectures, concerning the form 'dnd
quantity of thefe antediluvian years ; they have
been fo far from undertaking to prove, that not
one has met with fufficient ground and encourage
ment, to fuppofe them to be tropical folar.
The fubject of this treatife is, I well know, at
a very low ebb, and in fuch a fettled difefteem,
notwithftanding all the learned and elaborate dif-
fertations and volumes which have been wrote
upon it, and publifh'd in one age after another,
that fhould any one affert in public converfation,
that no one part of pradtical mathematics was
more demonftrably certain than the Scripture chro-

( 233 )
chronology, not only in the general, but in every
diftindt branch and period, the perfon that fhould
make the affertion would be look'd upon as a fan
ciful dogmatift, or as not knowing what he faid,
But how paradoxical foever it may be found, and
how ftrongly foever prejudicate opinion may op-
pofe the reception, we fhall find it in the refult,
after fo many contfOverfial wranglings, to be real
matter of fact.
The two moft diftinguifh'd and the moft im
portant years in the aftronomical canon of Pa
triarchs are the year of the creation, or A.M. i,
and the year of the deluge, or A. M. 1656: in
the 1 ft, the Mofaic hiftory recites the origin and
rife : in the 2d, the total fubverfion and moft;
terrible devaftation of this terraqueous globe ;
and he reduces his ;Circumftantial narration and
account under thefe five heads. 1 . Its impulfive
caufe. 2. Its. efficient caufe. 3. Its infirumental
caufe. 4; Its chronology. 5. Its aftronomy.
Firft, the impulfive caufe of the deluge is re
lated, by Mojes in very affefting, but the efficient
caufe in very emphatic terms. We will confi
der all of them diftinctly and briefly.
Firft, the impulfive -caufe of the deluge is thus
recorded by Mojes, Gen. vi. 5, 6, 11, 12.
Ver. 5. And God Jaw that the wickednejs of
man, was great in the Earth, and thai every ima
gination of the thoughts of his heart was only evil
continually. G g Ver,

( 234)
' Ver. 6. And it repented the Lord that he had
nthn on the" Earth, and it grieved him at his
heart. Ver. ii. The Earth alfo was corrupt bejore God,
and the Earth was filled with violence.
Ver. 12. And God looked dpon Earth, and be
hold! it Was corrupt : for all fiejh had corrupted
his 'wdy upon ihe Earth.
idly, The efficient caufe of the deluge was
vindictive juftice armed with omnipotence, and
is thus related by Mojes. Gen.vi.y, 13, 17. -
Ver. 7. And the Lord faid, I will defiroy mCn
whom I have created fr 6m the face of the Earth,
both man and beafi, and the Creeping things, and
the fowls ofthe air, jor it repenteth me that I have
made them.
Ver. 13. And God faid unto Noah, the end of
allfiefh is come before me, for the Earth' is filled
with violence through them; and behold! I will
defiroy them with the Earth.
Ver. 17. And behold! I, even I, do bring a
flood of waters "upon the Earth to defiroy dllfiejh,
wherein is the breath of life, from under Heaven:
and every thing that is in the Earth Jhall die.
3dly, The infirumental caufe of the deluge in
the hand of divine providence was the waters
which are above, and the waters which are under
the Earth. Gen.

(235)
Gen. vii. ii. All the fountains of the great deep
were broken up, and the windows (Gr. cataracts)
of Heaven were opened.
4thly, Its, chronology, or exact time when it
began, is thus determin'd and ftated. Gen.
vii. ii.
Ver. ii. In the fix hundredth year oj' Noah'j
Ufa, in the 2d month, on the 17th day of the
month, on the fame day.
We have in this determination, year, month,
day, the name of a Patriarch, and his age ;
when we read this, can we reafonably imagine,
that Mofes implicitly took up with a mere political
computation? We meet with nothing like it a-
mongft the moft antient nations, at in any other
hiftorical records.
Berofus, a prieft of Belus, by bir,th a Babylo
nian, wrote the Chaldaic hiftory ; and we find in
the fragments of Abydenus and Apollodorus, taken
out of Berofus, and preferv'd by Eujebius in his
Greek chronicon, that the Chaldaans had pre
ferv'd in their traditions feveral circumftances of
the deluge, exadtly as they are recorded by Mofes
in his hiftory ; efpecially that of fending out a bird
3 times fucceffively to fee if the waters were a-
bated, and its returning no more after the 3d
time. But omitting the fimilar circumftances of
the hiftory, which have been fo often noted, I
fhall only compare the chronology of the prieft of
Belus, with that of the Jewijh legiflator.
Gg 2 And,

( 236 )
And, ift, As there are 10 generations from
Adam to Noah, according to Mojes ; fo, alfo,
there are i o generations from Alorus to Xijuthrus,
according to Berojus.
' 2dly, As God revealed to Noah his intentions
to drown the world by a flood, in thp 6ooth year
of his life, in the 2d month, on the 10th day of
the month ; and that it fhould -begin on the 17th
day of the fame month, at the diftance of 7 days,
or a compleat week from thence, according to
Mojes : fo likewife, God revealed unto Xijuthrus
his intentions to defiroy the world by a flood, in
Jome one year of his life, and that it fhould begin
on the 15th day of 'the Macedonian month Dafius,
according to Berojus.
3dly, Mojes gives us an ordinal number, viz.
the 2d month ; Berojus, a political month, viz.
Dafius. ¦
4thly, The ordinal number of Mojes diredts us
to an aftronomical epoch of the year ; the politi
cal month of Berofus pins us down to a civil
one. 5thly, Noah lived 950 vears according to Mo
fes; Xijuthrus lived or reigned 43 200. years, ac
cording to Berojus,
6thly, ' The years of Noah's life may be afcer
tain'd by the aftronomer, becaufe exadtly com-
menfurate to an equal number of folar revolutions :
But the years of the life or reign of Xijuthrus,
are not to be eftimated by the motions of the hea
venly bodies, but by Chaldaan Sari, Niri, and
Sofi. And,'' If

( 237 )
If we. admit the hypothefis of the learned
Monks, Anianus and Panadorus, each Chaldaan
Sarus will be equal 103600 day-years ; which
contain 10 Chaldaan years, of 3 60 days each. A
Nirus will be equal to 600 day-years, equal to
the 6th part of 10 Chaldaan years,1 of 36b days
each. And a Sofus will be equal to 60 day-years,
equal to the 6 th part ofaChaldaan year of 360 days.
Berofus wrote his annals in the reign, and by
the command, it is faid, of Ptolemy Philadelphus,
not long after the Hebrew Scriptures had been
tranflated into Greek ; his place of refidence was
the ifle of Cos, amongft the Grecians, fo that he
might be well acquainted with the Macedonian
ftile : but what ! is the Macedonian month Da
fius to be extended back to the year of the de
luge, to the days of Noah? And to an age— in
which the remoteft'anceftors of the Greeks had
no being or exiftence, but only in the loins of Ja-
phet ? This is too abfurd to be fuppofed, and
too extravagant to be granted.
And now let the reader judge from this com-
parifon, which of thefe two chronologies is the
moft fikely to gratify his enquiries, and to fettle
rightly the year* of the deluge, that of Mojes, or
of Berojiis ?
And no' wonder that Mojes, fo far excelPd, may
fome fay, — For he was educated (Gr. Et«mJ^w9>;)'
in all the wifdom of the Egyptians, as the Proto-
Martyr, St. Stephen has long fince attefted. Afts
vii. 22. And did the /Egyptian Sophoi indeed in-
ftrudt Mojes, in the laws of true aftronomy ?
Then

(238)
Then have we not juft grounds highly to efteem
thefe fplendid fragments o£ the Pentateuch, which
have alone tranfmitted to us, the genuine remains
and authentic monuments of the old Egyptian
learning ? But nothing is more remote from the
truth than; this ; for alas ! had not Hermes play'd
at dice with the Moon (fo relates the truly an
tient mythologic fable) and won from her the 7 2d
part of 360 days, the Egyptians, it is poflible,
might never have recovered the quinque Epagome-
na, from the reign of Thoth, to the death of
Cleopatra. The correction of the dfd. Egyptian year, from
360 to 365 days (for they knew nothing pf the
tetarton or quadrant many hundred years after)
was made, as we are told by Georgius. the Synr
cellus, of the Patriarch Taracofius, in the reign
of Afeth : but in what age this king Afeth
reigned, whether before or after the time of
Mofes, Perdofti certant, & adhuc fub judice lis eft.
Let thus much fuffice in general for Mofes's
account of the chronology of the deluge, which
leads me,
jthly, To its aftronomy. The facred hiftorian
has let lateft pofterity know, that as chronology is
the life and foul of hiftory, fo aftronomy is the
life and foul of chronology. And fhould any one
be prompted by a weak incredulity, to doubt or
call in queftion, the reality and certainty of the
much

( 239 )
much characterized yeat of the univerfal deluge,
he muft firft put out the Sun and the Moon from
the expanfe of the heavens; which give their
united arid irrefragable teftimonies to the Very
times of this ftupendous revolution, and moft
dreadful cataftrophe.
As A. M. i , the year of the creation, and A.
M. 1656, the year ofthe old world's diffolution,
ftand very diftinguifh'd by their hiftory, we
might be induc'd to expect, that they would be
as diftinguifh'd by their aftronomy; and fo we
fhall find that they are; we fhall find, I fay, that
the aftronomy of that year in which the world
was created, and of that year in which it was de
firoy 'd by a flood, may be collected and ftated
with fuch a minute exaetnefs, from the princi
ples^ data, and terms laid dbwn and given in the
Hebrew text of the Pentateuch^ as will plainly and
clearly lead us to a full and perfect knowlege of
all the fundamental laws of Sun and Moon aftro
nomy, and to all the neceffary rules of calcula
tion. I will take the' ffdedom to fuppofe, that the
reader has already perufed, and with fome atten
tion confider'd, Tab. I. II. p. 15. which exhibit
the aftronomy of thefe two remarkable years : if
he has, he will be the better prepared for the
more ready apprehenfion of the following illus
tration of them. But fince thefe fable's are very
concife, and muft needs be thoroughly undefftood
by thefe, who are defirous to acquaint themfelves
with thisTcheme, and the calculations which fup port

(24© )
port it, I- fhall not fcruple to fet them down again
in this place.
The pofitions of the Sun and Moon, both in the be*
ginning, and in tbe end .of the year of the crear
tion, and of the year of the deluge, compared to-1
. gether.
Here we muft carefully remember,; that the pri
mary pofition A. M. o. is the fundamental datum-
of the Hebrew Pentateuch.

0
O
M. o. < 15
Zohoraim

Tab. I.
A. M. 1.
354 O 11
339 * 2b

©
A. M. 1655, ending £
Ol5
Bvker

Tab. IL
A.M. 1 656.
354 <" "
339.O 26

Although the circumftances of the inverted po
fition of the two great luminaries, in the begin
ning and conclufion of the old world, are too ob
vious not to be perceiv'd ; yet it may not be Su
perfluous to note the particulars.
1. A. M. o. On the, 4th. of the Hexaemeron,
which was the autumnal aequinodtial day, the laft
day of the (chaotic') lunar year, fuppofed to be
computed from full Moon (O) to full Moon (0),~
fell upon the laft day of the (chaotic)foliar.
1. A, M. 1655, ending the laft day of the
lunar year, computed from new Moon (c) to
nevv

( 24i )
hew Moon ( ff ) fell upon the laft day of the1
folar. 2. A. M, i. A compleat lunar year of 354
days, computed from full Moon (O) to full Moon
(O), fell within the cardinal limits of the folar.
2. A.M. 1656. A compleat lunar year of
354 days, computed from new Moon (f ) to new
Moon (f ), fell within! the cardinal limits of the
folar. 3. A. M. i. 339 days of the new Moon (<)
lunar year fell within the cardinal limits of the
folar. 3. A.M. 1656. 339 days of the full Moon
(0) lunar year fell within the cardinal limits of
the folar:
4. A. M; 1. The full Moon epadt, or the di
ftance bf the full Moon (b) evening from the
autumnal aequinox, was O- 1 i. days.
4. A.M. 1656. The riew Modn epadt, or the
diftance of the neW Moon ( c ) evening frdm the
autumnal aequinox, was < 11. days.
5. A. M. 1. The new Modn epadt, or the
diftance of the new Moon ({) evening from the
autumnal aequinox, Was (T. 26 days, including a
full Moon evening; for c 2,6 — 15=0 n.
A. M. 1656. The full Moon epadt, or diftance
of the full Moon (o) everiirig frorn the autumnal
aequinox, was O 26 days, including a newModri
.evening; for 0 26 — 15=C n. '
Now no one will fufpect me of inventing this
aftrdnomy ; no one will offer to charge me with
H h forging

( 242 )
forging thefe charadters at fo large an interval
from each other ; much lefs will any one afcribe
to me the power of commanding the Heavens
to fet their J'eal to the truth, at the diftance
given. It will be without doubt concluded, that I owe
them to the aids and affiflances of aftronomical
tables and calculations. But I can with truth
reply, that I never confulted them ; nor has phi
lofophy and fcience ever yet difcovered, or fo
much as fuggefted the double epoch or radix of
the Moon's year, and of the twofold computation
arifing from it, the one facred and ecclefiaftical,
the other civil and hiftorical, as has been already
obferved. Nor am I as yet at all fenfible of any
juft grounds and reafons, which might either
oblige or incline me to retract what has been af-
ferted under Propofition X. viz.
That the form ofthe patriarchal twofold, i. e.
both folar and lunar year* is no where to be found,
but (only) in the patriarchal line.
Upon the joint aftronomy then of thefe 2 impor
tant years (which ftand charadteriz'd in fuch a pe^
culiar manner) I lay the foundations of my proof.
And he that can undermine this foundation, muft
neceffarily overthrow the fuperftructure together
with it : they muft both ftand and fall together.
But I am under no apprehenfion at prefent, of any
fuch confequence ; I am rather in hopes, that
what has been hitherto offer'd, tho' deftitute of
its proof, will tend to conciliate a faypurable TOpi-
. . .., . nion

• 1; .

( 243 )
nion of my undertaking, to excite a due atten
tion to the proofs, and to awaken the mind of
the intelligent reader to a ferious confideration
and enquiry, whether there may not be, at laft,
very good grounds to expedt fomewhat very ex
traordinary, and even in a ftate of perfection,
from the fcheme of genuine facred chronology,
fromv the principles, ' data, and terms of the He
brew Pentateuch.
I fhall now return to the folution of the, que
ftion propofed, p. 209, viz. What was the par
ticular form, and the determinate quantity of that
year, and likewife, what were thofe unerring
rules of computation which could enable the an
tient lfraelites to obferve the three great anniver-
fary feafts of the law, in their divinely appointed
feafons, and this too, throughout their genera
tions, by an ordinance for ever ?
This one precept is alone fufficient to affure
and convince us, that the 'Hebrew term Shanah
muft neceffarily infer and exprefs a true folar re
volution ', and we may with equal reafon con
clude, from the fundamental principle ofthe Pen
tateuch, and God Jaid — haju lejhanim, let them
be for years, that it muft alfo denote and include
the annual period of the Moon.
Thefe truths have been the fubject of much
and long enquiry amongft the learned, tho' hi
therto attended with little or no fuccefs.
The compilers of the univerfal hiftory were
learned and judicious perfons, and we may pre-,
fume, that in the profecution of their defign they
Hh 2 omitted

( 244 )
omitted no endeavours to furnifh themfelves with
all the neceffary lights and affiftances they were
able to procure : and yet, in the preface to Vol. i .
p. 54. they implicitly admit, . that the antediluvi
an year confifted of juft 36,0 days, and are of opi
nion that this is Jufficiently proved in that difcourfe
of Mr. Allen, formerly fellow of Sidney college,
which Mr. Whifton has inferted (by Mr. Allen's
permiffion, as he himfelf tells us) in his theory of
the Earth.
Had thofe gentlemen confulted the Pentateuch
only, and had they diligently examined, and
carefully confidered it's principles and data, they
could not have patronized a notion fo contrary to
nature, fo derogatory to Mofes, and fo intirely
fubverfive of the aftronomical chronology of the
antediluvian world, as ftated and determined in
the original Hebrew text.
The following fheets then undertake, upon the
fole authority of the Pentateuch, to render it unT
deniably, becaufe demonftrably certain, that
Mofes's table of the genealogies of. the patriarchs,
both before and after the flood, is a moft accurate
aftronomical table ; and that the original, patri
archal year was the true filar ; with which the
lunar year was conftantly connected, and carried
all along together with it, by the laws of an ex
tremely curious, and mofi exaft aftronomy.
Here the reader's attention, efpecially if he be
an aftronomer, will begin to be awakened ; and
no wonder if it fhould, for
.Nova j tamen antique, loquimur.
The

( 245 )
-The Hebrew chronology reckons from the cre
ation to the end of the year of the deluge, 1656
Mojaic Shanim, or folar tropical years. Now fhould
fome eminent aftronomer be required to deter
mine the pofition of the Moon to the Sun, in the
beginning and coaclufion, in the firft and the laft
year of this interval, or in any affigned interme
diate one, without being allowed the privilege of
ranging amongft the fixed ftars, of calculating the
.Sun's place in the ecliptic, or the Moon's in it's
orbit, and the ftations of both in the Julian ca
lendar, and all this, in a retrograde method, from
fome known fixed radix ; he would think it no
reproach to his fkill in fcience to decline the im
poffible tafk ; nor would he be naturally led to
conclude, that the principles, data, and terms of
the Hebrew Pentateuch, were in themfelves a fuf
ficient aftronomical directory, as I am now going
to prove that they are.
In the interval from the 4th ofthe Hexaemeron
to the end of the year of Noah's life 600, we
have three exprefs Mojaic aftronomical data.
Firft, the characters of the original pofition ;
or, the Sun's beginning it's courfe, from the au
tumnal aequinodtial point, on the 15th day from
the new Moon (c) evening. Secondly, 1656
true folar revolutions, all connected with each
other, and beginning and ending at the autumnal
aequinox. Thirdly, the termination of the laft
1 2-month lunar year on the new Moon ( ( ) even
ing, at the diftance of 1 idays, from the original
cardinal point. is-

( 2,46 )
1 5 — 1 1 =4. We have here 3 epacts, 1 real, viz.
11, and 2 chaotic or imaginary, viz. 15. \. For
if we compute backwards one whole year from
Mojes's account of the origin of time, or the epadt
15, the Sun will be calculated to enter Libra,
on the 4th day inclufive, from the new Moon (( )
evening. We have now obtained 3 Mojaic radi
cal numbers (fo I beg to call them) viz. 4. 1 1. 1 5.
1 1 — 4=7. The number 7 is an exprefs Mo
jaic datum, God .bleffed the yth day, fays Mojes,
Gen. 2. and hallowed it. We have now 4 Mo
jaic radical numbers, viz. 4. 11. 7. 15.
The Hebrew Chodejh contains 3,0 days, and is
another exprefs datum of the Pentateuch; we
have now 5 Mofaic radical numbers, viz. 4. 1 1.
7. 30. 15.
The number 360 is the arithmetical mean be
tween the quantities of the folar and the lunar
year ; and it is evidently compounded (of which
more hereafter) of 15, and it's quadruple 60.
From hence I collect 6 Mojaic radical numbers,
viz. 4. 11. 7. .60. 30. 15.
He muft be a very negligent and difqualified
fearcher after firft principles, and efpecially the
fundamental principles of Sun and Moon aftrono
my, who could overlook the perfection of unity.
A fmall degree of abftradt reafoning will make
us fenfihle, that the whole flux of time, or of fuc
ceffive duration, is meafured by a continued feries
of units, in this manner, i+i-j-i+j.4-1, &c. eve
ry unite denoting a compleat diurnal revolution,
not of the aequator, but of the Sun from a given
cardinal

( 247 )
cardinal point of the day, to the fame cardinal
point of the day again ; and is, in nature, an ab
solutely perfedt meafure of time.
By thefe feveral fteps we have collected 7 Mo
jaic radical numbers, which are the aftronomical
mediums and inftruments of the following inte
gral calculations. We fhall range them in this
order, tho' it is arbitrary.
The arithmetical mean proportion — 360 —
The 7 Mojaic radical numbers, viz. 1. 4. 11.
7. 60. 30. 15. '
As a previous knowlege of thefe radicals is of
indifpenfible importance , throughout the calcula
tions, I fhall here fubjoin a recapitulation of them,
with fome additional neceffary remarks, of moft
of which the reader, if he thinks it, worth his
while, may eafily frame in his mind clear and di
ftindt ideas.
1 denotes a complete diurnal revolution of the
Sun, computed megnereb gnad gnereb, from the
time of it's fetting to the time of it's fetting, on
the aequinodtial day. This is neceffary to be
noted and remembred.
4 is the root, origin, arid foundation of the
epadts, and it arifes from the fimple fubftraction
of 1 1 from 15. Or, it may be obtained in this
manner: The 12 th month of the Patriarchal fo
lar year is of 35 days, and of the common lunar
year of 24 days. Then 35 — 15=20. Again,
©
24-20=C4. „ ThIs

( 248 )
1 1 is the 3d radical, and includes j diftindt den'c^"
minations. ( 1 ) It denotes the full Moon epadt at
the end of A. M. 1. (2) The new Moon epadt
at the end of A. M. 1656. (3) The inhering
meridian epadt, hereafter to be explained;
7 contains a fyftem of days,- called a week,
and is of pofitive divine inftitution. This hebdo-
matic meafure is infallibly an aftrondmical medii
um of proof, thro' the whole feries of the world's
chronology. 60. Every integer whatever, relating to time",
may be fuppofed capable of being divided into
fexagefimal parts ; but the number 60 ftands here
as the quadruple of 15. For, 1 : 4 : i 15 : 60,
30 contains the number of days in the pri
mitive and patriarchal Chodejh ; . and it's propor
tional divifions, hereafter to be explained, will
manifeft the divine perfections of revealed aftro'^
nomy. Thefe divifions are colledled from the
appendant* proportions of the original pofition of
the two great luminaries.
1 5 is the original (chaotic) new Moon epadt,-
and the fundamental datum of the Pentateuch.
Additional neceffary remarks.
(1) We borrow, for brevity's fake, in the cal
culations thefe algebraic characters, + (more) the
fign of addition, — (lefs) offubftraction, x (into)
of multiplication, 4- (divided by) of divifion, =t
(equal to) of equality.
(2) The 2d radical number 4, is the fquare of
2, the leaft affigriable root. This fquare 4 is of
fuch

( 249 )
fuch fignal ufe in the arithmetical deduction and
demonflration of the true quantity of the Sun's
annual courfe, as may, in a high degree, merit
our particular notice,- attention, and "confidera
tion : For,
(3) N. B. The 3d radical number 11 is re-
folvable into 7. 4.
(4) 15 is refolvable into 1 1. 4; and, alfo, into
4. 7. 4. fo that it is geometrically bounded, in itV
twd extremes, by a fquare. Let this be noted.
(5) 30 is refolvable into 4. 11. 4. 11. and,
alfo, into 4. 7. 4. 4- 4. 7. 4.
(6) 60 — n-f-15, remainder =4.
(7) 360 — n-f-15, the remainder =4.
1 c 1 50 2
(8) -^ ¦=. — , or one quadrant. -7- = — , or
v ' 60 4 ^ 60 4
two quadrants. ^ = — , or three quadrants.
Thefe Mojaic partitions are evidently eftablifh
ments of nature, and we are, in a manner, fenfi-
bly directed to the obfervation of them.
(9) The quantity of the Julian year may be
thus exprefs'd, 365 4- ^.
D- i«
(10) 365 4-z^ x 60 = 21915 fexagefimal
parts ; and 60 is the jth radical number.
(11) 2 19 1 5 fexagefimal parts -r 15 =. 146 1
quadrants, in a Julian year.
(12) If the quantity of the Julian year be re
duced to fexagefimal parts, thefe being divided by
15, the remainder will be = o.
Ii (13) Here

( 250 )
(i 3) Here I lay down this axiom. If the true
quantity of the folar tropical year:, which we will
now call x, be reduced to fexagefimal parts, thefe
being divided by 15, the remainder muft necef
farily be 4, the fquare of 2. This I offer as a fure
geometrical teft and criterion of the juft aneApem or
exaetnefs of that arithmetical calculus which un
dertakes to determine the quantity of the Sun's
year. (14) Thefe fymbols and numbers, thus placed'
© 41
1, 60.
to each other, C 15. , reprefent and exprefs
the Mofaic root of time, the true foundations of
Sun and Moon aftronomy ; and they may be thus
tranflated into aftronomical language, viz. on the
4th of the Hexaemeron the Sun began it's courfe
in the end ofthe third, or beginning ofthe fourth
quadrant of the autumnal aequinodtial day, i. e,. in
a determinate meridian at noon, and on the 15th
day from the evening of the Moon's (fuppofed)
vifibility. Let thefe general remarks fuffice for the pre
fent. We fhall now again return to the folutiori
of the queftion propofed, which includes thefe
three ufeful, important, and fundamental parti
culars, viz. ift, the form ; 2dly, the quantity of
the primitive two-fold year ; 3dly, the primitive
laws both of the folar and the lunar computations.
Firft, by the form is meant the manner of
computing and adjufting the months, which has
been already made fuflkiently clear from Mojes's
account

( 251 )
account of the flood in the 7th and 8th chap
ters of Genefis ; and it would be needlefs to repeat
it here. Therefore, fecondly, I fhall proceed to
inveftigate and determine it's quantity; which
will lead me to the direct proof of my 8 th pro
pofition, which I fhall here fet down with fome
variation. VIII. The quantity of the Mojaic Shanah, or fo
lar tropical year, may be afcertained with
the minuteft exadtnefs, to an indivifible
point, from Gen. v. 23. All the days of
Enoch were 36 5 years-, in conjunction with
the 3 84th year of Noah's life, which be
gins and ends at the autumnal aequinox
with A. M. 1440, being the firft year of
commenfuration .
The creator of the luminaries has clearly in-
ftrudted us, by the hand of his fervant Mofes,
Gen. i. 14. to reduce years to days, or to calcu
late both the diurnal and the annual revolutions ;
therefore, unlefs we are able to make the mea
fure by days to correfpond to a point with the
meafure by years, the calculus and the conclufion
can never be faid, in exact agreement with the
conftitution of nature, to be divinely true.
All the 'Days oj 'Enoch (fays Mofes) were 365
Years.
It may be collected from this text, that the
fquare of a true folar revolution, precifely meafur
ed the whole temporary duration of the tranflated
I i 2 Patri-

( 252 )
Patriarch, as reduced by Mofes to an aftronomical
law. And no one can exprefs the age of Enoch,
when he was one year old complete, without beT
ing able, at the fame time, to exprefs the precife
root of this fquare.
We are therefore to conftruct, by the direction
6f this text, an exact aftronomical fquare of the
Sun's annual period, whofe extracted foot fhall be
aftronorriically true to a point, independent of any
previous knowlege either of the one or of the
other. This may be judged indeed, at the firft
view, to be impracticable : But the candid reader
will be prevailed upon to fufpend his judgment
aWhile; becaufe, poffibly, he may not think
himfelf, as yet, fufficiently acquainted with the
inherent aftronomical powers, and the latent pro
portional properties and affedtions of the 7 Mofaic
radical numbers.
Mofes' 'sfiyle of chronology alone di ftates the follow
ing Problem.
It is required to reduce years to days, or to dc
tefmine how many diurnal revolutions of the Sun
correfpond" in nature with a given number of the
annual, under thefe limitations and reftrictions,
viz. Firft, without confulting the folar tables, or
being fuppofed to know that there are any folar
tables in being.
Secondly, without affumirig any quantity of the
folaf tropical year, or being under the neceffity of
knowing it. I fhall juft remark, Thirdly,

( 253 )
•Thirdly, when the integral calculation is fir
pithed, the remainder, over and above complete
days, will ever be either i, or ¦£, or 4, or o..
And in this conftant prefervation of the integra
lity of the quadrant, a conclufion, which the frac
tional calculations, of the moderns cannot poffibly
attain to, ljes fecreted a very inftrudtive leflbn of
practical aftronomy, if a theory of determinate
and equidiflant meridians may be efteemed fuch.
The meridians are moveable circles in the Hea
vens, without number, without any perceptible
diftindtion ; yet paffing thro' the center of the Sun
in a conftant, regular, and orderly fucceffion,
from Weft to Eaft. And altho' we cannot indeed
flop the career and mark thefe ever tranfient, ever
variable circles, yet are we able to circumfcribe a
determinate number within determinate limits;
then exadtly calculate the fucceffive approach of
any one of thefe determinates, and arreft the per
petual mover in it's moment of time. This will
be exemplified in the demonftration which we
have now in hand.
The reafon why I have taken occafion in this
place to fay thus much of meridians, is, becaufe
.the folution of the problem entirely depends upon
the being able to afcertain the computed meridi
an : by the computed is meant that meridian in
which the Sun began it's courfe, on the autum
nal aequinodtial day at noon. There is no neceffity
to controvert this epoch of the computation, be
caufe taking in all the meridians pf the globe, it
muft

( 254 )
muft be true in nature, whether we can rightly
adjuft the geography or not.
To be able to difcover 'and fettle the ftandard
of the folar tropical year, and to prove it to be
the ftandard, muft furely be of prime ufe, and a
neceffary fundamental in practical aftronomy. Sci
ence cannot offer a more curious, or a more fubtile
inveftigatidn ; and it's evident importance may de
mand the notice and attentive regard of the moft
fkilful aftronomer. ,
Euclid has clearly demonftrated, L. III. prop. 2*
that a fphere touches a plane but in one point, al-
tho' matter is allow'd to be indefinitely divifible.
Now quantity of time is as indefinitely divifible, as
quantity of matter, and yet, in the conftruction
of an exact aftronomical fquare of a folar revolu
tion, we are required to difcriminate and fix one.
individual point ; that very interriiediate point of
a quadrant of the aequinodtial day, in which the
Sun finifhes it's 365th annual period (having firft
connected this given interval with the 4th of the
Hexaemeron, and the Mofaic radix) and in the
fame determinate point completes it's fquare, in a
computed meridian ; then from this point of a
two-fold termination, to deduce and demonftrate
the true quantity of the Sun's year ; and all this,
a priori, or without the precarious and exotic aid
of any one poftulatum.
To render every ftep of the procefs plain, eafy,
and intelligible, we may transfer the Mofaic radix
from the 4th of the Hexaemeron, and bring it
down

( 255 ) ••
down to bur own times ; then the problem may
be ftated thus, viz.
Suppofe the Sun to enter Libra, in any year,
in the meridian of London at noon ; then, query,
in what quadrant of the autumnal aequinodtial day ?
in what intermediate point of that quadraflt? or,
in our ftyle, in what hour of the day, and in
what minute of that hour (the reafon why I do
not afk, in what fecond of that minute, may ap
pear as we proceed in the calculations) will the
Sun again enter Libra* in the meridian of London,
at the end of the 365th revolution from thence ?
for the conclufion muft needs be the fame, in
both cafes, by the uniform arid immutable laws of
aftronomy. Mr. Keil, in the preface to his aftronomical
lectures, with a fecret exultation declares, " That
" among all the liberal fciences there are none in
" which there remain fewer difficulties to be ex-
" plained, objections to be anfwered, or fcruples
a to be removed, than there are in aftronomy,
" and no fcience has yet attained fo great a degree
" of perfection as it has." If he means here Sun
and Moon aftronomy, as taught and explained in
his ledtures, I am extremely forry I cannot impli
citly allow it's perfection; when we come to ex- .
amine particulars, the reafons why I cannot, will
appear. It can be no impertinent digreffion to take oc
cafion in this place to enquire into the proceedings
of the aftronomers, and the feveral methods they
have had recourfe to, in order to find out and de
termine

termirie the quantity ofthe Sun's year, or in what
fpace 9f time precifely the Sun paffes from any
one cardinal point of the ecliptic (fuppofe from
Libra) to the fame cardinal point of the ecliptic
again. And it will appear in the iffue, that their
conclufions have been various, and, confequent-
ly, ambiguous and uncertain.
Bp. Beverege wrote his chronological- inftitu-
tions fomewhat more than 80 years ago, viz.
A. D. 1667, and, B. II. c. 2. p. 140. de aquinoc-
tiis &folfiitiis, he ftates the cafe, as it ftood in
that age, thus : " Quanta vero fit anni trOpici
" quanti t as ac menjura ; "nondum inter ipjos con-
" venit afironomos. Nos Longomontani, qui
lt earn exquifitiffime venatus efi, ample ft entes Jen-
" tentiam, annum hunc tropicum, diebus 365,
" h.$. 48.' ^" definimus. Aufer h. 5. 48/ ^."
" ex. h. 6. o.' reftduum eft, h. o. 11.' 5."
L. II. p. 145. we meet with the following ac
count of Tyco Brake's obfervations.
" Porro nulla accuratius invent a funt aquinoc-
l< tic, quam qua Tyco Brahaanno ara Chrifiia-
" na 1584^ JequentibusUraniburgi obfervavif.
I will here fubjoin a table of Tyco's moft accu
rate obfervations ofthe Sun's entry into the aequi
nodtial and folftitial points, for 4 years fucceffive-
ly, in the meridian of Uraniburgh.

( *57 f

A Table of Tyco's Obfervations^

i Anni Chrifti,

Biff. 1584
1. .585
2. 1586
3- '?»7!

-Periodi
Jtlanffi;

6297 62986299
630O'

jEquinodlia verna.

D h '
Maf. 10 9 30
Mar. 10 15 19
Mar. 1 o 2 i 8
Mar. 1 1 2 ;6

Solftitia sftiva.

D h '
Jun; 11 14-13
J\in. 1 1 20 i
Juti. 12 1 49
Jun. 12 7 37

^Equinoftia autumnalia.

D h '
Sep. 13 4 q
Sep. 13 9 49
Sep. 13 15 38
Sep. 1 3. 2 1 26

Solftitia
bVumalia.

D h
Dec. 11 14 44
Dec. 11 20 33
Dec. 12 2 22
Dec. 12 811

From this table I gain the knowlege of thefe
unequal divifions of the ecliptic :

D h ':
y3 4 43
93 13 47

1 . From the Vernal aequinox to the
fummer folftice •-
2. From the fummer folftice to
the autumnal aequinox
3. From the autumnal aequinox td?Q
the winter folftice $8° J0 44
4. From the winter folftice to the
vernal aequinox

• 89 00 35

Whether later obfervations are fuppofed to
come nearer to the truth than Tyco's has not fal
len in my way to know, nor would it be of much
moment to make the enquiry, as I judge from
Keil's fentiments, Left. XXII. p. 271.
 " If again the next year, the Sun's en-
" try into the aequator be obferved in the fame
" rhanner, the time elapfed between the two in-
" grefles is the fpace of a tropical year, or time
" wherein the Sun (or rather the Earth) com-
** pleats his courfe in the ecliptic.
K k :  " But

¦  u But by obfervations that are made at
" the diftance of a year, wc cannot fafely rely
"-upon the- true quantity of the year collected
" from them; for a fmallerror of one minute,
" being- confianfcly- increafeid and multiplied by
" the number of years; in procefs of time would
" amount to a prodigious miftake in the place of
"the Shn. Therefore the aftronomers more ac-
"• curately determine the quantity ofthe year, by
" taking the obfervations of two aequinocties, at
" many years diftance from one another ;. and di-
*' vidjng.;ijhe' time between the obfervations, by
" the number of revolutions the Sun has made,
" the quotient will fhew the time of one revolu-
" tion, or nearly the period of the Earth in her
" orbit. For by this means; if there beany mi-
" flake made in the. obfervation, it will be divi-
11 ded into fo many parts, according to the num-
" ber of years, that it will be. infenfible for the
" fpace of one year.
P. 272. " The fpace of time belonging to the
" tropical year is, by, this means, found to con-
te fift of 365 days, 5 hours, 48', and 57".
We have now obtained 3 different quantities of
the tropical year, to which I fhall add a 4th from
Dr. Holder's account of time, p. 55. where, to
ufe his own words, " the true folar year is.com-
" puted to be conftituted of 365 days, j;hours,
" 49', and 16", fo it falls fhort of the odd 6
" hours, by 10' and 44". The

( 259 )
The tropical year then contains, nh ' "
y i . Tyco's obfervations 365 5 #S. o
according to >*' ?r- tiolde,'s a,cc°unt 365 5 4 '6
Si %?TZ 'Tl^correaior, 3*5 5 4« 5*
J 4. bir i. Jyeivto/i s 3 - 365 5 48 57
Longomontanus has corrected jfjfco's obfervations
by 5" annually, and Sir I. Newton by 3". But
the annual difference of 2" between thefe two cor
rections would create a difference in the Sun's
place of 3 h. 1 1' j6" in the fpaCe of 5758 years,
and yet the error is infenfible in the fpate of one
year. Now/if we reduce 365 years to days, by tables
made from the 3 laft affigned quantities of the
tropical year, thefe feveral reductions will produce,
according to, Difference from Complements of
the Jtdiati it- the quadrant.
duElion.
D h ' " d h ' " d h ' "
1. Dr. Holder * 333 1 3 12 42 202 17 17 40
2. Longomontanus 133313 10 34 3; 2 19 25 25 cio 1 25 25
3. Sir 1. faewuton 133313 10 46 45 2 19 13 1500 1 13 15
From this variety of conclufions, and two of
them by the moft approved, and the mofi able
practitioners, we are led to conclude, that had
there been no poflible way of afcertaining the
quantity of the fokr tropical year, independent q£
obfervation, and all artificial rules, it mufi have
remained an ambiguity to the end of time.
The folution. of every problem is more or lefs
difficult, according as, the principles on which the
folution deperids are more or lefs evident and cer
tain. Hence fome, it is likely, may think that
£h 2 " the

( 26° )
the fcripture chronologift is in a very unpromifing
ftate and condition, who aims to penetrate and
explain the hidden fecrets of Sun and Moon aftro
nomy, under the direction, feemingly, of but a
faint and glimmering light, fupported but by ve
ry fcanty inftructions, viz. a very little more than
the previous knowlege of the quantity of the Ju
lian year, and the data of the Pentateuch ; amongft
which are reckoned the 7 radicals, with the arith
metical mean 360. Tho? flight as this founda
tion may feem, yet it is in fadt amply fufficient for
an uniform, proportional, and magnificent fuper-
ftrudture'. vr:h •
To proceed then to the Mofaic reduction of
thefe 365 years to days', which will manifeft the
inherent aftronomical powers, and, as we proceed
farther, the latent proportional properties and af
fections of the arithmetical mean 360, and the
y Mojaic radical numbers,
•CO (*)' (3) !,,-(4) '¦ (s) (6) (7)
1. 4; 11. 7. 60. 30. 15.
which I here fet down again for the fake of the
indices, as they will help the reader immediately
to perceive how and in what manner they are ufed)
and applied in the calculations.
The whole of this reduction of years to days,
without the folar tables, maybe comprehended
under thefe Very few plain arid eafy rules.
The rules of feduftion.
Rule I. Divide the given number of years by the
7th radical numher 15, rejecting the
remainder if lefs than 15. Rule

< 26 1 )
Rule II. Multiply the precedent quotient by the
3d radical number 11, andreferve the
product-.
Rule III. Divide the referved produdt by the ftand
ing and unalterable divifor 24 (obtain
ed by dividing the arithmetical mean 360
by 15) and the quotient will give the
number of quadrants to t>e fubftradted
from the fum total 'of quadrants in the
given number of years.
Rule IV. As there are in a Julian year of
D
3 65 -}- t, 146 1 quadrants, or 4th parts
of a natural day, multiply the given
number of years into 1461, and divi
ding the produdt or fum total of the
quadrants by 4, the quotient will give
jtlie whole amount of Julian days, with
the appendant quadrants.
Rule V. From the fum total of Julian quadrants
fubftradt the quotient obtained by
Rule III, then dividing the remainder
by 4, this laft quotient will complete
the reduction if a year of commenfura
tion be given ; of which we can reckon,
as yet, no more than 3 ; but if it be
not fuch a year, then the Rule how to
proceed will be given, after the quanti
ty of the tropical year is determined,
and the meridian epadt is known. At
prefent, the calculations proceed upon
the radicals only, and aflume nothing
as known/ The

( 262 )
The arithmetical operation for the given number
of 365 years,.
Years
,Rule I. 365 ¦*¦ 15 = 24, remainder 5, which rejedfc.
Rule II. 24 X 11= 264.
Rule III. 264 — 24 = 1 1 .-quadrants to be fubftra&ed.
Years ' D
RuleIV.365X 1461 =533265 quadrants, +4= 133316 +£7»/. reduflion.
RoleV  —u
 7- D
533254 quadrants -4-4=133313-1-! folar redudlion.
Difference from. "Julian z-*\.
As Sir I. Newton's conclufion, p. 259, may be
confidered, in fome fort, as a mean between that
of Dr. Holder's on the one fide, and that of Lon-
gomontanus's on the other, we will therefore reject
both thefe (the one as a defedt, the other as an
excefs) and compare the reduction by the radi
cals, with that of Sir I". Newton's only, and fet
down the lefs under the greater.
Days.
1. The integral calculation 1333 -13 -}- -J oo- 00
• D. h ' "
2. Sir I. Newton's reduction 133313-^-10 46 45
According to Sir I. Newton's reduction, the
folution of the foregoing problem may be thus ex-
prefi'd in words at length.
If the Sun enters Libra in any year; in the me?
ridian of London, at noon, then in the end of thp
365th revolution from thence, it will again enter
Libra, in the fame meridian, 46' 43" paft 10 at
night.

( 263 )
night.. Here are evidently very foecious appear
ances of truth and exadtnefs ; for in this calcula
tion we have not only the hour of the day, but
the minutes of an hcpr ; and let me add, — to the
confutation of the whole — the feconds of a mi
nute. I fay, — to the confutation of the whole — ¦
for there are not wanting arguments to prove,
thatf econd minutes cannot be admitted into the fo
lar computation, without a diredt oppofition and
repugnancy to the ftandard of nature. And not-
withftanding thefe foecious appearances, I cannot
think myfelf under any obligations to renounce
my right of examining, whether thefe things
are fo ?
As far as I can perceive at prefent, the
only Prop which fupports the whole, is but
an affumption (.for proof there is none) that
D
365 5I1 48' 57" exactly measure the folar tro
pical; year. Invalidate this affumption, and the
whole fuperftrudture immediately falls to the
ground ; we have then, neither an exact root, nor
an exact fquare ; all muft be efteemed- as an ap
proximation only ; but approximations in aftrono
my are by no means to be allow'd of, for they
difconcert the harmony of the fyftem.
The Britifh philofopher laboured full 20 years
in this one inveftigation ; I think, from A.D.
1680 to the end of A. D; 1700. But what was
there in nature to limit his refearches to juft 20
years ? why not one year more ? or why not one'
year lefs ? It may be faid, that juft 20 years were
fufficient

( 264 )
fufficient to 'anfwer the end' he aim'd at; but this0
has neVer been yet proved, and, perhaps,, never
will be.
It is-a miftake, which no authority Can juftify/
firft to labour out the quantity of the folar tropi
cal year, by .obfervation and rules of 'art ;• then ta
acquiefce in the determination as true, and frame
the> folar tables at a venture. It muft be obvious'
to common apprehenfion, that fuch a procedure
muft almoft neceffarily be attended with fome ad-*
heringfmperfeftion, and will be ever liable to the
demand of fome further proof: for where indeed
is the touchftone ofthe genuinenefs and authenti
city of fuch a conclufion? where are thearga-
ments founded upon a medium in nature ?
If we take a view of the reduction by the radi
cals, and of that of Sir /. Newton's, as fet down'
together, we may obferve a very near agreement
betwixt them; for they each ' of them collect
1333 13 complete days. And as the computation1
is dated from noon, the laft of thefe days muft-
alfo end at noon. Then there will remain, on the
one fide, 2 entire quadrants, which we will fepa
rate into I -j-t, and on the other fide 10 h 46' 45",
which we will feparate into 6 h -J- 4 1146' 45".
This feparated quadrant and thefe feparated 6 hours
refpedtively meafure from noon to Sun fetting in
the computed meridian. Then the remaining intire
quadrant will meafure from Sun fetting to mid
night, which is the firft ofthe autumnal sequinoc-
tial day. In fome one intermediate point of this *
intire quadrant, -the Sun will finifh it's 365th an->
nual

( 265 )
nual revolution, and in the fame individual mo
ment complete it's fquare ; now the integral cal
culation undertakes to difcriminate and fix the
computed meridian which interfedls' the very point
of this two-fold termination, and to exprefs in
fexagefimal parts (by the affiftance and direction
of the arithmetical mean 360, with the ift and
5th radicals 1. 60.) it's precife diftance from Sun-
fetting on the weft, and from midnight on the
eaft, which are the two aftronomical extremes of
the firft quadrant of the autumnal sequinodtial nuc
themeron. We will at prefent reprefent the intermediate
point fought by x, and help the reader's concep
tion by the following Scheme.

360 Meridi-Qans
A  :  1  B
Weft. Sun fetting. x Midnight, Eaft.
Let the ftrait line \A B "denote the firft qua
drant of the autumnal' aequinodtial day, bounded
in it's weftern extreme by Sun-fetting, and in it's
eaftern extreme by midnight.
Let this quadrant be divided into 360 diftindt
and equidiflant meridians; now the problem re
quires to determine which of thefe 360 meridians
interfedls the point of termination fought, and to
exprefs in fexagefimal parts it's diftance from each
of the extremes, both eaftward and weftward,

LI <tbt

( 266 )
The rules of the calculation.
Rule I. Multiply the collected number of days in*
to 4, and to the fum add the remain
ing quadrants, if there be any; the
product will be the fum total of the
quadrants.
Rule II. Multiply the fum total of the quadrants
into the arithmetical mean 360, and the
produdt will be the fum total of fexage
fimal parts.
Rule III. Divide the intire fum of fexagefimal
parts by the given number of years, and
the quotient will give the number of
fexagefimal parts in one year, and the
remainder will be the fexagefimal mea-p
fure fought.
The arithmetical operation for the given number of
D. 36 5 years.
RuleL 1333 13 X 4=533252-h 25=533254
quadrants. •
Rule II. 5332 54 quadrants X 3 6° = 1 9 ! 97 ! 440,
fexagefimal parts.
Rule III. 19 1 97 1440 fexagefimal parts -f- 36 5 ==
525949 fexagefimal parts in a folar
tropical year, rernains 44 the meafure
fought.
The precedent calculation does not explicitly
determine the quantity of the folar tropical year
(that will be the office of a fubfequent operation) it

( 267 ) -
it orily afcertains it's fquare in fexagefimal parts,
which are here found to be 525949; we are at
prefent more immediaiely directed to the remain
der 14, which is the fexagefimal meafure fought j
for fubftradt ^^ from 360, the remainder 305 dis
criminates and fixes the computed meridian which
interfedls the point of termination ; and the pro
blem may be folved in this language.
If the Sun enters Libra in any year, in the me
ridian of London at noon, then in the 365th re-
Volution from thence it will again enter Libra in
the fame meridian, in the end of the 305th meri
dian or fexagefimal part (for ^i. is the equable mea
fure of thefe diftances) from Sun fetting on the
weft, and in the beginning of the 55th from mid
night on the eaft, in the firft quadrant of the au
tumnal aequinodtial day, as in this Scheme :
^b
A © B
Weft ©305' I 55' Eaft. _
Gnereb X Chatzi laijelah.
Thus are we able to circumfcribe a determinate
number of equidiflant meridians, within determi
nate limits ; then exadtly calculate the fucceffive'
approach of any one of thefe determinates, and
arreft the perpetual mover in it's moment of time :
and if we would reduce this moment to our me
thod of computation by hours and minutes, we
need only divide 305 by 60, then the quotient
will give 5 hours, and the remainder 5 minutes.
L 1 2 The

( 268 )
The 6 fubftradted hours, p. 264, meafure frorri
noon to Sun-fetting ; thefe being added we have
i.ih 5', confequently, by this calculation, the
Sun enters Libre in the computed meridian, and
in the end of it's 365th revolution, .riot 46' 45"
paft ten, but 5' paft eleven at night precifely,
which is 18' 15" later. This difference of the
times between thefe two ingreffes in the fame me
ridian (fo that one of them muft "be erroneous)
may be properly noted, within the limits of the
fame quadrant, in this manner :

O

A h
W. Sunfett. O 4 46' 45"

o

" -8'

D

1S l

B
55' © Midn. E.

Reduce 18' 13" to feconds, and divide the pro
dudt 1095" by 365, the quotient will give 3"
for the difference of the 2 roots. The conclufion
is evident, without the trouble of any farther cal
culations, for 365 d 5I1 48' 57" -^j- 3" =
365 d 5 h 49' 00" : which, as will be evident
prefently, is the quantity of the folar tropical
year. I muft here beg the reader to take notice, that
I am not undertaking to difcover a truth unheard
of before^ but only to fettle that for a certain
truth, -- which .the aftronomers feem not to know
for a certainty to be one : I am only undertaking
to prove, both by calculation and by argument, that

(269)
that in the eftimation pf the folar' tropical year,
365 d 5I1 49' o" 1'" is too much ; or on the
other hand, 363 d 5h 48' 59" 59'" is too little.
My meaning is, that 365 d 5I1 49' 00" is not
an approximation, but adequately exact.
Some perhaps may imagine that the annual ex
cefs or defect of 3 feconds of time, in the cafe
before us, can be of no great confequence either
way. But I will fay, that the annual excefs or
defect of a fingle particle of time cannot be dif-
penfed with in the perfection of the folar fyftem.
It may be thought, (and indeed it is) very fur
prifing, that the arithmetical mean 360 (concern
ing which I have fome very particular and impor
tant remarks to offer) together with 7 almoft un-
compounded numbers, fhould be invefted with
fuch imperceptible andunfufpected powers. And
it may juftly excite our wonder and admiration to
perceive, in the courfe of the calculations, that,
in their right ufe and application, they, indepen
dent of known fcientific principles, uniformly pro
duce conclufions fcientifically true. Yet farther ;
it is more admirable ftill, that they lead us directly
to nature, they conduct us immediately and at
once into her penetralia and inmoft receffes, with-
* out any adhering imperfections, any tedious and
operofe calculations. Scarce any one point in
practical Sun and Moon aftronomy can be propo
fed, whofe folution may not be effected with a
required exaetnefs, by the incomprehenfible effi
cacy of thefe Mofaic numerical data.
When

( 270 )
When I confider in what degrees of perfedliort
the praxis of Sun and Moon aftronomy was ori
ginally taught mankind, by the Creator himfelf^
I can the more readily account for the inaccurate
conclufions of the moderns ; who build altogether
upon obfervation and inadequate rules of art ; who
unweariedly confult the archives of the Stars, and
meditate, day and night, on the book of nature:
But altho' we allow it's charadters to be ever fo
clear and legible, yet not being born with telefco-
pical eyes, we are, at leaft, liable to miftake it's ,
accents and it's points, which may give a different
turn to the fenfe.
When I look into the writings of our aftronov
mers, I am not fully taught; and I go away diffatis-
fied, becaufe I find myfelf left in a ftate of doubt,
hefitation, and uncertainty. I want to know, for
inftance, by what eftablifhed law, and in what
eftablifhed proportion, a given point of the day
annually varies from a given point of the year. —
But before I proceed farther, it may be proper to
confider thefe few Pracognita.
(i) The Sun makes no flay in the aequinox; it
only interfedls a point, and paffes obliquely on.
And there are good reafons to think that Tyco ob
ferved the very article of time in which this inter-
fection was made, Sept. 13 d 4h o' A.D. 1584,.
in the meridian of Uraniburg.
(2) The Sun ends and begins it's north and
fouth declinations in an immutable point of the
year,

C 271 )
year, but not in an immutable point of the day,
which annually fliifts and changes.
(3) That the point of the day annually fhifts
and changes is evidently manifeft by obfervation :
^_As, for inftance, had the Sun enter' d Libra
this prefent year, A. D. 1751, on the 12th of
September, 44 minutes paft noon, in the meridian
of London, at the end of the 4th year from hence
it would have again enter'd Libra, in the fame
meridian, exadtly at noon.
This being premifed, I return to the queftion,
by what eftablifhed law, and in what eftablifhed
proportion, is this change in the point of the day
with refpect to a given place annually made ?
When I make my appeal to the books of aftro
nomers, concerning the former I find a moft pro
found filence ; concerning the latter, there are al
moft as many determinations as there are aftrono
mers. Longomontanus informs me that I muft
exprefs it thus, 44' -f- -ri-"- sif I- Newton thus,
'*£ _]_ ^'. Dr. Holder thus, 41' -f- 44". Now
which of thefe muft we take for a directory ?
In the exigence and ftrait of fuch evident am
biguity, I apply myfelf, in hopes of fatisfadtion,
to Tyco's table of obfervations, p. 257, began
A.D. 1384, and ended A.D. 1587, where, un
der Brumalia Solfiitia, I meet with this quadrien-
nial feries, 44^ u' -&' ri' &"• Now I engage
to fupport this determination, and to render
it certain, that Tyco's index 44' is the index of
truth, and the very original proportion eftablifhed
by the Creator, whilft all the reft are artificial la
bour'd

( 272 )
labour'd anomalies, and a fad diflocation of pro
portional parts. So that Tyco's correctors may be
juftly faid, in this cafe, to ftand in need of cor
rection. Take then the 5th radical 60 for a denomina
tor, and make the 3d radical 11 the numerator,
and fet them by each other.
Tyco's index 44'. The 3d and 5th radicals 44'.
Now let the aftronomers, one and all, declare,
which of thefe two indices either exceed or fall
fhort ofthe exact truth, and how much.
I fhall affign my reafons in another place, why
I call this index 44' the meridian epadt, and make
ufe of it at prefent to complete the Vth rule laid
down, p. 261.
Rule V. p. 261.  If the given year be not
a year of commenfuration, then multiply it into
the meridian epadt (= 44') and dividing the pro
duct by the arithmetical mean 360, the^-quotient
will give the number of quadrants to be fuflradted
from the fum total of the quadrants, and the re
mainder will be the true fexagefimal meafure
fought. The arithmetical operation.
365: years.
X 11
360) 40 1 5' ( r 1 quadrants to be fubftradted.
remains ^^ ==¦ to the fexagefimal meafure fought.
60' 'As

( 273 )
As this concife and eafy calculation exactly
agrees, both in the quotient and in the conclufi
on, with the two foregoing arithmetical opera
tions, p. 262 and 266, they happily confirm and
eftablifh the truth of one another.
We muft now go back to p. 266, and confider
the quotient under Rule III, which exhibits, in
525949 fexagefimal parts, the exact aftronomical
fqUare of a true folar revolution : but by
Axiom, p. 256. (N° 13.)
which we will here repeat with fome additioris j
If the quotient contains the entire fum of fexage
fimal parts by a reduction of the true quantity of
a folar tropical year, thefe being divided by 15,
the remainder (by argument, d priori, founded
on the radical numbers) muft neceffarily be equal
to 4, the fquare of 2.
On the other hand, If, after the divifion by 15,
the remainder be lefs than 4, then the comple
ment of the fquare will be ever equal to the fum
of the annual defect, and vice verfd.
Again : If the fum ofthe annual defect be mul
tiplied by the given number of years, the product
will be equal to the fum of the defect, and alfo
equal to "the complement of the fquare of the
whole, and vice verfd.

The arithmetical operation.
i5)525949'(35o63 .. '
The remainder = 4 the fquare of 2.'

•r;

r.l

Mm We

( 274 )
We mqft now undertake to afcertain the root
of this fquare by the affiftance of the numerical
data, or their compounds ; which will lead me to
a difcovery of the years of commenfuration, and
to the proof of their certainty.
Firft then, if we divide the fexagefimal quo
tient 525949 by the arithmetical mean 360, and
the quotient arifing from this divifion by 4, this
laft quotient being prefixed to the remainder will
enable us to exprefs the folar tropical year indepen
dent, of hours, which (confidered as the 24th
part of a natural day) have no place in thefe, cal
culations, but, only by reduction.
The arithmetical opey-ation.
525949-4-360=1460^ remains 349,.
Then, 1460-4-4=365 -f- -i4l-=the tropical year.
But 360 — 349= 1 1 the meridian, epadt..
If we divide 34,9 by 60 the 5th radical num
ber; the quotient, it will be faid, will give 5
hours, according. to our computation, andthe re
mainder 49 minutes of an hour.
I would not have, it thought that I fuperftitiouf-
ly reject our method of computing hours ; ftill; I
continue to fay, that, notwithftanding the follow
ing reduction of 349 will produce the fame num
bers j and 40, yet we are under no neceffity to
denominate the former 5 hours, as ufed and un-
derftood by us, nor the latter 49 minutes of an
hour.

( 275 )
ift, Divide 349 by 15, the quotient will give 23
quadrants of 60, and the remainder, 4
fexagefimal parts, which referve.
2dly, Divide 23 quadrants of 60 by 4, the quo
tient will give 5 integers, and the remain
der, 3 fexagefimal parts. ,
3dly, Multiply the remainder 3 by 15, and, to
the product 45, add the firft remainder 4,
we fhall then have ^4 and 44.
Here it will be infilled upon that this conclu
fion ftands exprefs'd in our ftyle ; for do not we
divide the hour into 60 minutes, and are not 15
minutes a quarter of an hour ? yes, undeniably ;
and it is allow'd, that thus far our computation
falls in with the ratio of the radicals, and the ori
ginally eftablifhed fexagefimal meafure ; but if we
proceed one ftep farther, and confider the hour
as _4th of a natural day, then I muft equally in
fill upon it, that the calculation, under this view,
has no more immediate reference to the hour,
than it has to fub-fexagefimal parts, or fecond
minutes, which are utterly excluded from the
quantity of the folar tropical year, by the appoint
ed aftronomical unit, or minimum ^4.
Thus we have, at length, by gradual advances
obtained both the fquare and the root fought, in
a, method a priori, or without any fuppofed pre
vious knowledge either of the one or of the other.
Euclid's doctrine of the fedtion of flrait lines
is vaftly curious ; but here is the fedtion of a qua
drant (which may be reprefented by a flrait line)
propofed, altogether as curious, and as truly geo-
Mm 2 metrical,

( 276 )
metrical, I had almoft faid, as any in the feconc}
book of his elements. For what can be more
mathematically exact than the difcrirnination, by
a plain, eafy, numerical calculus, of that very inr
dividual point, in a limited fpace of time, in „
which the Sun finifhed a given annual period, and
Jn the fame individual point completed it's fquare?
fuch a conclufion in aftronomy, without the aid
bf any known aftronomical principles, was fcarce
ly to be expected. And I am pretty certain, that
if the whole prqcefs be judicioufly examined,
weighed, and confidered, it will approve itfelf tp
the examiner.
Before I proceed to another argument, I beg
here to remind the reader, that the principal end
which I have in view is, to render it indifputably
Certain, that Mofes's table of the genealogies both
of the antediluvian and poftdiluvian Patriarchs is,
in itfelf confidered, a moft accurate aftronomical
table, and that it is founded upqn £hefe two laws,
viz. I. f*he years of the lives of the Patriarchs are
niade, by an aftronomical reduction, to run.
parallel (i. e. to begin and end together at
the autumnal asquinox) with the years of the
world. And, confequently,
II. Every Mojaic Shanah is a true fqlar year.
Upon this account, order required me, in the
firft place, to afcertain the meafure of the Hebrew
Shanah ; and I am, in the fequel, tp dernonftrate
that I have afcertained it ; that I have fet the
quantity of the tropical year in it's proper point of
light,

( z77 )
light, and rendered it more
certain than ever it was before,
as being now by analyfis redu
ced to it's original Mojaic prin
ciples. •Had I been obliged to have
.poftulated the quantity of the
folar tropical year, or could I
not have immediately deduced
it, by the affiftance of the Mo-
KJaic data, the fcheme of facred
chronology would have been
deprived of the fupport of it's
chief corner ftone; and the
aftronomer, it is probable,
might have hinted the juftice
of paying the fmall tribute of
a grateful acknowlegement to
his labours. ¦
I will now make a table,
by which any given number
bf folar tropical years, within
the limits of 6000, may eafi
ly and readily be reduced to
days.

A fable of reduflion of
folar tropical year?
to days.

Yea?:

Days'

H

49

I

365

5

2

730

11

38

3

*°95

*7

27

4

1460

23

16

5

1826

5

5

'6

2191

10

54

7

2556

16

43

8

2921

22

32

9

3*87

4

21

10

3652

10

10

26

7304

20

20

30

10957

6

3°

40

14609

16

40

5°

18262

2

5°

60

21914

13

00

70

25566

23

10

80

29219

9

20

90

32871

*9

30

100

- 3^524

5

40

290

73°48

11

20

300

109572

l7

00

400

146096

22

40

500

182621

4

20

,60.0

21 9 1 45

10

00

700

255669

r5

40

800

292x93

21

20

900

328718

3

00

1000

365242

8

40

2000

730484

17

20'

3000

1095727

2

0

4000

1460969

10

40

5000

1826211

19

20

6000

2191454

4

0

We

( 278 )
We will now reduce, by this table, 365 years
to days, in order to fhew it's exact agreement
with the precedent arithmetical calculus by the
radicals, independent of all tables.
365 years feparate themfelves into this feries,
300. 60. 5. fet them down in this order, and
the correfponding days., hours, and minutes in the
fame, over againft them.

iTears

D.

h.

/

300;

-109572

J7

ob

60J

* contain^

' 21914

13

00

5*

D

: 1826

5

5

J333i3

11

5

Coroll. Should the Sun enter Libra, in the men?.
dian of London, or elfewhere, in any year
exactly at noon, then by this table, and
the precedent calculation, it would again
enter Libra, in the fame meridian, j mi
nutes paft eleven. at night precifely, by an
invariable law, in the 365th revolution
from thence. D. h. ' "
1, Ifto Sir/ Newton's reduction, 1333 13 10 46 45
we add the fum of the defeft, 18 1 5 p. 268.
2. It will be equal, by Axiom, p. 273, ? _
to the complement of the fquare 5LJ'3iJ,311 i vu
I could with that the following queftion might
be thought a proper thefis in aftronomy to be put
up and difcufs'd in the fchools, viz. Whether

( 27? )
Whether the difference of 3" in thefe two af
figned roots ought to be eftimated as an annual
defeft, or as an annual excefs ?
Now I undertake, againft all oppofition, to
prove, that they ought to be eftimated as an an
nual defeft ; and that the odd 57" of Sir I. New-
ton's. determination of the quantity of the folar
tropical, year ought to be completed into a fexa
gefimal part.
Without any regard had to the foregoing cal
culations, and their refult, I will ftill, confider the
meafure of the folar tropical year as an unknown
quantity ; and I am to difcover and fettle it's ex
act meafure from the firft year of commenfuration j
not that I am confined to the firft.
Was it a queftion put, and referred to the de
cifion of our aftronomers, whether the Creator
has eftablifhed a commenfurability between the
diurnal and the annual motions, or not ? it muft,
upon their principles, be pafs'd in the negative.
And yet this eftablifhed commenfurability is the
alone medium in nature which can enable us toaf-
certain, with the mihuteft exaetnefs, to an indi-
vifible point, the true meafure of the Sun's, year.
I fay, the alone medium in nature, for that it may
be (at leaft, nearly) attained by the rules of vul
gar arithmetic, Sir i". Newton, was he living,
would not decline to teftify.
It is a dream and a delufion to talk of the per
fection of aftronomy, in the prefent ftate of fci
ence, and the rules of it's determinations. Mofes

( iSo )
Mojes', in the introduction to his Pentateuch,
has happily taught us more in thefe few words,
God Jaid, let them be for days ond years, than the
moderns yet know, or have ever been able to find
out. For they cannot make the meafure by days
to correfpond exadtly with the meafure by years,
and therefore their conclufions are artificially im->
perfect, inftead of divinely true.
Our aftronomers fay, that the folar tropical year
(whofe quantity is not certainly kndwn) gains a
whole day of the Julian ; in other words, that
it's head goes backward in the Julian calendar,
and fo it begins a whole day fooner, in about 130
years. If you demand exaftnefs of truth, you
will find the calculation perplexed and entangled
with fecond minutes, to the utter exclufion of
truth. The aftronomical effects and confequences of a
commenfurating year are attended with an ap
propriated Angularity ; for in this diftinguifhed
year only, the meafure by integral days is the
fame, without excefs or defect, with the meafure
by integral years. Both computations jointly be
gin and end in the fame cardinal point of the year,
in the fame cardinal point of the day, and in one
and the fame meridian ; all which particulars may
be thus reprefented to the view :
=£» 2103 796 days = 5760 years — o =^=
©  r— 0
Zohoraim, Zohoraim,
Noon. Noon. Now

( 28 1 )
Now, I fay, that the modern aftronomer can
not, upon his avowed principles of calculation,
and the Newtonian correction of Tyco's obferva
tions, either confirm or confute this conclufion.
It may be true, or it may be falfe, for any thing
he can prove to the contrary ; for it entirely de
pends upon the doctrine of a commenfurability :
the queftion then that remains, is, whether this
be matter of fact, or not ? which is the fubject of
my prefent enquiry, and I thus introduce it.
From the beginning of A.D. 1700, we have
reckoned 1 1 days difference between old ftyle and
new, or between the Julian and the Gregorian ac
counts ; but altho' this is the 5 1 ft current year fince
this' reckoning commenced, yet if we make a cal
culation by any of the folar tables now in ufe,
they will give us to underftand (fo inaccurate have
we been in the folar computation, as adapted to
civil ufe) that thefe 11 days difference between
the two accounts, are not yet completed. I afk
then  —
In what year of the Dionyfian vulgar sera will
thefe 1 1 days difference be exactly Completed ?
Here our aftronomers will find this plain, fim
ple queftion, a difficulty as infuperable as that of
fquaring the Circle. And they will be reduced to
the Dilemma either of giving up Dr. Halley's and
Sir I. Newton's folar tables, or of attempting to
prove, that the doctrine of a commenfurability be
tween the diurnal and the annual Motions is not
founded in nature, and muft be rejected as a ficti
tious and chimerical notion.
N n Now

( 282 )
Now fince the true meafure of the Sun's year
may ftill be confidered (after fo many diligent,
fkillful, and follicitous refearches, and endeavours
to attain it) as, quid indeterminatum, or, as an
uncertain quantity ; and fince Longomontanus has
corrected Tyco's obfervations by 5" feconds annu
ally, and Sir I. Newton by 3" feconds annually,
we will affign ex hypothefi 5 different quantities of
the tropical year, all terminating in fecond mi
nutes, from 55" to 59", and then bring them all,
if it may be, to fome teft and touchftone of their
truth. A Table of $ affigned quantities of the Jblar tro
pical year, all terminating in fecond minutes.

The tropical/^
year fuppofed>3
to contain V. 4
J5

D h
3^5 5 48'

^" Longomontanus.
56" A.
Sy" Sir I. Newton.
58" B.
59" C

The council of nice was held A. D. 325, which
being fubftracted from A. D. 1750, remains
1425. Therefore from the year of the council
of nice to the current (A. D. 1751) exclufive,
have elapfed 1425 Julian years, which being re
duced, contain 520481 days, 6 hours.
In the next place, reduce thefe 5 affigned quan
tities of the tropical years to days, then fubftract-
ing the feveral products from the Julian reduction,
the differences will fhew refpedtively how much thefe

( 283 )
thefe 1 1 computed days want of their exact com
pletion. Here follows
A Table of calculated reduftions, and their re
fpeftive differences from the Julian, in the fpace
of 14.25 years, or from A. D. 325, to A. D.
1750 inclufive.

D h ' " ( 1 )
365548 55 Longomont.

D

h ' "

Julian 520481

6 00 00

Solar - 520470

6 46 15

Difference 10 23 13 45

D h '- " ( 2 )
365 5 48 56 A.

D

h ' "

Julian 5.2048 1

6 00 00

Solar- 520470

7 10 00

Difference

10 22 50 00

D h ' " (3)
365 5 48 51 Sir 1. Newt.

D h ' " (4)
365 5 48, 58 B.

D h ' ' "
Julian 520481 6 00 00
Solar- 520470 7 33 45

D h ' "
Julian 52048 1 6 00 00
Solar -520470 7 57 30

Difference 10 22 26 15

Difference 10 22 2 30

D h
3°~5 5

/ //
48 $9

C.

;s)

Julian Solar -
Differe

D
520481 520470

h6 8

00 21

r!
00 !5

nee 10

21

38

45

The next Step we are to take is to calculate
the neareft approximation of thefe feveral differen
ces to the completion of the Day, and to fet down
Nn 2 the

(284)
the refpedtive years in which they will be found ;
for not one of thefe affigned quantities will, by any
calculation, produce an exadt completion. And
I urge this exadt completion of the day, as one
genuine criterion, for I have another , in ftore, of
the authenticity and truth of the affigned quantity j
and fo, vice verfd.
J Table o/ the neareft approximations ofthe cal-
, cula'ted differences, and ofthe refpeftive years of
the Dionyfian vulgar ara, in which they are
found, with the fums of the feveral defeft s.

(I)A.D.I754.

(2) A.D. 1756.

(3) A.D. 1758.

D h ' "
10 23 58 5

D h ' . "
10 23 56 24

D h ' "
10 23 54 39

Defect 1 5$

Defect 3 36

Defect 5 21

(4) A.D. 1760.

(5)A-D. 1762.

D h
10 23 52 50

D h ' "
10 23 50 sy

Defect 7 10

Defect 9 3

It is obvious to perceive that the addition of
one year more would, in every inftance, caufe a
proportionable excefs above 1 1 days, as they now,
in a certain proportion, fall fhort df them: And
it becomes undeniable matter of fact, that our
aftronomers have no theories, principles, or laws
of calculation, which can fo much as fuggeft the
hint, much lefs lead them into the difcovery and
know-

¦ ( 2*5 )
knowledge of a commenfurating year. Nor can
they poffibly folve the plain, fimple queftion pro
pofed, but upon the forementioned terms and con
ditions; viz. without either giving entirely up
their moft elaborate, and moft approved folar ta
bles, or rafhly impugning an eftablifhed law, an
original ordination ofthe God of nature, arid in
finitely wife Creator ofthe folar fyftem.
It is no wonder if the doctrine of a commen
furability, between the diurnal and the annual mo
tions, fhould occafion fome fufpenfion of judg
ment and affent, fince it is fo entirely new and
unheard of before'. It is evident that Dr. Holder,
in his account of time, had no apprehenfion, or
even the leaft fufpicion of it, as appears from p. 22.
" The day is no aliquot part of the year, (ftrict-
" ly fpeaking) neither to compound nor divide
" the year, fo much as by units. If the year
" comprehend days, it is but as any greater fpace
" of time may be faid to comprehend a lefs, tho'
"" the lefs fpace be incommenfurate to the greater.
<c And from thefe differing properties of day
" and. year, arife difficulties in carrying on and
" reconciling the fupputations of time, efpecially
" in long meafures. Altho' it muft be confefled,
" that for vulgar ufe, where is no need of, or
" regard to, exadt calculation^ we have no bet-
" ter meafure of a fingle year, than the day, and
" the artificial folar month, confifting of even
" days.
" But if we thus meafure many ages of years
,( by even days, our computation will be perplexed. " For

[ 286 ]
" For the year (without regard to days) ends,
" and is terminated, with an odd day, and odd
" hours, and odd minutes, and odd fecond mi-
" nutes, if we go no farther : fo that it cannot
"be meafured by any even number of days, or
" hours, or minutes." Thus far Dr. Holder; but
That the Creator has adtually eftablifhed fuch
commenfurability, the Mofaic ftyle, principles,
terms, and data, will furnifh us with a direct and
irrefragable proof.
Firft then, I am not only to offer the Rule
how to find out thefe diftinguifhed years, but al-r
fo to fettle their feries, or true order of fueceffbn
in the world's chronology.
Secondly, having fettled their feries, or true
order of fucceffion, I am to deduce^ from their
effential properties and affections, the true mea
fure of the Mofaic Shanah, or folar tropical year.
Thirdly, from the tru e meafure ofthe MofaicSha-
nah to fhew the exact completion of the nth day.
We are now entering into the depths of this
fcheme; and indeed, there are more depths in
this original fimplicity, more inftrudtive arcana in
the aftronomy of the Pentateuch, than the Rea
der, perhaps, upon a bare view of my general
propofitions, might be readily induced to imagine.
Tho' poffibly he may have fome apprehenfions of
this kind, if he will give himfelf the trouble td
read and confider thefe neceffary
Pracognita.
(i) The arithmetical mean 360, and the 7 ra
dical numbers include in them a geometrical pro
portion,

< 287 )..
portion, and 4 diftindt ratios. (1) A fexagefimal.
(2) A quintodecimal. (3) An undecuple. (4) A
quadruple ratio. Thefe are fet down and noted
in the following table (with their complements
or fourth numbers) in the form of proportionals.
A Table of geometrical proportions.
4 : 1 : : 60 : 15
4 : 1 : : 11: 2 45
1 : 60 : : 2 45 : 165
15 : 1 : : 165 : 11
11: 1 : : 1 65 : 1 5
1 : 4 : : 360 : 1440 the ift year of commenfuration.
1 : 4 : : 365-k: 1461 quadrants in a Julian year.
It may feem incredible, but the refult and it's
proofs may evidence, that the calculations of Sun
and Moon aftronomy are refolvible, not fo entire
ly into principles of fcience founded upon obfer
vation, as into predetermined ratio, and fettled
geometrical proportion.
We will, at .prefent, examine more particular
ly the number 360, the multiple of 60 and 15,
which are the 5th and the 7th radicals. And
there are fpecial reafons for this ; for we can fcarce
ly ftir a ftep in the integral calculations, without
the help and concurrence of this well known (and
yet, methinks, unknown) auxiliary, together with
it's fub-multiples. Here I beg to be informed
with candor and ingenuity, from whence had we
the divifion of the ecliptic and the aequator into
360 equal -.parts? nature directs not to it; and
Mofes,

( 288 )
Mojes, in his recorded aftronomy of the. year of
Noah's life 600, has enlarged the circle of the
year into 365 parts. Will the aftronomer fay,*
that as it has defcended down, by a ufage imme
morial, from his forefathers, and the days of old,
that therefore he has a great veneration for it's
high antiquity? or will he choofe to fay with Dr.
Holder, in his account of time, p. 27. " that it
" is artificial and arbitrary, but well chofen and
" pitched upon, as being a number that abounds
" with integer aliquot parts, and therefore mofi
" apt fdr partition?" He makes this fhort def-
cant upon it, p. 28. " The number 6 is celebra-
" ted for having all aliquot parts, viz. 3, 2, 1,
ct and for being compofed of the aggregate of
" them all, and therefore is ftyled the perfect
" number. And 10 is the firft ofthe faracenical
ce figures, or figures with cypher, that great friend
" to calculation, or rather, which changeth cal-
" culation, ftrictly fo called, into eafy computa-
" tion. Now the number 360 confifts of the
" fquare of 6, viz. 3 6 multiplied by 10, or ha-
" ing a cypher added to it.
It is a prevailing notion, and the learned feem
to give an unanimous fuffrage to it, that we re
ceived thefe 360 days from the antient /Egyptians,
Chaldeans, and Grecians. If indeed they are con
fidered as an imperfect meafure of the folar year,
the hypothefis may be'fo far admitted : but if as
an aggregate of 12 equal 30-day months, then I
have manifefted from the Pentateuch, that it is
not true, and muft be rejected. So far is this no-
' tion

( «%> )
tion from having any juft foundation, that, on the
contrary, the firft of. thefe 12 equal 30-day
months, fixes it's head in the 4th of the Hexae-
meronj and is cozetaneous with the annual motion.
The' wife Architect of nature, and Framer of
the original aftronomical year, did not inveft this
fexagefimal and quintodecimal number 360 with
fueh eafy 1 and complying properties arid powers,
for mean, frivolous, and inadequate purpofes.
The table annexed, which is conflrudted from;
this, great Friend both to the folar arid the lunar '¦
coriiputation, by it's fub-multiple 15," will fuper-
fede the ufe of every folar table, which does not
correfpond with the fame laws of proportion.

\

CO

!'- | C-)

Oo Afexa-

•5s -

¦o
-Os W

s sX
f

-bs.
"s— '

loO '"^O
^MH O
01 'LO$@,i>-i;

. ¦" m ¦ ' -)
LO O Lft, O'
<rrtM o;
cOsO OS NT

LO O LO O
t|- co m o
+ NO M
N CM «*» CO

LO O LO O
TJ- CO M O
LOOO i-i tJ-
co co -^h Th

LO O LO O
Tj- CO Hi O
sO Os N lo
Th Th lo LO

LO O LO O
Th co -> O
bs. O COSO
LosO sO sO

^^ vo O «n'0"
-. ¦ \0 ro 0s«0
1£, ; « 'co s^>o
i . - -

LO 0s LI", O'
M OS LT) «-
OO OS •"< P"j

LO O Lo O
CO lo w oo
ThsO OO OS

lo O »o O
i-l CO ri-sO
N N N N

LO O LO O
O Nt^O
OO Os w CO
« N CO CO

LO O LO O
sO CO OssO
ThsO t^. Os
CO CO CO CO

•O'iOi^O' On O OOO)
«0-sO -sO sOls©'sQ sQ*<o.

OOOO
sO sO sO so

OOOO
sO sO sO SO

OOOO
sO sQ SO sO

OOOO
sO sO sO so

Th

?*¦ M CO TP
>- -N TO Th

LrjsO t>iOO"
-LhsO bsCO'

Os O M N
OS i- <M CO

CO t}- losO
Th loso t\

b-sOO Os D
OO Os O N

l-H N CO Th
CO Th LOSO
N N N N

CO
s>>

w-, o *o O
sO CO Os-sO
•I-I CO.-**©

LO O Ll") O
N OS Lo N
GO Os >-i CO

lo O lo O
oo lo « oo
t)-xO OO Os

LO O LO O
Th « t^Th
>- co ThsO
N N N M

lo O lo O
O NcoO.
OO OS i-c CO
W M CO CO

LO O LO O
sO co OssO
ThsO t's. OS
CO CO CO CO

lO^^^f)

LO LO LO VO

U-) LO LO LO

LO LO LO LO

uo lo Lo Lo

LO LO LO LO

*»— ' -t>-.
¦^o o lo o;
n cOTf-sO
*0 O lo O
NOO N
*o O "O O
co ^sO OO
LO O LO O
Os i-i M Th
•0 0*0 0
«*} OnOO O
« M N «1
""> O «o O
I-I CO ThsO
CO CO CO co
m w ro ¦+
'OsO b-sOO
Os O " <M
crs ^J- «Ovo
bsOO Os O
i-i N CO Th
c« w N ea
J ^P§1
( 291 )
$. .c^ntinu^c® of neceffary
Pracognita.
1(2) The number 360 (fo alfo the 7 radicals)
may be gonfiderefi and ufed under different denpr
minations and values, as the fubject matter in hand
fhall require, and it will be equally applicable,
and wiU 'equally adapt itfelf in the calculation, to
all and every one of them. Thus, for example,
we may fay, ejjher 360 years, as in the table, or
equaj. moptfys, or day$, or quadrants, or degrees
and minutes, or hours and minutes —r but lower
t^n primes we cannot defcend, as the integral
calculation entirely difcards all fecond minutes.
(3) When any of the radical numbers have a
foecific denomination given them, fuppofe, for
ipftance, 1 j days, the fettled proportions will be
jnyariably preferved ; for let 60 denote any inte
ger whatever, 15 is ftill it's fubquadruple, and
affumes ihe fame denomination.
(4) 15, the iquadrant of 69, may be meafured
by 3 and 5 ; fo that 5 js equal to 4, and 3 to 4 of
15. This may be properly noted, becaufe the
fquare of a folar revolution terminates by the cal
culus, in one of thefe aliquot parts of 15.
(j) If the 3d radical number 1 1 (without fpe-
cifying it's denomination or value) be multiplied
info tthe- 7th radical number 15, the produdt 165
being divided back ;again by 15 will give in the
quG>t-i€$nt 1 1 quadrants. And the dividend 1 65
will be the quadrant of the number ,660, which
being divided fey-joo, the quadruple of 15, will
give in the quotient a numher made up of like fi-
Oo 2 gures,

(2^2 )'
gures, but in a quadruple ratio to the former.
This may be illuftrated from the table, as may be
feen, by fetting the numbers1,' Index i, Col. (2)
(3) (4) over againft the numbers, Index 4, Cdl.
(5) (6) (7)-
Index 1. ,.15 165 11 quadrants. Index 4. .. 60 660 11 Integers.
In like manner. . . 15 360 24 quadrants  60 1440 24 Integers.
We, for inftance, in our computations of time,
divide the nucthemeron, or natural day, into 24
equal parts or hours, every one of which equal
parts is meafured by 60. But the table above di
vides the quadrant of the nucthemeron into 24
equal parts, every ione of which is meafured by 15.
Hence it comes to pafs, that the number 24 is
made a ftanding and unalterable divifor, in the
arithmetical operations, where years are propofed
to be reduced to days.
(6) It is neceffary to take particular notice, and
to bear along in our minds, that thefe inftrumen-
tal^ operative, and efficacious numbers, collective
ly taken and confidered, are both fimple and com
pounded, and that the greater integrally include
the leffer. The number 360, for inftance, may
be meafured by 4, 60, 30, 15, whilft the 3d ra
dical number 1 1 is the fum of 4 and 7, &c. vide
p. 249, where thefe partitions are all noted, and
they are mentioned again here, ' becaufe, being
amongft the effentials and fundamentals, they are
neceffary to be remembered as well as known* •
From a clear view and experimental conviction
of the inherent aftronomical powers, and the na
tive

( 293 )
tive geometrical proportions, of thefe Mofaic nu
merical data, I am inftructed (nor have I any other
preceptor) to argue and conclude with an inde
fectible ' certainty 5 and from hence alone was I
enabled to lay down that aftronomical axiom,
p. 250, and 273, which I ftill offer and urge as
a fure criterion.
1 (7) When the true meafure of a folar revolu-,
tion is allowed to be afcertained, with the minu-
teft exaetnefs, to an indivifible point, and, by a
general confent, acquiefced in as fuch, then it will
be proper to give a more explicit account of the
above < folar table. In the mean time, it is no
hyperbole, but a juft recommendation of it to fay,
that in it's ufe and application (an inftance of
which will be given in a fubfequent calculation)
it is abfolutely perfect, infallibly certain, and un
erringly true : that it's proportions are exactly
conformable to nature, and it will be impoffible
ever to convict it of error.
What a bigoted enthufiaft is here ? fays an
aftrbnomical Deifl\ Let him enter the lifts then
with this bigoted Hebraician, and bring to the
teft the aftronomy of the Pentateuch.
To proceed :- The advantage and importance
of the prefent refearch terminates, not in the bare
• fatisfadtion of being able to difcover and determine
the adequate meafure of the Sun's year, and to
perfect the approximations of the moderns (tho'
this is of no fmall weight in it's felf confidered)
but in a view of the whole refult, and of a train
of confequences, which dilate and expand them felves

( ?94 )
felv.es into the ejft&blifhmg m msUtnt theory of
meridians, which lie concealed, at prefent, from
.philofaphiq foqeulatjon, and muff,, withojjf fome
farther improvement, continue to do fo to the
end of time.
The particular circumftance of our more imme
diate enquiry is the rule how to find out thefe
commenfUratjng years j but here our iaboufs; will
be fhortened by the iabjg df geometrical n&cfmr
tions, p. 2.87, for in itbis parallel line
1:4:: 369 ; 1440
the 4th pr©portibikl is, as J fhall prove, the num-
ber fought ; whofe place or fituation in the lives
of the Patriarchs /and Mofhrs table of their genea
logies, may be eafily kjjowra. For Noah was
bom A. M. 10^6; but A. M. 1440 -*. iojo =
the 384th year of Noak}& lile, which hegins and
ends, at the autumnal qequinox, with the firjt year
of commenfuration.
The arithmetical mean 360 (whofe powers,
like it's extradl and origin, are truly divine, and I
might venture to fay, well nigh inexhauftible) is
the foundation anff aliquot part of thefe remarka
ble years ; fo that their feries, or *rue order of
fucceffion, ' in the world's chronology, may be
known and adjufted by only multiplying 360 by
the 2d radical number 4, and it's multiples, as m
the eafy calculation enfuing.
A. M.

<( 295 )
'" A,M.
" , ;;'^x 1440- i. 'l^^ofM^'siife 7 The 13th year of the
366 X 8 = 2886 II. > judgefhip of Ell the
J high prieft.
j The 8th year of the relgti
i2 = 4|2ovlII. > df: Conftantine the
3 great, A.D. 313.
)The&$7thyeaf from the"
serabf theCdnque'ft,

161 ==5760* IV ',

0
A. D, 1753,

Not' one intermediate" year can be proved to be
invefted with fhe fame properties and affections',
as thefe ibuf are ; foi being reduced to days, they
ioifttb/begin and end in One and the fame point
of lib© yeahr,. day*! and computed meridian. So
that pfishhive and patriarchal afkohomy teaches
us this hitherto unknown leffdn 3 it iriftrudtS us to
f&f, that in the' fpace of 1446 annual revolutions
of the Sun, One entire periodical revolution ofthe
iherMikh epadt is completed ; and from the com*.
paction of one entire periodical revolution of the
meridian epadt arifes the firft yeafr of commenfo^
ration. Moreover, the fum total of diurnal revo
lutions to be fubftradted, are equal in quantity to
the lunar epadt, which is alike . in figure to the
mefidlan tfiadt, (Merging the fame laws, and en-
creafing 'th ihe fame arithnie'tic&l pogreffion by
11.

( 296 )
ii. For in 5760 Mojaic Shanim, or folar tropi
cal years, there are included (1) 5760 12-month
lunar years ; and (2) 5760 lunar epacts '; and (3)
$y 60 annual feparate quadrants, adhering to the
lunar epadts, being the aftronomical bonds of con
nection, appointed to this office ab origine • and
(4) 5760 inhering meridjan epacts, which annu
ally encreafing by a creatM law, and in a created
proportion = ^jl, meafure the diftance from the
computed, meridian, to that meridian in which
the folar year and the folar day begin together.
Here we have a general view, draught or plan, of
the primitive laws both of the folar and of the lu
nar computations: .
To keep to the method propofed ; here are 4
years of commenfuration fpecified and determined :
we are then, from the fifft or the laft, or any one
of them indifferently, to deduce,: with the minu-
eft exaetnefs, to an indivifible point, the meafure
of the folar tropical year, and then to demonftrate
it's truth and certainty. For between deduction
and demonftration there is undoubtedly. a very
wide difference. Sir I. Newton; for inftance, has
limited this meafure to 3 65 d 5 h 48' ^y" '.: ¦'. But
who ever has, or will undertake, to eftablifh it's
authenticity? it ftands, at prefent, but as an ipje
dixit, liable to be controverted ; and it may, and
it ought to be corrected, not merely as being de
ficient 3 feconds of time, but as a repugnancy to
nature. We will reduce the firft and the laft of thefe
4, years, viz. A. M. 1440, and A. M. 5760. As

C 297 )
As for the rules of this reduction, I need only refer
to p. 261, where they are plainly taught.
Rule I. A.M. 14404-15=96.
Rulell. 96x11 = 1056.
RtileHI. 1056-^-24=44 quadrants.
Yrs. Quad. Quad'. Days Q^
R.IV. 1440x1461=2103840-^4=525960 0 Jul. redu£h
RuleV. - - - — 44
21037964-43:525949 o Sol. redufl:.
Difference from Julian 1 1 o o'
if we carefully look over and confider the fe
veral parts of this calculation, we- may perceive,
that, in the quotient of the Solar reduction, there
are juft as many days as there are fexagefimal
parts, in a Solar Tropical year : and alfo, in , the
number 1440, there are juft as many years as there
are fexagefimal parts in one diurnal revolution of
the Sun. Hence thefe two numbers, 1440' and
525949', maybe reckoned homogeneous quanti
ties : therefore, if we divide the quotients, both
of the Julian ahd the Solar reduction by 1 440,
and the remainder by 6q, the quotients arifing.
from this divifion will exhibit, the one the quan
tity of the Julian, the other of the Solar Tropical,
year^

P p The

( 293 )
The arithmetical operation.
Years Days D h '
1440') 525960' (365 6 o the Julian year,
60) 360 (6
Years Days D h '
1440') 525949' (365 5 49 Sol.Trop.year.
,60) 349. Differ. 44'= Merid. epadt.
%, E'. F.
In the next place, we will reduce by the fame
rules 5760 years, and carry on the calculations
jointly, ftep by ftep.
RuleL A.M. 5760-^15=384.
Rule II. 384x11=4224.
Rule III. 4224424=176 quadrants to be fubffra&ed.
Yrs. Quad. Quad. Days
R. IV. 5760x1461=841536044=2103840 JuIianreduH.
RuleV, - - - - — 176
841518444=2193796 Spl. reduction.
Difference 44 0 o' Yeafcs

( 299 )
Years Days D h '
5760') 2103840' (365 6 o the Jul. year.
460x4=240' - - - 1440 (6

Years Days D h '
5760') 21,03796' (365 5 49Sol.Trop.year,
4-60X4=240'- " - I396 (5 | Differ. £y=Merid, epadt
4) *96 (49
& E. F.
Rule V- p. 2,6-1, is thus drawn up and expreffed.
From the fum total of Julian quadrants fubftradt
the quotient obtained by Rule III. then, dividing
the remainder by 4, this laft quotient will complete
the reduction, if a year of commenfuration be
given. Confequently, if, according to the direction
ofthe latter part of Rule y. laid down, p. 272,
we multiply the given number of years into
H = to ;the meridian epadt, and divide the pro
duct by the arithmetical mean 360, the quotient
will give the number of quadrants to be fubftradted
as before, but the remainder will be =0, And
k neceffarily mufl be fo, becaufe in fuch a year
the computed meridian is revolved to it's firft fta-
tion precifely ; in other words, the original car
dinal point of the Solar day (viz, noon) is again
aftronornically connected with the original car
dinal point of the year, viz. the autumnal equinox.
And this is what I would be underftood to mean
Pp 2 by

( 300 )
by the effential properties and affectiops of a comr
menfurating year.
The arithmetical operation. [Vide p. 272.]
A.M. 1440

360) 15840 (44 quadrants.
Remainder o
A.M. 5760 Xii
360) 63360 (176 quadrants.
Remainder o
We need carry on thefe joint calculations but
one ftep farther. I fay then, laftly, if we mul
tiply the fum total of the quadrants [vide p. 266.];
into the arithmetical mean 360, and then divide
the fum total of the fexagefimal parts by the given
intervals, or refpedtive number of years; the quo
tients will contain the exadt number of fexagefimal
parts in the Solar Tropical year, whilft the remain
ders will be refpedtively =0, as before, and for
the reafons juft now affigned. . the,

< 3°i >
The arithmetical operations.
Quad.
I. 2103796X360=757366560' fexag. parts.
II. 1440') 757366560' (525949' in a Trop. year,
Remainder o'
Again :
Quad.
I. 8415184X360=3029466240' fexag. parts.
II. 5760') 3029466240' (525949' in aTrop.year.
Hemainder o'
Having deduced the meafure of the Mojaic
Shanah, or of a true Solar revolution, from the
firft and the fourth years of commenfuration ; and
by the fame calculations having rendered indifpu-
tably certain the doctrine of a commenfurability
between the diurnal and annual motions ; I am
now, by the method laid down, to demonftrate
its truth and certainty : I am to make it ap
pear, beyond the power of confutation, that —
3656. 5I1. 49' o" are not an approximation, but
true, irt nature, to an indivifible point.
My firft argument fhall be taken from the com
pletion of the day, which alone and in itfelf con
fidered is irrefragable, becaufe founded upon the
bafis of commenfurability. *
The interval from the vernal aequinox, A. D.
3 2 j, which was the year of the Council of Nice, to

( 3°2 )
to- the vernal aequinox, A.D. 1750, meafures 1425
Solar Tropical years. Reduce thefe 1425 years
to days by the table, p. 277; then, fubftracting
the fum total frpm 52048 id. 6 h. or the Julian
reduction,thedifferencewill fhew how much the 1 1
computed days want of being exactly completed,
and which not one of the precedent calciftations,
according to our aftronomical laws, could complete.
The reduction of 1425 years to days by th table t
P-277'
Years D h '
1000 -\ r 365242 8 40
4°° C ^ntain ^ ^6o96 22 4°
20 C J 73°4 20 20
5J -C 1826 s 5

.520470 08 45

From the Julian 520481 06 00
Subftradt - - 520470 08 45
Difference 10 21 15
Deficient - - 2 45
Now then from 1440 fubftradt 1425, the num
ber of years elapfed, and with the remainder 15
enter the fexagefimal and quintodecimal Solar ta
ble, p. 2 90, where, in the firft column of the firft
parallel line,: we fhall find the fame number of
years

( 3^3 )
years placed the firft irt order of thofe which are
fet perpendicularly in the fame column, and all
equally encreafing by 15. As the firft and the
laft parallel lines of this table include the whole
ratio of the calculus, made ufe of by me in the
reduction of years to days, I will here tranfcribe
both of them, with all their appendant numbers.
A tranfcript of thefirfi and the lafi parallel lines
of the jexagefimal and quintodecimal Solar table.

24

CO
Years

15

360

(2)

r5

15

(3)

165

396°

(4)

11

264

(5)

60

60

(6)

*S

3960

(7)

2 45

66 00

The prefent calculation will afford a proper op
portunity to illuftrate the aftronomical properties
and powers of this Solar table, in its ufe and appli
cation. If we look back to the laft conclufion,
we may' obferve, that the difference between the
Julian and the Solar computation, in the interval
given, was 10 d. 2ih. 15', and the deficiency
2 h. 45'. In the 7th column of the firft parallel
line, over-againft 15 years, we find thefe very
numbers 2. 45. and they are the numbers fought.
Here it is worth our while to take notice, with
what an exquifite prae-adaptation, I may fay, with
what an a^arenfly divine mechadfm and con-
ftruction,

( 3©4 )
fiructiow, they naturally connect themfelves with
the calculated terminations, 2ih. 15', and mea
fure to a point "the complement of the 1 ith dayw
For, D h '
To 10 21 15
Add 2 45
Sum total 1 1 o o
juft in like manner, when we calculated, p. 297^
the firft commenfurating year, having fubftraeted
the quotient of the Solar reduction, viz. 525949
days, from the quotient of the Julian reduction,
viz. 525960 days, the difference between the two
accounts was, as here, 1 1 days precifely. May I
not venture, in this place, to fet down the initials,
g^E.D.? For if this conclufion, arifing from
Mojaic principles, and the Mojaic numerical data*
be not admitted as demonftrably certain, I muft
renounce all pretenfions to demonftration, and even
to the idea of it : for where, in the whole procefs ,
is any arbitrary affumption, or precarious and dif-
pu table pofiulatum ?
Having calculated the exact completion of the
1 ith day, we muft go on to fix the year of its
completion. In order to this, to A.D. 17,50 add
15 years, which will carry us forward to A. D.
1765. Then from A.D. 1765, the year of com
pletion, fubftradt A. D. 325, which is the epoch
ofthe computation : remains 1440, or the firft year
of commenfuration. From hence arifes the force
of my argument : from this ground it appears that

( 3°5 )
that I have, in fact, deduced the quantity of the
Solar Tropical year, with the minuteft exadtnefs,
to an indivifible point : nor can the exadt com
pletion of thefe 1 1 computed days be obtained,
from any other affigned meafure, but that of
36jd. 5I1. 49'. 00".; nor from any year, but that
of the 1440th from the head ofthe account.
I conclude then, from my firfl argument, that
365 d. jh. 49'. o". is the ftandard of the Solar
Tropical year, and that all the Solar tables ought
to be reduced to it,
My fecond argument fhall be taken from the
exact completion of the quadrant, as my firft was
from the exadt completion of the day.
In order to eftablifh this conclufion, reduce
5760 Solar Tropical years to days, p. 277 ; and
alfo, by Sir 1. Newton's.
In the next place, fubftradt the leffer number
from the greater, and the remainder will be equal to
the complement of the quadrant ; and alfo, to the
fum of the defect in the given number of years : e.g.

The, Integral Calculation affigns

The Newtonian Correction afligns

for the meafure ofthe Solar year

for the

meafure of the Solar year

D h ' "

D h ' '"¦

365.05 49 00

365 05 48 57

Years D h ' "

tD h

5000^.30826211 19 20 00

-

- 182621 1 15 10 00 ,

700 >%4 255669 15 40 00

-

255669 15 05 00

603 Sed 2I9'4 J3 °° °o

21914 iz 57 00
Integ. Days 2103796 00 00 00
2103795 19 12 06
— 2103795 19 12 00
-
- ¦ r
Difference - - - 4 48
a
J\
According
[ 3°6 ]
According to thefe different conclufions, the
fourth quadrant of the Solar day, which meafures(
from fun-rifing -to noon, will > be divided by the
Sun's entry into Libra, in the computed meridian,
as in this fcheme : h 'e ' h o
Weft Sunrifing © i 12 J 48 4 f Noon Eaft.
In the integral calculation we have a collected
fum of integral days, which as the computation
commences at noon, muft end at noon ; and by
the effential properties and affections of a commen-
furating year, they muft alfo terminate in the au
tumnal aequinodtial, or original, point, and in
the fame computed meridian. That the given
year, A.M. 5760, is the fourth yearof commen
furation, has been fufficiently proved, in the pre^
ceedent pages: therefore I argue, that Sir 7.
Newton's reduction, which calculates the Sun to
enter Libra 1 2' paft 7 in the mdrning, or 4 hours .
48' before noon, muft be defective ; or more par
ticularly, that the complement of the 4th1 qua
drant of the Solar day, equal, in this cafe, > to
4 b, 48'. is the fum of the defect, in the given
number of 5760 years, ^ E. D. From the
force of this fecond Argument, I conclude as be- .
fore, with refpect to the afcertained meafure
of the Solar Tropical year.
My third Argument fhall be taken from 'the
completion of the fquare 4, which arifes from"
the divifion of the number of fexagefimal parts in

( 3°7 )
in a true Solar revolution by 1 5 ; but ultimately,
and originally, from the fubftradlion of the 3d
'radical number 11, from the fundamental datum
of the Pentateuch i£; for 15— 11=4, vide
p, 246, where thefe partitions are noted, and
amongft others, we may obferve that 1 5 is re-
folvible in 4, 7, 4, of whofe aftronomical ufe and
application, we may have fomewhat to fay hereafter.
When we contemplate thefe components 4,
7, 4, and find them terminating in 2 fquares,
the, integral and geometrical exaetnefs has
fomething in it very ftriking both to the eye
and to the underftanding ; but if it either has
been already, or may be, rendered certain, that
it likewife correfponds with true aftronomy, and
the inmoft conftitution of the fyftem ; this muft
needs carry along with it a forcible and convincing
proof of the wifdom and geometry ofthe creator.
If we compare Longomontanus' s calculation, and
that of Sir L Newton's with this, they will jointly
appear in this form :
Integral Calculation 4 00 | oo-f-74-47
Longomontanus • 3 55 I 05-\-7~{-4^'z=:'I5
Sir Ifaac Newton 3 57 \ °3-\~7Jr4^
It is obfervable, in the table before us, that
thefe two..- eminent mathematicians, are fo far
from aiming to -fquare the circle, that, on the
contrary, they directly and refpedtively tend to
unfquare the fquare, and to fubftitute the Trape
zium in its flead. Although the parts of 15 are
(Tq 2 indeed

(308 )
indeed preferved by both, yet the true quantity
and partitions of time are preferved by neither.
When we take a clofer view of thefe diflocations
and anomalies, thefe perceptible deviations] from
aftronomical accuracy and proportion, we are 1e
a high degree prompted to make it a doubt and a
queftion, « o ©so? ywy-n^el; whether the creator
geometrizes in his works or not? for where is
order and regularity? where is the beauty and
perfection ofthe fquare?
If nature can be preffed to give herjanftion to
either of thefe fractional conclufions, then it may
be faid, that "nature operates by the Trapezium :
And if it can be proved that nature operates by
the Trapezium, then Sir I. NeWton}s philofophy
would be fundamentally erroneous, becaufe a
geometrical antithefis to irregular nature.
But my third argument, taken from the exadt
completion of the fquare 4, in every termina
tion of the Solar Tropical year, may be brought
to a fhort iffue ; for in the following table, the
reader may have a clear perception both of it's
meaning and of it's truth, tanquam in Jpeculo.

Longomont. ~\ — 5
A." ¦ y'fuppofes the^ p. , , — 4
Sir /. iV. \ Solar Trn.r U _o
D. J

j\.~ ' ?luppoles the^ p.
Sir /. N. \ Solar Tro- (. 6 " —3
B. £ pical year T * 5 5 49 — 2
to contain J • — 1

55+3=4 56+3=4
57+3=458+3=459+3=4
00 4 o

4J. E. D. —00
I may with equal confidence appeal to this ar
gument for the truth and certainty of my deduc
tion. ¦ What

( 3°9 )
What I earneftly plead and contend for (upon
demonftrable grounds, and with a view to im
portant ends and confequences) is the entirely ca-
fhiering Jecond minutes from the meafure of the
Sun's year : for they are ungeometrical ; they
diffolve the ligaments of created fymmetry ; they
untune the mufic of the fpheres, and introduce a
jarring difcord into the proportional harmony of
periodic motion. God has made all things in
number, weight and meafure
The Newtonian approximation within 3" fe
conds of the root, and in confequence of that,
within 1 8'— |— 15" of the fquare, may be imagined
to bear fome refemblance to the cafe of a mariner,
who, after having traverfed the four great feas,
and almoft the circumference of the globe ; upon
his returning back to the place from whence he
took his departure, was drowned in flepping out
from the fhip to the fhore.
Having I hope fufheiently afcertained (by accu
mulated arguments, calculations, and proofs) the
true quantity of the primitive and patriarchal Solar
Tropical year; I fhall now go on to confider and
explain the Hebrew term Shanah, as it is applied,
in the Pentateuch, to the Lunar year.
That the Lunar year makes a paft of the Mo
jaic Computations is too evident to be made a
matter of doubt : Te Jhall obferve, fays Mojes
to his lfraelites, (Lev. 23) the feaft of. the inga
thering on the 15th day of the Vllth month (of
the Lunar year) in the end or revolution (i. e. on
the cardinal point) of the Solar. Exod. c. xii.
v. 2.

( 3io )
v. 2, this (VHth) mpfith jhall be unto you the be
ginning, of months ; it Jhall be unto you Rifhon,
the head, the beginning, thefirfi month (Hafhanah)
ofthe (Lunar) Tear.
There was a time, when the facred and eccle
fiaftical Lunar year (could it have been regained;)
would have been received, and gladly embraced,
with a due venerationand efteem, by tlie univerfal .
church. Nor are there wanting fome, even in
this aftronomical age, who would be very well
pleafed to fee the Tropical Solar ( beyond all hopes
and expectations) become once again, as in days
of old, the civil and vulgar year.
Should public authority, upon a full conviction
of the expediency and neceffity of it, refolve to
enter upon a due regulation and correction of the
errors and miftakes, which through a long tract
of time have crept into, and fenfibly diflurbed, our
civil and ecclefiaftical, our Solar and Lunar, com-
' putations ; where muft we apply for the rules
of thefe corrections ? Muft we have recourfe to
the antient facred records? or, to the lectures of
modern philofophy? to the determinations and
conclufions of modern fcience ?
There are reafons to apprehend, that, notwith-
ftanding all our boafted improvements and attain^
ments in this age, the aftronomers ftand as much
in need of the revelations of the Pentateuch, and
of the Oracle truly divine, as their predeceffors in
fcience, and their firft mafters and teachers the
Greeks formerly did. The

( 3n )
The Grecian year in elder times was in a very
imperfect ftate and condition, not at all corref
ponding with the motions of the two luminaries :
'fo that Arifiophanes reprefents the Moon (reginam
fiderum) complaining from the clouds of their
total difregard to her. The Greeks thought this
imperfect ftate of their year (which they knew
not how to remedy) a juft occafion to cdnfult the
oracle how they muft facrifice, which admonifhed
them that they muft facrifice, k*t* r, /. e. accord- >
ing to Three. Geminus in Ifagoga, c. vi.
It is well known, that the Greeks were the firft
practical aftronomers. Being excited by the oracle,
they began to ftudy the Mdori's courfe, and at
tempted to calculate its motions, its periods, and its
fynods. They invented cycle after cycle, With in
defatigable pains, that they might bring to an exadt
reconciliation and agreement the motions of the
two luminaries : For they interpreted the oracle
to mean, that they muft reckon their years by the j
courfe of the Sun ; and their months and days by
that of the Moon ; whilft (as Strauchius perti
nently fays) they only took up water in a fieve.
I do not in the leaft doubt, but that the ambi
guous oracle aimed to direct its blind and fuper
ftitious votaries to the Mojaic three, viz. days,
weeks, and years : but not being able to interpret
it rightly (and it was impoffible they fhould) they
were led into a miftaken computation, which we
have adopted and perfift in.
I could not well omit the mentioning of this
extraordinary piece of antient hiftory, which .fo
• ¦ plainly

( 312 )
plainly informs us of the origin and rife of Lunar
Jynodic months. We learn from hence, that they
are entirely of Greek extraction, and of a latter date,.
The primitive patriarchs computed them not, and
therefore Mojes has not recorded them.
Since then thefe Lunar months, which meafure
from fynod to fynod, had no admittance into the
primitive kalendar and computations, a principal
branch of our prefent enquiry muft be, from whence
did their Lunar year arife ? What were its confti-
tuent parts ? Upon what aftronomical bafis ancl
foundation was its frame and ftructure built ?
Here the affrpnomer will be in fome pain for
me : he will be cafting about in his mind, how I
fhall be able to calculate th§ Moon's true place
in its orbit ? How asquate its anomalies ? What
arts and fhifts I fhall have recourfe to, in order to
gain admittance to this inacceffible planet ?
But here it happens very luckily for me, whp
am no natural philofopher or phyfical-ratio aftro
nomer, that I am clearly inftructed, by the prinr
ciples of the Pentateuch, that in the exact adjuft-
ment of the Lunar year to the Tekuphoth or re
volutions of the Tropical Solar, we are not re
quired, much lefs under the neceffity, to calculate
the Moon's motions in it's orbit at all 5 any more
than we are in order to determine the Sun's place
in the ecliptic.
The aftronomer wants not to be informed!,
that the orb of the Moon circulates rdund the
Earth, and by this circulation finifhes its periods,
by a proper motion in its orbit : whilft the, Lunar orbit

C 313 )
orbit itfelf, in an infeparable union with the orb
of the Earth, is carried round the Sun, and, by
this circulation, finifhes its annual period or Sha
nah'. Now this circulation, this annual period,
or Shanah, I am able' to calculate and adjuft, for
this very plain and obvious reafon, becaufe it is
equally and uniformly meajured by the diurnal mo
tion, the alone meaj'ure of time to us. For, I fay
it again; the diftindtion of years arifes not from
the diftindt motions of the Sun and Moon 5 but
it is a created diflinftion, and is to be reckoned
amongft the original eftablifhments, and the pri
mary conftitutions of the God of nature.,
Let us attend to and confider the terms of the
fundamental texts, Gen. i. 14, 15, 16. God
made two great luminaries,
1 . Lehair gndl Haaretz, to enlighten the Earth.
2. Lemognadim, for (facred) feafons.
3. Lejamim vejhanim, for days and years.
.Now I fay, firft, if the Moon had not an orbit
of its own, and a proper motion in that orbit, how
would it be qualified to extend its light to both
the poles, and fometimes beyond them ? But we
are not required to underftand the phyfical laws,
or even to calculate thefe unequal unmeafuring
motions, or to proceed one fingle ftep in our en
quiries after them, beyond the evidence of fenfe.
In the next place, if the orbit of the Moon was
not carried round the Sun, in an infeparable union
with the orb of the Earth, from whence could
R r be

(3H)
be continued the diftindtion of Shanim, years ?
From what fource and origin could we deduce,
and by what laws could we calculate Jamim,
the days, both of the folar and the lunar Shanah ?
And without this annual circulation, how could
the Moon difcharge its original defignation, ap,-
pointment, and office ? God, fays the PJalmifi,
appointed the Moon Lemognadim : we have here
juft fo much of the folar fyftem revealed to us, as
is neceffary for our civil and religious ufes.
What we have therefore to do, is to find out
and determine the annual variation of this created
dijtinftion, or feveral diftances of the Moon's en
lightened orb, from the Mojaic Tekupha, or au
tumnal aequinodtial point. Now the integral lu
nar computation is nicely adapted to prove, that
this annual variation of the lunar epacts is propor
tional and periodical : and in this proportional and
periodical variation of the diftances of the new
Moon c and full Moon O evenings from the ori
ginal Mofaic Tekupha, lies the excellency, and
the admirable perfection of primitive Sun and
Moon aftronomy, fufficient to convince us, that
the antediluvian patriarchs were undoubtedly
GioMcuiToi, primarily taught the praxis of aftrono
my by the creator of the luminaries himfelf.
From what is here faid, we- may already begin-
to perceive a confiderable difference between the
lunar computations of the antient patriarchs and
of the moderns. Nor need this be thought ftrange,
fince the original ftrudture ofthe lunar year (the
fob-

(3*5 )
fubject of our prefent enquiry) is not underftood,
and therefore has never been rightly explained.
Let us firft hear what the moderns fay upon
this head. Mr. Kfiil, Ledt. -xxviii, p. 361. gives
us the following account. " The civil year is
" the fame with the political year, eftablifhed by
tc the laws of a country, according as it is defign-
*< ed to be regulated by the motions of tlie Moon,
** or ofthe Sun. There are two forts of lunar
" years ; the one moveable, the other fixed ; the
" moveable year confifts of \2 Jynodic months, or
" of 12 lunations, which are completed in 354
" days, and after tbfit time- the year begins
" again."
We may obferve here, that he plainly makes a
diftindtion between the political and the aftrono
mical year, and vifibly adapts his expreffions to
it.-"-" According as it is defigned to be. {not ac-
" cording as it is truly) regulated by the mo-
*{ tions of fhe Moon, and of the Sun." But this
modern diftindtion the patriarchs were entire ftran-
gers to ; for in the firft ages of the world, the
civil year, and the aftronomical year, both folar
and lunar, were identically the fame,
Mr. Keil, in the clofe of his account, exprefsly
fays, " That a moveable lunar year confifts of
" 12 Jynodic months, or of 12 lunations, which
" are completed in 354 days." . This conclufion
is partly trpe, becaufe a lunar year may have 3 54
days, but then it is abfolutely impoffible, in na
ture, that 354 complete days fhould be the ade-
R r 2 quate

( 3i6 )
quate refult of 12 Jynodic .months, or of 12 luna-
tionSi as ftated by Keil.
It will appear, as we proceed, that a lunar
year confifts fometimes of 354, and fometimes of
355 integral days ; never lefs than the one, never
more than the other. So that there is no room
left for appendent hours, minutes, and feconds,
&c. no pofiibility of , difpenfing with excefs or
defect. Thefe two quantities, (whofe difference
and order of fucceffion is regular and determinate)
are, by their integrality, nicely fitted and prepared
by nature, to meafure the diftance from the new
Moon (c) or the full Moon (Q) evenings, neareft
to the autumnal aequinox in one year, to the new
Moon (C) or the full Moon (O) evenings, neareft
to the autumnal aequinox, in the end of the next
year. But how obvious is it to perceive, and how
eafy is it to prove, that neither the collected fum
of 1 3 periods of the Moon, nor of 1 2 fynodic
months, or 1 2 lunations, can ever be made pre-
cifely commenfurate, either to 354, or to 355
integral days ? And, by thefe integral meafures the
antediluvian patriarchs computed their lunar Sha
nim. , .
If the Moon finifhes its period, according to
mean motion, as fome aftronomers calculate it to
do, in the fpace of, iyd. yh. 43'. 5". thefe
multiplied by 13, will produce 2>5\d. 22I1. 36'
5". which both exceed and fail fhorflbf the inte
gral days.
Again, if according to Keil, p„ 374, a lunar
aftronomical month, or lunation, confifts of 29 d.
I2h„

( 3i7)
I2h. 44'. 3'.'. thefe being multiplied into 12,
produce for the quantity of the lunar year, 354d.
8h. 48'. 36". But if we compare this produdt
with the twofold quantity of complete days, we
fhall find, with refpect to the one, an excefs ;
and with refpect to the other, a defect. So that
12 lunations cannot be the aftronomical conftitu
ents of the integral lunar year ; unlefs we can ad
mit for an axiom, that all the parts taken together
may be both greater and lefs than the whole.
Thus far my argument has been negative, and
has only tended. to, fhew, that neither the 13 lu
nar periods, nor the 12 fynodic months or luna
tions, (eftimated by the mean motion or the true)
could be ordained, ab origine, to frame and con-
ilitute the facred and ecclefiaftical, the civil and
hiftorical lunar year. , '
1 I muft now then proceed to the pofitive part
of the argument, and manifeft its true, effential,
and divinely appointed conftituents ; which can
not fail to produce 354, and ^55 integral days,
without any adhering excefs or defect, by an ori
ginal invariable law.
Here I cannot help making a fhort reflection ;
it often happens, that a much: defired and ufeful
truth is placed in a flrait line directly before us,
and yet by an unhappy fatality we over-look it ;
it is often very near us, on our right hand, or our
left, yet we fee it not, nor apprehend it.
I fell into this reflection, upon my reading and
confidering what Mr. Keil had advanced con
cerning the moveable lunar year's confifting of
12

¦(3*8 )
1 2' fynodic months,; or lunations, and that they
were completed in 3 54 days. Whereas by the pre
cedent calculus it is evident, that no affigned quan*
tity of a fynodic month or lunation can ever divide
exactly 354 days. It is true indeed, if from 290*.
12b. 44'. 3". we throw off the odd hours, mi
nutes, and feconds, there will then remain 29 in
tegral days. On the other hand, if we complete
thefe odd hours, minutes, and feconds, into a
day, we fhall then have, but ftill by reduction,
30 integral days : and if we add fix of the one to
fix of the other, the amount will be, exadtly as
Mr. Keil has concluded, 3 54 days. But would
he have us only confider this, as a political, lunar
year, eftablifhed by the laws of a country, which
will be found to be an eftablifhment of the king of
Heaven ?
It is' plain that the calculated lunation is here
yielded up by Mr. Keil, and a true conclufion fub-
ftituted in its ftead, upon principles not under-*
flood, and therefore paffed by unmentioned.
Thefe ,30 and 29 days are miftakenly. called by the
Greeks, Jews, Turks, and the aftronomers, lunar
months ; when they are no more regulated and de
termined (as caufe and effect) by the motions of
the Moon in its orbit, than the days of the week
are. They are inadequate to the lunar motions
(or rather the lunar motion? to them) both perio
dic and fynodic; and muft be reckoned amongft
the primary conftitutions, and fettled ordinations
of the creator. God has appointed, by a law as
old as the creation, and to be continued, without any

( 319 )
any future revocation or repeal, that the Moon's
enlightened orb fhould firft appear to the inhabi
tants ofthe Earth, at the end of every 30 and 29
diurnal revolutions. Hence they become, the in*-
mutable aftronomical meafures of the diftances
between one new Moon (t) or full Moon (O)
evening and the next interchangeably, though
not without fome interruption ; fo that in what
certain order they follow one another, no aftro
nomer can readily determine. No aftronomical
calculation, how accurately foever made, can as
certain, by any known general rule^ or any known
law of certainty, the actual vifibiiity ofthe Moon,
in every inftance. If fuch a rule has been laid
down, andacquiefed in, what is it ? If the aftro
nomers have it not, nor are able to attain it, what
are the obftrudtions ? I will be bold to fay, that
fitch a general rule, fuch a law of certainty, and
perpetual motion will be found out upon one and
the fame day. Here the phyfical-ratio enquirer,
a«d inveftigator of the Moon's motions in its orbit,
will be non-piufed, and muft be contented to
fobmit to the plain fimple principles of the Pen
tateuch. But here, probably, fome : one will afk, what
reafon is there to fuppofe, that thefe 3 o and 2 9 days
are amongft the principles of the Pentateuch ? Or
that thefe unequal meafures are the very aftrono
mical bafis and foundation, on which the frame
and ftrudture of the primitive lunar year was built r
For in the foregoing pages, was not the patriar
chal lunar year fet down1 in this form, viz. 330
-f24-

( 320 )
-f-24days? But it muft be allowed, that in a
continued feries of ii equal 30-day months, there
is noappearance of unequal aftronomical meafures.'
And therefore the inference muft be, either that-
this form of year is fictitious and imaginary, or
tha't thofe primitive old men were quite unac
quainted with any' intermediate aftronomical mea
fures. It muft be owned, that from a bare curfory1
view of the form of the patriarchal lunar year, as
it ftands expreffed above, fuch inference muft ne
ceffarily be drawn ; but in order to extricate my
felf from the feeming weight and preffure of this
objection, I beg the reader to look back to p. 168,
where I have given a fcheme of the original two
fold year. If he examines Tab. II. of the altered
lunar year, he will readily perceive by the column
of collected days, that from the autumnal aequinox
to the vernal, the antient lfraelites reckoned 1 80
days ; whilft from the vernal aequinox to the au
tumnal aequinodtial new Moon (<) evening; they
computed no more than 174, days. Their lunar
year had 12 months, and is. here partitioned into
6 months and 6 months; divide then 180, days
by 6, and the quotient will give 30 days ; but if
we divide 174 by 6, the quotient will give 29
days; thus we deduce thefe unequal meafures/
from the form and ftructure of their year. To
proceed a ftep farther; if we divide 354 by 12
(the number of months in their lunar year) in the
quotient we fhall have 1 1 equal 30-day months,
and in the remainder 24 days for the 12th, Thefe

( 321 )
Thefe eafy and obvious calculations inform us,
that the frame and ftrudture of the original an
tient lunar year was both political and aftronomi
cal. A« it was political, it was computed and ad
jufted by 1 1 equal 30-day months, allotting 24
or 2 5, days for the 12th. As it was aftronomical,
it included fix meafures of 30 days, and fix of 29,
in exact conformity to nature : Ifay, to nature ;
becaufe at the end of 30 and 29 days, the Moon's
enlightened orb firft appears to the inhabitants of
the Earth.
From thefe annual, and thefe intermediate aftro
nomical meafures, each confifting of integral days,
and in a juft correfpondency to nature, the inter-
gral calculations derive their claim to truth, cer
tainty, and perfection.
The .queftion in debate (viz, what were the ef~
fential conftituents, and what the aftronomical
bafis and foundation of the primitive lunar year)
will receive its folution, and the pofitive part of
my argument its conclufion, from the two follow^
ing tables,
A table reprefenting the true feries, fituation,
and fucceffive alternate order (though not with
out interruption) of the divinely appointed aftro
nomical meafures of 30 C and 29 C integral days,
in every poflible variety, through the whole courfe
of time. Sf , Index

f 322 )

Index I

29

1. 29

i" 30

2. 30

..

3-

3°

3°

2

3°
59
29
59
3°
60
3
29
88
3°
«9
29
89
4
3°
118
29
<i8
3°
119
5
29
H7
30
148
29
148
6
3°
l77
29
177
3°
178
7
29
206
3°
207
29
r207
8
3°
236
29
236
30
237
9
29
265
3°
266
29
266
10
3°
295
29
295
30
296
n
29
324
30
325
29
325
12
30
354
29
354
30
355
(1) This table is digefted into 3 columns of
collected days, marked 1, 2, 3, at the top.
(2) The odd numbers of the index, (viz. 1.
3. 5. 7. 9. 11.) point td a collected number of
days in the ift column, which are refpedtively
lefs by 1, than the collected number of days over
againft them, in the 2d and 3d columns.
(3) The even numbers of the index, (viz. 2.
4. 6. 8. 10. 12.) point to a collected number of
days in the ift and 2d columns, which are re
fpedtively lefs by 1, than the collected number of
days over againft them' in the 3d column.
(4) A lunar year of 3 55 days arifes from the in
terruption of the alternate order in the 2 firft aftro-
ndmical meafures prefixed to the 3d column of
collected days. (5) This
( 323 )
(5) This interruption of the alternate order of
thefe unequal aftronomical meafures is, in my
apprehenfion, a point ofthe moft difficult accefs,
in the Whole compafs and extent of Sun and Moon
aftrofiomy. And its inmoft grounds and reafons
niuft be learned, not from the gazer of the Hea
vens, not from the abftrufe argument of multi
plied lunar aequations; .but from the moft perfect
and determinate aftroriOmy of the patriarchal te-
traeteris, or the firft 4 years of the world, confider
ed both as folar and lunar.
Now whether I am able to enter into this
fecret, or folve this' difficulty or not, (and I dare
hot take upon me to fay that I am) yet the
moft fkilful and the moft experienced aftronomer
will be fcarcely qualified to reproach rriy igno
rance. But at prefent I may look upon, myfelf as
s?» Bs*Kf, or out of the reach of gun-fhdt, if I may
be permitted to pafs my judgment upon the fol
lowing extract from Mr, Keil, Ledt. xxix. p. 374.
i( Becaufe a lunar aftronomical month confifts
" of 29 days, 12 hours, 44 minutes, and 3 fe-
*' cohds, (which the motion of the Modn re-
cc quires, p. 3ys) the common people, who cannot
u diftinguifh the fmall particles, of time, make the
" lunar month to confift of entire days, without
"fractions, and on fhat account they alternately.
" put one month of 30 days, and the next of 29
" days. Thefe are called hollow or cave, that
<c is, deficient months, the others full"; the 12
'* hfiurs over the, 29 days requiring this alterna-
''L S f 2 " tion :

( 324 )
<c tion : but becaufe there are 44 minutes befides,
" which is almoft 3 quarters of an hour, in every
" lunation; in 32 lunations, thefe minutes will
lt make up a whole day, which is to be added/ to
tc a hollow month; and by this means the luna-
" iions of the kalendar will nearly agree with
*c thofeof the Heavens."
Should a controVerfy arife, it might be brought
to, a very fhort iffue, and the whole refolved info
this fingle queftion, viz. to which of thefe two
very different accounts does the vifible fettled ftate
of nature give its fanctioh ?
The antithefis here is fomewhat very extraordi
nary, and may be thought worthy of a remark,
viz. What Mr. Keil afcribes to the incapacity ipf
the common peoplej who cannot diftihguifh, fays'
he, the fmall particles of time ; this fcheme refers
to an original created law,- to a primary conftitu
tion in; the very firft rife and origin of nature^
Now I leave the argument to the judgmerit of the
reader, but before he paffes a final decifion, h6
may, if he pleafes, look over and confider the
following table which includes thefe unequal aftro
nomical meafures,' in the political frame and ftruc-
ture of the primitive lunar year. ' ,
II.
A table reprefenting the feveral aftronomical di
ftances ofthe new Moon (C) evenings, &c. from
the beginnings of the equal 30-day months,
throughout the patriarchal lunar yean ', i '. '.
This

< 32i )

.1

15+15

3°

3°

I

J5+i5

30

3°

II

I5+I4+1

30

60

II

r5+i5

3°

00

m

15+15

3°

'90

III

^5+14+1

30

90

IV

I5+H+i

30

120

IV
*5+*5
3°
120
V
15+15
3°
150
V
15+H+1
30
150
VI
I5+i4+i
3°
180
VI
15+15
3°
180
VII
XS+J5
3°
210
VII
i5+x4+i
3°
210
VIII
15+H+i
3°
240
VIII
i5+!5
3°
240
IX
J5+I5
3°
270
IX
i5+J4+i
3°
270
X
15 +H+ 1
30
300
X
15+15
3°
30°
XI
15+^5
3°
33°
XI
i5+r4+i
3°
33°
XII
iS+9
24 <
354
xii
15+10
25
355
This table is corona operis, and will enable us to
adjuft the returns of the lunar phafes at unequal
times; I fay, unequal, for reafons which our philo
fophy has not yet explained. It alone holds forth to
lis the law of certainty ; fo far forth as it was fettled,
conftituted, and appdinted by the creator--:- i# the
^beginning. It will render it demonftrably Certain,
"that the primaeval kalendar ! was not only nicely
adapted, by its uniform Conftrudtion, to civil and
political ufes ; but was al'fo, in' itfelf confidered,
a moft true and faithful aftronomical index;,
both folar and lunar. Where is there a kalendar,
amongft all the nations ofthe world, exclufive of
the patriarchal line, which may he compared unto
it? Or which may ftand in any degree of compe
tition with it? "¦" -¦-'-
1 We, being led by the example of the Greeks,
arreft the Moon in its drbiti, 12 times within fhe
compafsof a folar year, Tor the fake of the fynods;
by this means, 27 days -|- 8 hours -j- 2 days -j~
¦ ' v ¦ - * ¦ .- \ . 5 hours,
{ '326 )
5 hours* become, the numerical meafure. of a fyno
dic mohth, or luriatiori H That is, ift other words,
a fynodic month, or luriafidn, demands for its
artificial complement; , one . entire lunar peridd,
and part of another. So the fidbreal year includes
one entire tropical ye*ar± and fjart of another: but
the aftjrdnOmers very ingenudufly call this the
Sun's anomaliflieal year, ,or the Earth's anotha-
liftical period in its orbit. Fot the famd reafon,
artd with the farne propriety, we may call a fy
nodic month, ot lunation, the Moon's anomalifli
eal pet'iod.
I meet with it indeed fometimes under the fpe-
cious appellation 'and title of the menfirual revolu
tion of the Moon. But if a fynodic month may
be efteemed a menfbruai revolution ofthe Moon;
then why not a dichotohiicai ? Why not a panfe-
lenian? Why not an amphicurtal lunation ? Why
may not a revolution he calculated from any given
point of the Moon's orhit, to a certain point of
the ecliptic ? What is there fo obftruct our com
puting from every fchematifm or configuration,
which the Moon, -<& ilkkowsb Eccluf. in its continual
multiplied variations, is capable of affuming ?'
I would fain know, and may be reafonably in
dulged the queftion, whether we were directed
to this mutilation of the Moon's periods, by na
ture, or by the Greeks ? ! ,
The aftronomers, perhaps, may take this point
info confideration, and judge it meet to reflore to
the' Moon its mutilated and divided period ; it is
its right arid property by nature. Befides, is it
not

( 327 )
not a tacit reproach, tofyrnifh, grounds for faying,
that the ffewtonian aftronomer truckles to thefug-
geftions of the Delphean tripod, and fuffers himf
felf to be juggled jnto an artificial computation, by
the ambiguities of adaembn ? Though not indeed
immediately and directly, yet by a fervile and ig
noble imitation of the heathenifh, fuperftitious,
and idolatrous Greeks. ..,.-,
Here Merlinus Anglicus, Philomath, and Wing,
with the reft of the climbers up, to Ohvpvt* cfy<w«s,
will begin to be one and aU alarmed ; they will
fire with ipdignant rage at the heretical impugner
pffundamental^odtrines. What, fay they, muft
we renounce the Syzigia, the only fubftratum of
eclipfes, the moft ingenious (and eke the moft
laborious and the moft operofe) calculation Ev
KuKAotfet/JVw. Not calculate an eclipfe ? Why, it
is the very medulla of an almanac, and the im
portant prophecy of the book/: aqd all this, upon
the fole authority, and the lordly didtates of a
new-fangled fcheme — whofe truths are as old as
the creation,.
But why fo indignant, ye celeftial fages ? My
artillery is not planted againft fundamentals. To
convince ye of this, I beg the "favour of your pa^
tient attention to one lecture in aftronomy, conr
cerning the circumftances, characters, aqd appen-
dent proportions of the original pofition of the
two great luniinaries, which may immediately
follow the publication of this treatife, but is too
large to ^comprehended within its limits, The$ ye

(32&)
ye may return to your prognofiications, to your
malevolent and benign ajpefts, and conjure away,
m a chriftian country, (as the damon of the
Greeks fhall injjnre you) as faft as ye pleafe, with
a — cum privilegio imprimatur: ¦
In the mean time, Mofes, my Hebrew praecep-
tor, gjves ye to underftand, for ye know it not
as yet, that the creator of the folar fyftem has
placed the original feats of the eclipfes, in chaotic
foaces, amongft the eccentricities of nature j nor
can the great clock of time be compelled to de
clare, when the firft folar or lunar eclipfe might
have happened, but by a proleptical computa
tion. From this wife and providential difpofition of
the chaotic conjunction, and of the chaotic oppo
fition, it was impoffible, in nature, for the created
full Moon (< 15. O) to arife upon the Earth with
an intercepted light: and the primary command
impofed Was, Lehairgndl Haaretz, to extend its
light from pole to pole. The creator has fo ef
fectually fecured every the leaft approach of con
junctions or oppofitions, even to the utmoft verge,
to the moft outward limits and boundaries of the
two interfering circles, that no eclipfe of the Sun
could ever darken the mornings of the firft day of
the 7th month — Sabbaton, ziccaron terogneh.
Levit. 23, 24. Nor an eclipfe of the Moon ever
darken the beginnings of Chag haafiph. Hence
we have a divine direction from what cardinal
point of the day, and from what quality of the
Moon

( 329 )
Moon (viz. Megnereb C) to compute the primi
tive Rijhon, Gen. viii. 13. and to terminate the
primitive full Moon day on the 15th evening
from thence exclufive of it. The primitive new
Moon evening then is the fecond from the con-
jundtion; and the primitive full Moon evening is
the fecond from the oppofition.
Thefe new Moon and full Moon evenings would
annually be found, at the autumnal aequinox, in
the central points of two interfecting circles, if
not prevented by the eccentric diftortions of cal
culated conjunctions, dichotomies, and oppofi-
tidns, according to your greciz'd almanac aftro
nomy. In the Julian months of Auguft and September,
and in this current year A. D. 1751, the unequal
unmeafuring lunar mptions are quartered, by your
puzzling, intricate, and perplexed calculations, as
in-the table fubjoined, which is your own.
Auguft, A. D. 1 75 1.
NewMoonioday.at 2 morn. d. h. conjunction.
Firftquarter^dayat 11 night 7 21 dichotomy.
Full Moon 2 5 day at 13 aftern. 7 16 oppofition.
.' r. September. , h ,
Laft quarter 1 day at 10 morn. 6 19 dichotomy.
New- Moon 8 day at 3 aftern. 7 5 conjunction.
Firft quarter 1 6 day at,5 aftern. 8 2 dichotomy.
Full B4oon ^ 4 day at 2 morn. 7 9 oppofition.
T t Now,

( 33° )
Now, who, from thefe inequalities, thefe acce
lerations and retardations, can trace out the per
fection of a circle and its center? Or who can ap
ply this fpecuktive ingenuity to any ufes what
ever, either civil or religious? But if inftead of
laborioufly purfuing the unequal lunar motions, ye
had made the original Mojaic epadt 15, , and the.
principles of the Pentateuch the rule of ybur cal
culations, your whole and fole guide and directo
ry, they would have enabled you, with great fa
cility and expedition, to have adorned and em-
bellifhed your almanacs, with this geometrical
fcheme. A. D. 1 ys 1.
Auguft. September.
c  o  c  O
From this diftant hint ye may be fenfible,
what a fine practical aftronomy ye have loft by
your grecizing. Diftum Sapientifat efi.
If the annual returns of the new Modn (c) and
full Modn (O) evenings, with a gebmetrical ex
aetnefs, to the centers of two interfecting circles,
had been difcovered, and its demonftration pub
lifhed by fome modern philofopher, eminent for
his fkillin' fcience ; no blazing ftar of the firft
magnitude would have excited a more univerfal
gaze, or a more intenfe fpeculation. But if, on
the contrary, the amanuenfis of theGod of nature
hai gracioufly fupplied the defects of human fci
ence j if the pen of the divine legiflator has alone
opened

( 33i )
opened, to us thefe central perfections (which were
co-exiftent with the firft motion of time, and will
continue through its whole extent) it is hard to
fay, which fhould exceed the other, our admi-,
ration or our gratitude.
Mr. tmdal, amidft his adventurous exploits,
attacks the Mofaic Cojmogeny, with this very puif-
fant and heroic argument. " What a fad blun-
" der, fays he, does (Mofes) the hiftorian .make,
<f at his firft fetting out ? When he talks of the
<c Moon's being a great light, when every one
*c knows that it is an opaque body."
If my eyes and my upderftanding fail me not,
Mofes, the hiftorian, calls the Moon, Gen. i.
Hammaor Hakkaton, the leffer luminary ; as in
the fame chapter he calls the Sun, Hammaor Hag-
gadol, the greater luminary.
Alas, poor Tindal! that thou fhouldft under
take (by the help of fome inaccuracies in the Eng
lifh tranflation, and the biafs of an infatuated zeal)
not only to fcoff, ridicule, and degrade, but to
confute too, the revelations ofthe Pentateuch I but
fuch felf- confiding infidelity is as daring and pre-
fumptuous, as it is blind, ignorant, and ftupid.
But to return to our fubjedt. It has been plain
ly made to appear, that the frame and ftructure
ofthe original lunar year was made up of 12 inte
gral aftronomical meafures, confifting alternative
ly of C 30 C and C 29 ( days, in a juft agreement
with the ,fettled ftate of nature. The next que
ftion, which, in a regular dourfe, offers itfelf to
our examination is this, viz. Since the lunar mo-
T t 2 tions

( 332 )
tions are confeffedly ihcommenfurate to thofe en
tire days, what are their effential integral confti
tuents ? Where fhall we find, within the limits
of created nature, the latent and true aftronomi
cal components of thefe unequal meafures ? A more
fubtile problem Cannot be prbpofed to be folved,
nor a more intricate queftion to he anfwered. In
the laft extract from Keifs xxixth Lect. p. 290.
we were fully informed of his reafonings and Sen
timents concerning thefe entire days, without frac
tions ; towards the end, we read as follows :: 
" But becaufe, there are 44 minutes befides, which
*{ is almoft 3 quarters of an hour, in every luna-
tc tion; in 32 lunations, thefe minutes wilhmake
*' up a whole day ; and by this means, the luna-
" tions of the kalendar will nearly agree, with
" thofe of the Heavens."
Mr. Keil fays, 44 minutes multiplied into 32,
will make up a whole day. ^ Let us try the exaet
nefs of this. Now 44X32=1408'. but in a day
there are 1440 minutes. Therefore they will
not make up a whole day ; they will only, as
he fays, nearly agree, — with- a confiderable diffe
rence. ,'<¦>
The calculations of the moderns produce inac
curate and inadequate conclufions. They cannot
afcertain one fingle truth, they can only approxi
mate. Their language and ftile is indeterminate,
and in no exadt conformity to the ftandard of na
ture. They cannot rightly read the Heavens,
nor attain the celeftial orthography. . And for this
evident reafon ; becaufe they have never once con*-
fulted,

( 333 )
fulted, but fhewn a total (or perhaps, a fuperci-
lious) difregard to the only true Principia, laid
down in the Pentateuch of Mofes, where they
might long fince have read the clear, full, and
perfect Inftrudtions of the Creator of Heaven and
Earth, the all- wife Architect of nature himfelf.
If all the members of our Royal Society were
to meet together, and to hold a Oonfultation upon
the queftion propofed, would they be able to
agree in the debate? or could they make any notable
improvements upon Keil's conjectural and incon-
clufive calculus ? Could they, as enquirers into na
ture, folve the Problem, and give a juft aftrono
mical anfwer to the queftion? Perhaps, they
could not.
Now the folution of this fubtile and deeply fe
creted problem, is clofely connected with, and
ultimately depends upon, the truth and certainty
of the following propofition.
¦ When the Sun enters Libra, in any place at
noon, on the 15th day from the new Moon
(C) evening; then, I fay, that in the end of the
4th revolution from thence, it will again -enter
Libra, on the 14th day from the full Mooh{0)
evening, and on the very day in -which the new
Moon (() evening fhall fall; by an uniform and
invariable law.
1
, The feveral fteps of the, demonftration.
In the firft place, fet down a folar year, and
under it a lunar year, with the epadt, and an
nual quadrant. ' . A folar

((334 )
. A folar year; 30o-h5-K-.
A lunar year 354-r"I'"-H*;
...,»•¦ - ' '
,I^OW then, I fay, (i) That every tfpJaK year
has a concomitant lunar year.
(2) Every lunar year has an. attending epadt,=
11 days, or 10 days. , ,,
(3) Every lunar epadt has an adhering annual
feparate quadrant.
(4) Every annual feparate quadrant has/ an in
hering meridian epact,= 1 1 fexagefimal parfs.
(5) The fum "rtot&l of the fexagefimal parts of
the multiplied meridian epacts is always, greater
than the fum total of days, produced by an equal
multiplication of. the junar epadls, by as- many
units, as there are lunar years of 355 days.
(6) In every lunar Triacontaeteris or period of
30 years, there are 19 of 354 days and 11 of
355. And they follow one another nearly in this
order of years, 2. 5. 7. 10., 13. 16. 1.8. 2 1. 24.
27. 29. I fay, nearly, for this is a nice and dif
ficult point which requires pradtice. ¦ , -
Thus much being premifed, I want to calcu
late the integral, diftance of the full Moon (O)
evening, from the autumnal aequinox, in the
end of A. M. 4, the original pofition being known
and admitted. Now this calculation will be ex
tremely eafy and concife, requiring no more than
thofe few fteps. 1. In 4 folar years there- are
1 46 1 days. 2 .In 4 concomitant lunar yearSi there
is one of 355 days j now then, from 1461 days
fubftradt

( 335 )
fubftradt i, and dividing the remainder by 354,
the quotient will give the number of 1 2-month
full Moon (O) lunar years; and the remainder,
if lefe than 1 5, the integral aftronomical diftance
of the full Moon (O) evening from the aequi
nox. But if after the divifion, the remainder be
more than 15, then divide 15 or its multiple, and
this remainder will be the aftronomical diftance
fought. The arithmetical Operation.
From 146 1 folar days.
Snbftract 1
E>ivide.the remaind.by 3 54)1460(4, 1 2-m. Iu. yrs-
1416
. . From the remainder .Subftradt
Remains Q 14 the full Moon
epadt fought.
But why the full Moon (O) epadt? may one
fay ; why may not the calculation be fuppofed to
determine the diftance of the' new Moon (t) even
ing from the aequinox, in this'cafe, as welLas the
full? Dr. Prideaux, in his Hiftorical Connect.
part 1. 1. 6. takes occafion to fpeak of the cycles
of the Greeks, and having mention'd the excefs
of the Dieteris, "for the lending of it, fays
"he, the Tetraeteris was introduced, which
"'was a cycle of 4 years, wherein it was thought " that

( 336 )
" that an intercalation of one month would bring
" all that to rights, which was overdone by the
"like intercalation of the Dieteris. But 4 folar
" years exceeding 4 lunar years 43 , days-)- 12,
" hours, the adding one lunar month of 29^. 12b,.
" (of which it confifts) fell fhort of curing this
lt defect full 14 days"-:  which agrees, it is
true, with the calculated conclufion, but then; he
gives no intimation, that thefe 14 days difference,
between the folar and lunar reckoning, muft be
computed from the full Moon, and not from
the new.
Here the reply will give me an opportunity to
manifeft the reality of the double epoch or ra
dix of the Moon's year, and the certainty of the
charadters of the original pofition ; a principal one
amongft which is, that the primaeval full Moon
day was coincident with the autumnal aequinox:
Hence it came to pafs, and under thefe circum
ftances it muft neceffarily have been fo, that the
lunar computation commenced on the evening of
the 4th of the Hexaemeron, with a facred and
ecclefiaftical full Moon year; fo that the firft 4
integral lunar years correfponding with the. firft:
4 folar tropical years, protruding the epacts, -; may
be exprefs'd with their fymbols in this manner.

01234 0
O 354- C 354- O 35+ O 355- O 3°- O *4— itf'i Sol. days.
On

('337 )
On the other hand, if we would calculate the
integral aftronomical diftance ofthe new Moon "(c)
evening from the Equinox, in the end of A. M. 4,
we muft not only again have recourfe to the
charadters of the Mofaic radix, but fome addi
tional rules, to be derived from thence, will be
neceffary. In the end of the feries of the 4 full
Moon knar years, and within the cardinal limits
ofthe 4th folar year, we have thefe two numbets,
0
O 30. O 14. Now if in this place, we fet Q
down the characters of the original pofition, C 15
we may obferve, that thechaotic or imaginary new
Moon (C) evening was at the diftance of 15 days
from the autumnal aequinox ; fo that the former-
computation begins 15 days after the latter, and
mftft alfo terminate 1 5 days after it. Now divide
O 30- O into 15 and ij,» and note the divi-
vifions with their refpedlive fymbols ; being thus
divided and charadteriz'd by their fymbols, they
>.,.¦... 6
will appear in this manner, Q i5« * 15. O H*
From this fcheme it is evident to fenfe, that the
new Moon (C) evening is 15 days before the full
Moqn (Q) and confequently, by fo many days
more djfJant from the aequinox. Now then tQ
the cak?uljated remainder Q 14. add C 15, and the
fum < 29 C days, will terminate at the aequinox,
and the full Moon (O) evening will be 14 days
U u diftant

(338 )
diftant from the new C, according to the propo
fition, and the calculation. To complete the
procefs, as from thefe terms O 15 * 15 O we
fubftradted the two laft, viz.C 15, and added them
to the calculated remainder O I4> fo to the two
former, O 15, add the given epadt C 15, and we
fhall have c 15 O 15 Cjbut C i5-j-i5C=C30C.
and C I5-|-I4C=:C 29 C; but are not C 30 C
and C 29 C days, the unequal aftronomical mea
fures, in their true order of fucceffion, and bound
ed , by nature, in their refpective extremes, by
the lunar phafes ?
Now if the aftronomers can prove, that we are
not under a neceffity, by the laws of aftronomy,
to admit the truth and certainty of the propofition
laid down above ; by the fame arguments it may
be concluded, that I have not rightly traced out
the origin, and formal conftitution, of thefe un
equal aftronomical meafures of 30 and 29 days.
Affuming thefe conclufions as true, fince the
propofition is not yet confuted, we will go on to
fhew, that -thefe unequal aftronomical meafures
of 30 and 29 days are fo far from owing any
thing to the lunar motions, or from having any
connection with, or dependence upon them,
as caufe and -effect, that they are adtually and in
fact compounded ofthe integral lunar epacts, and
the annual' feparate quadrants; thefe are their
effential, internal, and aftronomical conftituents,
as the following calculations will clearly prove.
But before I go on with my' accdunt of thefe
30 and 29 days, which the Creator has appointed
to be the immutable and alternative aftronomical meafures

(.339 )
meafures ofthe diftances between one new Moon
(C) evening, and the next, or the full Moon even
ings, > refpedtively ; I fhall acquaint the reader
with the motives that induced me to make fuch, a
diligent enquiry after them, efpecially fince they
are of fuch great ufe and importance in this inte
gral fcheme of practical aftronomy. It is no in
vidious impeachment of modern fcience, nor any
unbecoming reflection upon its adepts to fay, that
there.are fome particulars of no fmall confequence
in the praxis of aftronomy, that are not yet clear
ly underftood, and have never been properly
explained. Two inducements prompted me to the prefent
refearch. In the firft place, I confider'd that there
is an- effential difference, tho' it is not duly re
garded, .between the parts of time, and the mear
fure of time, which is refolvible into the alone
equable. motion of the asquafor. And whoever is
defirous to underftand the primitive laws ofthe
lunar computation, he muft abftradt his thoughts
entirely from every fpecies of calculated lunar mo
tions. , For whatever their phyfical caufes may be
(of which I can fay nothing, becaufe I know nor
thing) they were appropriated, ab origine, by the
Creator, to ferve a particular end : and that par
ticular end is (ipfe dixit Mofes) lehair gnal haaretz.
Hence it has come td: pafs, that we have never
been able (whilft the naturalifts have been great
ly perplexed how to account for it) either exactly
to inveftigate, or to apply to any civil or facred
ufes thefe appropriated motions,
U u 2 There

( 34° )
There is a like difference in nature> between
thefe appointed meafures of 30 and 29 days^ iartd
an aftronomical month or lunation, calculated fo
confift in a mean of 29 d. i2 h. 44'. 3". asthere
is between the equable all-meafuring motion of
-the aequator of the Earth's orb, and the unequal
¦unmeafuring motions ofthe Moon's orb. >
Thefe calculated lun&tionS are, properly fpeak
ing, neither parts nor meafures of time i, they are
•an -artificial heterogeneous compound, which can
never be reduced, by the art of man, loan inte
gral commenfuration ; and the moment theaftrd-
nomer give's them up, he will be freed from an
ufelefs and, unintelligible puzde.
I cannot readily believe that God (who is not
the Author of perplexity and confufiort, but of
order and regularity) has defigned us tb meafure
the faered and coaeval lunar year, with fuch ina
dequate parts. And it was moft undoubtedly a
very unhappy, as well as incompetent hypothefis
of Keil' s, that the reduction to entire daygj without
fractions, was owing to no higher caufe than the
incapacity and ignorance ofthe vulgar. But thefe
fuppofed reductions do not conftitute lunar months;
they can no more be faid to be meafured by the
motions of the Moon in its orbit, than by the
•belts of Jupiter.
But befides thefe reafonings and convictions, I
was led into this enquiry, by recollecting the
pradtice of the latter Jews, who lived in the third
period ; of which Dr. PrideUx, in his-preifkse <tb
the firft book of his Hiftorical Connection, gives us

( 34* )
us this account, p. 5. " when they faw the new
*' Moon, thenjfhey began their months, which
" fometimes confifted of 29 days, and fometimes
-*' of 30 alternatively, according as the new
"Moon did Jdoner or later appear. None of
" them had fewer than 29 days, and therefore
" they never looked for the new Moon before
" the night following the 29th day, and if they
" then Jaw it, the next day was the firft day of
" the following month. Neither had any of
." their months more than 30 days, and therefore
" they never looked for the New Moon after the
*' night following the 30th day; but then, if
"they, faw it not, they concluded, that the ap-
", pearance was obftructed ; by the clouds, and
_'¦¦?-, made the next day the firft of the following
" month, without expecting any longer ; and of
". ill of thefe months their common year confift-
?5 ed." From hence, and not from the redue-
tions of the common people, I was inftrudted to
.conclude, that thefe regular and determinate, tho*
unequal returns; of the new Moon evenings,
were the effects of an original eftablifhed law, by
110 means depending, as caufe and effect, on the
Junar motions.
Here fome, probably, will ask on what then
are they dependent? what are, in nature, the
caufes which produce thefe effects ?
The calculation which folves this queftion has
fomething in its conclufion fo very furprifing and
imekpscted, and yet fo extremely obvious to an
inquirer, when once the right path has opened
i itfelf

( 342 )
itfelf to his view, that it may- poffibly excite the
curiofity of fome to read it ove&fmdre than onc£,
in order thoroughly to fift and examine it.
I muft now alter the method of my proceed
ing, for the prefent calculation requires me, iff,
to reduce the given number of folar years to days,
then to lunar years,- and in the laft- place, thofe
lunar years to days. And if, from -the collected
fum of lunar days, we fubftradt 1 5, (=the! Cha
otic new Moon epadt)- and then place the 3 re
ductions under one another according to their re
fpective quantities, they will be rightly prepared
fortheconclufion. -.-•.;...¦-¦ .'-¦
As to the reduction of folar years- to days, fince
in the prefent cafe, there are no more than 4, and
confequently there' is no neceffity to have any- re
gard to the number of meridian e-pacts to be fub-
ftracted, we need only multiply ^'66 d. -j-5 d. -}- ~
X 4, and the product will be 146*1 days.
But in order to reduce folar years to lunar years,
multiply 360 by 4- then divide the product 1440
by '30/ and the quotient 48-4-12, will give the
number of 12-month lunar years, abftracted from
the epacts and the quadrantSj which are to be ac^
counted for : e. g.

. , , 30)1440(48 months-M 2 —4 lun.yrs.
If we are required to reduce lunar years to days,
lefs in number than j, firft fet down the days of
both

(' 343 )
both years, with the epadt and quadrant in this
manner. : V. D. D.
The days of the fojar year 3 54-f-6-J-5-|~£,
The days ofthe lunar year 3 54-J-6-]— 5— j-^r.
Then to 354 folar days add the disjoined 6,
the fom 360 will be the arithmetical mean be
tween the quantities of the two years. Confe-
quently, 360 — 3 54=6 days, and, 360 — 355=5
days. Now, in 4, lunar years there are 3 of
354 days, and 1 of 355 days. Multiply then
6X3 and' to the produdt 18 add 5, which will
make 23 days: fubftradt thefe 23 days from
i44o(=36oX4) and the remainder 1417 will be
the true number of days, in 4 12-month lunar
years, one of which is of 355 days.
Carry forward? the 23 days (=6X3+5) anc^
add to them 20 (= the 5 remaining folar days
X4) the fum 43 will be equal to the fum total
ofthe epadts. For in 4 lunar years there:are 3
epacts of 1 1 days, and 1 of 10 ; but 1 iX3~33
-[-10=43, But the fum total of fexagefimal
parts of the multiplied meridian epacts are, always
greater than the fum total of days, .arifing from an
equal multiplication of the lunar epadts, by as
many units as there are lunar years of ^^^ days.
Now 11' X4a=44' — *43d.= i'.
: To thefe 43 days add 1 (=4 X 4) an^ the fom
44 will be equal to the fum of 4 integral epacts,
and 4 integral quadrants. - ,:
li The

( 344 )
The collected number of lunar days (commen
cing from the evening ofthe full Moon (O) day
have been found to be O 141 7 O days. From
thefe fubftradt 15, and the remainder C 1402- C
will be the number of lunar days, computed from
the chaotic new Moon evening, and ever termi
nating within the cardinal limits of the folar year,
full 1 5 days fhort of the other.
Set down thefe three reductions, accdrding to
their quantities, under one another ; then, fub-
ftradting the lunar days from the folar, the re
mainder will exprefs the integral, aftronomical
diftances both of the new Moon ({) and of the
full Moon (O) evenings from the autumnal aequinox.
e. g. Solar days © 1 46 1 ' «
F. Moon lu. days O 1417 O 61 — 17=0 44 O
N. Moon lu. days C 1402 C 461— 402=1 59 C
It appears from the calculation in the margin
that if, throwing off the two firft fimilar figures
14, the two laft 17 be fubftracted from 61, the
remainder 44 (O) meafures the diftance of the
full Moon evening from the autumnal aequinox,
as the remainder 59 c does ofthe new Moon even
ing, but 59— 44 = C 15 O
But as the marginal numbers, O 44^0 and C
59 C, each of them include an aftronomical mea
fure of 30 days, add 30 to both collections. Then
17 -}- 30 '= 47 O. And 02 i -f- 30 == 32 C.
But

(" Us )
o o
But6i — 47^0 14. And6i — 32C = «29C»
Again, 29 C — 14. s= C 1 5 O-
•Therefore I fay, that when the Sun enters Libra,
in any place at noon, on the 15th day from, the
new Moon (<) evening, in the end of the 4th
revolution from thence j it will again enter 'Libra
on the 14th day from the full Moon evening, and
on that very day on which the new Moon (C)
evening fhall fall, by an uniform and invariable law.
A* M. o A. M. 4*
O r£b
O O
C15. 0 14. c.
Q>E. D*
Tho' the principal point in view is irt a man*
tier already determined, in the courfe ofthe pre
cedent calculation ; yet if it was not, the deduction
is extremely obvious, and the conclufion ready at
hand. For if we examine the collected number
of new Moon lunar days, 1402 C. we may ob-
ferve,that they end C 59 C days before the autum
nal aequinox; but thefe 59 days naturally refolve
themfelves into the unequal meafures 30 and 29;
And thefe, as I fhall now make appear, into the
fum total of epacts and quadrants, from the be
ginning of the chaotic year (which we are obliged
to.include for the fake of connection) to the end
of the 4th, computed from the Mojaic radix.
Xx The

( 346 )
The epadt in the beginning of the chaotic year,
with its adhering quadrants, may be eafily afcer
tained by only fubftracting 1 1 % from 144, re
mains 3 *. Now the following table or feries of
¦epadts and quadrants, within the forementioned
limits, will cdndlude and complete the deduction.
A table of integral lunar epafts, with their ad*
hering quadrants from the head of fhe chaotic
year to the end of A. M. 4.
Epacts Quadrants,
D.
A. M. o. 3. |
A. M. o. 11. i

A. M. 1. n.
A. M. 2. 11.
A. M. 3. 11.
A. M. 4. 10.

¦
q - ~* The fourth quadrant ofthe
laft day which meafures
from neon to Sun fetting

C59C = 3oand29.

From hence we are, certified, and may indu
bitably conclude, that thefe appointed unequal
meafures of 30 and 29 days have no more depen
dence upon the lunar motions, can no more be
faid to arife from them, than the integral lunar
epadts, and the annual feparate quadrants, of
which they are formally compounded. Thefe are

( 347 )
are their effential, internal, and true aftronomical
conftituents. I fhall now proceed to the conftrudtion (and in
the calculations fhall illuftrate the ufe and appli
cation) of the aftronomical table, founded upon
the inverted pofition of the two great luminaries,
in the beginning and in the end of A. M. i ; and
in the beginning and in the end of A. M. 1656,
V. N. 600 ; or of the year of the creation, and of
the univerfal deluge.
To this table, and its demonftrable characters,
I appeal, as to a fure and unexceptionable teft of
the truth and certainty of the Mojaic fcheme of
aftronomical chronology, according to the Hebrew
text. Here then I lay down thefe 5 terms, viz.
(0(2) (3) (4) (5) , „
o 1 5 :: 24 11 for the bafis, which may
be thus explained.
(1) The cypher fubjoined denotes and expreffes
the no-diftance of the created full Moon (O)
from the 4th ofthe Hexaemeron, which was the
autumnal aequinodtial day: and, by means ofthe
invented pofition, the no-diftance of the new
Moon (() evening, from the fame tekupha, or
autumnal cardinal point, in the end of A. M.
1655, when the laft day ofthe 12-month lunar
year fell upon tbe laft day of the tropical folar.
(2) The fecond term 1 may be read thus; in the
beginning of A. M. 1, or of the year ofthe crea
tion, the firft day of the firft month of the full
Xx2 Moon

( 34« ) 
Moon (O) lunar year was coincident with the
firft day of the firft month of the tropical folar
yeaf'j and by means of the inverted pofition, in
the beginning of A. M. 1656, V.N. 600, or of
the year of the univerfal deluge, the firft day of
the firft month of the new Moon (c) lunar year
was coincident with the firft day of the firft month
of the tropical folar year.
(3) The third term 5 exhibits the difference,
between the 12th political month of the primitive
lunar year, which was of 24 days, and the 12th
aftronomical meafure of 29 days for 29—24=5.
(4) The fourth term 24 may be read thus.
Towards the conclufion of A. M. 1. or of the
year of the creation, the 24th or laft day ofthe
1 2th political month of the primitive full Moon
(O) lunar year, was coincident with' the 24th
day of the 1 2th month of the primitive folar tro
pical year: And, by means of the inverted pofition,
towards the conclufion of A. M. 1656, V. N.
600, or the year ofthe univerfal deluge, the 24th
or laft day ofthe 12th political mdnthpf the pri
mitive new Moon (C) lunar year, was coincident
with the 24th day of the 12th month of the pri
mitive folar tropical year. ' '.-
(5) The fifth term 1 1 denotes and exprefles
the integral aftronomical diftance of the fullMdon
(O) evehing, towards the end of A. M. 1. or of
the year of the creation, from the autumnal aequi
nox ; and by means of the inverted pofition? the
integral aftronomical diftance of the new Moon
(<) evening, from the fame tekupha, pr cardinal point.

( 349 )
point, towards the end of A. M. 1656, V. N.
600, or ofthe year of the univerfal deluge,
Thus much may fuffiee for the explication of
the 5 terms of the bafis.
I fhall digeft my farther proceedings into thefe
particulars enfuing.
( r) I fhall frame from the given bafis, 015:;
24 11, two diftindt tables, correfponding with
the tworfold quality of the Moon, and the cha
racters of the inverted pofition.
(2) To thefe I fhall fubjoin a table of reduction
to the Julian calendar, adapted to the autumnal
aequinox, and will hold true for the fpace of be
tween 5000 and 6000 years. I may venture to
offer this as a fingular curiofity, becaufe it iscon-
ftrudted without any previous calculation, either
arithmetical or tabular.
(3) I fhall fhew the plain, eafy, and fimple
rules, by which thefe tables are framed.
(4) I fhall give a general account of the feveral
proportions, and of the application and ufe of the
5 diftindt columns, and ofthe 30 diftindt parallel
lines of thefe folar and lunar tables.
(5) I fhall difcover and lay open their 3 effen
tial and moft diftinguifhed properties.
From the whole laid together, the grounds and
reafons will in due time appear, why I was em
boldened to prefix to it this promifing title :
A two-fold aftronomical table, both folar and
lunar, Mojaic and Julian, conftructed from the
inverted pofition of the two great luminaries, in
the

( 35° )
the year of the creation, and in the year ofthe
univerfal deluge; A. M. i. and A. M. 1656.
V. N. 600. which will ftand in need of no altera
tion or correction, from the firft to the laft mo
ment of time.
This table exhibits, in one entire view, the
feveral full Moon (Q) evenings, as appears by
the fymbol (Q) affixed to the firft and the laft,
and . underftood to be affixed to each, in
the refpedtive days of the 12th month of the
patriarchal folar tropical year, with their integral
aftronomical diftances, from the autumnal aequi
nox, in every poflible variety, thro' the whole
courfe of time.

Table

',*''¦ ¦ '¦ , , i . r— -r 1-1 )tr i i - -'- —
WHklUHMMMMHHHHNHHHHHHN I „„_„,
I O SO QO~q QsOl 4> OO 10 M O SO OO-vJ OsOl 4. OO 10 >h O SO OtfvJ OsOl 4^ OO » M I *3P"I

11 toil tow to 11 to m to 11 mm to 10m um um
SO 0C~J OsOt-fr-QO 10 M QsQ QO-^ QsPl.fr. £ g m Q sQ 00-5 Q^ ¦" yj g m rj

IS_"H » H MM m Mm Mm MmMm 10 m u m >«.Ili »— *
OsO 00-J QsOi.fr 00 M m QvQ OQ^i gs.Ui.gj; M m OsO g)-J QSQH.^O^ 5 M® I? I jj.

Ui I " 1H Mmmm MM Mm m Mm MM Mm m mm i •
w l4> 00 M m Q so oo^-J gsln 4> 00 M m Q so oo^t gsUi 4* 00 M 5 O js* oo<3 gsu. | j

Ml MM M MM
4" |Ol Os"-J 00SO O M M
0|O 

,.w,»0mM ,M mm MM m 4* M M MM
00 4* U> Os-^J 00SO O M M OO 4* Oi Os-^1 00<D O M N 00 4«
 _~  0

M re ? . M MW Jl HW U H »M MMOOM M OO M MM N M t» U M
m | Q SQ QQ^j OSO14.OO M M OS© 00>-J OMA^U Mm OSO OaM SslBl .£ to M M

>
8

c
a to1-t
<-f,
JO
cr

i>
w y»

crn

( 5SZ )

The fecond table exhibits, in one entire view,
the feveral new Moon (C) evenings, as appears by
the fymbol C affixed to the firft and laft, and under
ftood to be affixed to each, in the refpective days
of the 1 2th month of the patriarchal folar tropi
cal year, with their integral aftronomical diftan
ces, from the fame Tekupha, or autumnal cardi
nal point,- in every poffible variety, thro' the
whole courfe of time.

Table

( 353 )
Table II.
A new Moon (C) lunar stable.

MH

a
Q-
n
«
(0
(2)
fc)
(4)
(5)
-n
.©
I
C 0
I
5
24 C
11
2
11
12
16
*3
22
3
22
23
27
2
33
.4
3
4
8
21
'14
5
H
15
19
10
25
6
25
26
0
29-
6
7
6
7
11
i8i-l
17
8
*7
18
22
7-
28
9
2§
29
3
26
9
10
9
16
*4
*5
20
, ii
20
21
25
4
31
12
1
2
6
23
12
*3
12
x3
*7
12
23
14
23
24
28
1
34
*5
4
5
9
20
15
16
15
16
20
1
9
; 26 <
: 17
26
27
1
28:
7 '
18
7
8
12
17
18
' 19
18
*9
23
6-
2g
20
29
0
-4
25
! IO '¦
21
10
11
i5
x+
• 21
22
21
22
26
3
32
23
2
3
¦7
1
22
r3«
24
*3
H
iS
1 r ,
24-
25
24
25
29
0
35
26
5
6
10
•
T9
16
27
.16
z7
21
8
27
28
27
28
, 2
27
8«
29
. 8
9
?3
16 .
19 «
3£
09
20-
24
5-C
•30 '
1
C 0
i
-S
24 <
11
y
The
( 354 J
A table of redudlion to the Julian calendar, adap
ted to the autumnal aequinox, which will hold
true, for the fpace of between 5000 and 6000
years, from the creation.

Auguft.

September;.

OMober.

November.

1 120

1

89

1

59

1.

28

2 119

2

'88

2

58

2

2l

3 "8

3

'ii-

3

%

3

26

4 "7

4

86

4

4

25

5 1 16

5

85

5

55

5

24

6 1.15

6

84

6

54

6

23

7 "4

i

«3

7

53

7

22

8 113

82

8

52

8

21

9 i 12

9

81

9

5i

9

20

10 III

10

80

10

50

*o

x§

ji iio

11

79

11

4§

11

18

12 icJg

12

78

12

4&

12

*Z

13 io8

13

71

13

4fe

13

16

14 107

14

H

46

M

15

15 106

15

75

*s

45

15

14

16 105

16

74

16

44

16

i3

17 104

is

73

ii

43

17

12

18 103

72

43

18

"

19 102

l9

7i

l9

4i

19

10

20 IOI

20

70

20

40

20

9

21 100

21

69

21

39

21

8

22 99

22

68

22

38

22

7

23 98

23

¦a

*3

\

23

6

24 97

2*

24

36

24

5

*5 96

1!

65

25

35

25

4

26 95

64

26

34

26

3

27 94
28 93

27

63

2Z

33

27

2

28

62

28

32

28

1

29 92

29

61

29

3i

30 91

3«>

60

3°

30

31 90
3i
„ 2?
Thus
( 355 )
Thus much for conftrudtipn -, and we are now
to fhe y (2) the plain, eafy and fimple rules of
this conftrudtion.
It is obvious to perceive, by only cafting an
eye over thefe lunar tables, that they are each of
them digefted into 5 diftindl columns, equal tq
the number of terms in the bafis ; and alfo, into
30 diftindl: parallel lines, equal to the number of
days in a primitive month ; whilft the putermoft
column, on the left hand, fet at fome fmall di
ftance from the neft, and marked with no figure
at the top, is the index to the 30 numbers in each
parallel line.
The 30 diftindl numbers of the three firfl coT
lumns, and ofthe fifth, are produced by the con-
(>) (») (3) (5) '
tinual addition of 11 to — o t 5 — 11, cafting
off all the 30', till they return back again into
themfelves, which they will all do, after 30 un-
decimal additions are completed.
E. g. Take the lowermoft parallel line, whofe
(0 {*) (3) (4)
ift, 2d, 3d and 5th terms are, 19 20 24 — j:
(;)
then, 19-^-11=30 — 30=0. And, zo-\-n
c*> , (3)
=31—30=1. And, 244-11=35—30=5. (5)
And, 3o4-u=4I — 30=1,1. Andfo of all the
reft. The numbers of the fourth column are produ
ced, .vice verfd, by the continual fubftradlion of
11, adding 30, as oft as is neceffary, to make the
fubftradlion.
Yy2 E.g.

0356)*
E. g. Take the ift, the 3d, and the laft num
bers, viz." 24 2 5. Then 24 — 11=13. And,
24-30=32—11=21. And, 54-30=35—11
='24, where the fourth term of the bafis, viz.
fe) ''''...
24, returns back again into itfelf.
If we compare the feveral columns with each
other, we may obferve, that all the numbers of
the 2d exceed all thofe of the ift by 1. , Thofe
ofthe 3d, all thofe of. the 2d by 4. Thofe of
the 5th, all thofe ofthe ift by 1 1. .
¦ The 30 numbers ofthe ift, and of the 4th co
lumns, being added together, are ever equal to 24,
or 54. '- ¦ ' ,. . :,
< The 30 numbers of the 2d, and of the 4th co
lumns, being added together, are ever equal to 25,
or 55. '"':/, .",'¦'
Tne 30,-numbers of the 3d, and of the 4th co
lumns'; being added together, are ever equal to
29 ; /;. e. to the leaft of the two unequal aftrono
mical meafqres.
: ~ The 30 numbers of the^th, , and of the 5th co
lumns, being added together, are ever equal to
35-; i.e. to the number of. days in the ,12th
month of the primitive and patriarchal folar tro
pical year.
The numbers-of the 4th, and of the 5th co
lumns, are fet at fome diftance, from thofe of the
ift, 2d and 3d; becaufe thofe 3 exhibit the po
fitions of the luminaries to each other, with re-
fpedl to the beginning of the calculated year ; the
other 2,' at the end of it. ',.; The

( 357 )
The numbers of the 5th column, from ji at
the top to 30 at the bottom (excepting, 31 32
3 3 34 3 5) inclufive, reprefent in one entire
view the whole variety of the full Moon and new
Moon integral epadts, or neareft diftances of the
end ofthe lunar year from the autumnal aequinox,
which have ever yet happened, or ever will hap
pen in nature. >
The numbers of the 4th column, from 24 at
the top to 5 at the bottom inclufive (excepting
only as before) reprefent, likewife in one entire
view, the correfponding days of the 12 th month
of the patriarchal folar tropical year, in thV even
ings of which the autumnal full Moons and new
Moons ever have, or poffibly can, fall in their pe
riodic times. !
The oppofite numbers of the 4th, and of the
jth columns, are ever, without any limitation of
time, aftronomical indices to each other recipro
cally. My meaning is, fuppofe either the full
Moon or the new Moon epadV in any year to be
ii; then the oppofite number 24, in the 4th
column, will ever exprefs the correfponding even
ing, in the 12th month of the primitive folar
year. And we fhall ere long be convinced,
that the praxis of Sun and Moon aftronomy, as
God himfelf has adapted it, ab origine, to our
civil and religious ufes, is quid determinatum ;
and no more requires prolix tables, operofe* calcu
lations, and the abftrufe argument of asquations,
than the well-known time bf the Sun's rifing and

( 34» K
fetting upon thj «q.uinodiiaJ days, ift every region
and climate throughout the globe.
The numbers pf the i ft column', from the cy«
pher at the -top,, to 19 at, the bottom, arearepe^
titjipn of the numbers ofthe jth column (except
ing in the exopfs aboye 30) and confequently of
the whole variety of the full Mppn and. new ^P0**
autumnal aequinodtial epadls, which are here cqnrr
fidered as prefixed to the head or beginning of the
emulated folar year,
The numbers ofthe ad column, from j. at |&e
top to 20 at the bottom, i& the ift, 2d and 3d
years of every quadrienni$l folar revolution, are
tl^efeatsof theipquipoSi^fpint of the year, in
a correfpond^ ,me/i4iao : but in every 4th. year,
computed from the 4th of the Hexaemeron ex-
clufiye, the feat pf tfce aequ^pdlial point pf the
year* in what | c9.ll the ruling, meridian, istranf-
feredfrpm the injgnbeiis pf the jsd column, to a
number ©f ;the iwne value in the firft j and that
number ff the feme value in the firft column be
comes the boundary of the folar year, and the
quantity of the lunar epadl. This accounjt will
fee better upder ftopd, when we come to, treat pf
the folar, and of the lunar, indices of the qua
drants. «
If any one number in the ,i# column foe*fubr
ftradted from its correfponding number (i. e. in
the fame parallel line) in the 3d column, the dif-
¦.' • r (0 (3)
ference will ever be 5, from o — 5,- at the top, to
(0 (3) - /-'"'¦
19— £4 at the bottom j for 24 — 19=5. How
' fri-

( 359 )
irivolous foever this calculation may either feem'
orbe thought to be, yet it inflriidts us in a mate-
mi point, aftd fupplies us With a proper rule how
to afcertain the month and day ofthe month of the
fofei* y^ari Which "coincides aftronomically With the
grven month and day ofthe month of the concur
ring lunar yeat, Which, in its nature and by its
original frame, is incommensurate to the fblar :
fo that- from hence We are taught to read the dif
ferential number 5, arifing from the above ftib-
<o- - , ti)
ftra&ion of 19 from 24 in this manner: -vix:
whenever the new Moon (c) epadt is 19, the
24th day of the ift month of the lunar year, will
coincide with the 5th day of the ift month of the
ffplar: confequently, whenever the new Moon (<)
epadt is 1 1 (as in the end ©f the year of Noah's
life 000) the 27th dayof the fecond month of the
lunar year will coincide aftapnomically with the
1 6th day of. the fecond month of the folar year $
for 57 — 1 1 =46 — 30= 16. From hence we in
fer, that Mejes computes by the months and days
of the lunar year, and not by the months and days
ofthe folar. And fhould it appear upon a due
examination, that the new Moon (() epadl, ait
the end of A. M. 1656, was in nature 11, then
this argument will be decifive.
. I cannot recolledl, at prefent, any more parti
culars, which might be thought necefiary to be.
added, by way pf a farther explication in general
of thefe lunar tables. I fhall only lay, that how
plain and fimple foever their conftrudlion may ap-

,(36o>
pear ; yet in their ufe and application they are very
extenfive and complex. This will be evidenced
from what I have to offer in the laft place,, by the
method propofed, concerning their threefold and
moft diftinguifhed property} I mean, as they
pundtually exhibit the annual ftations of the two
great luminaries; firft, in the 12th 3 5-day month
ofthe primitive and patriarchal folar tropicalyear*
Secondly, in the form- of the Julian calendar, ren
dered , by this u ndecimal table, for ever commen-
furate to the Mofaic Shanah, or the true folar.
Thirdly, in the form of the Julian calendar, as
it is ftill ufed by us, and computed to confift of
365 days, 6 hours ; ever including and carrying
along with it, the annual encreafe of the meridian
epadts ; which muft neceffarily occafion a retro-
ceffion of the cardinal points of the folar tropical
year/ in the months of the Julian.
I fhall not prefently have occafion for the table
of redudlion to the Julian calendar, and fhall
therefore defer the explication of it, until it be
more immediately neceffary ; for methinks I hear
the tired and impatient reader fay, Corner prithee,
be expeditious, and fhew us, what we want to
know. ( 1) The true aftronomical law of connedl-
ing the lunar years with the folar. (2) Open to
us the long fecreted- and hitherto unknown aftro*
nomical reafons, why the day of the week is never
once exprefled in the Pentateuch, nor throughout
the Hebrew bible. (3 ) Make it . appear to us,
*' Upon fuch evidence and proof,- as will amount
** in the whole, withbdt exception or referve, to

" a

( 3°* )
" a mathematical certainty," that Mojes's table
of the genealogies of the patriarchs, both before
and after the flood^ is, in itfelf confidered, a moft
accurate aftronomical table, both folar and lunar.
(4) Compel us to admit, that it may be proved
to be fo, independent of any known principles of
fcience, of any known laws of aftronomy, or any
methods of computation whatever, but what are
founded on the principles, data, and terms of the
Hebrew Pentateuch, and the created pofition of
the Moon to the Sun : for if thefe things be'fo,
it would be; undoubtedly, no lefs than an arro
gant and prefumptuous theomachy to go about to
refift the almighty force of a demonftration, built
upon an original eftablifhment, a primary confti
tution of the- God of nature.
As I now look upon myfelf to be peremptorily
called upon to demonftrate the aftronomical cer
tainty and exadlnefs of the Mojaic folar and lunar
tables, I fhall readily- comply with the demand ;
and here I offer, for the grounds' of the de
monftration, thefe 3 aftronomical data of the
Pentateuch, which have been noted before :
viz. 1. The charadters of the original pofition.
2. A continued feries of 1656 Shanim, or true
folar revolutions, computed from the 4th of the
Hexaemeron, which was the autumnal sequinodtial
day, and ending in the year of the deluge, and on
the autumnal sequinodtial day of that year. (3)
The diftance of ii entire days from the new
Moon (c) evening, to the fame cardinal point ex
clufive, in the conclufion of the given interval.
Z z From

( 362 )
o o
c 15 c 12
From thefe data, 1656 years, we are plain
ly taught, that the aftronomical bonds of connec
tion, between the two extremes of this givenferies
of Mofaic years, were the Sun's tranfit over the
autumnal aequinodtial point on the 15th day from
the new Moon evening, in the head 0r beginning
of it ; and its tranfit over the fame cardinal, poin^
in the end of it, on the 12th day from the new
Moon evening. What I would advance, from
hence is this, that Mofes's conclufions in aftronpr
my may be eftablifhed, ipto general propofitions,
which will hold univerfally true in nature, apply
the epoch of the calculation to any meridian, or
determinate place, and to any intermediate age of
the world whatever : admit but of the circum
ftances of the former tranfit, the like circum
ftances of the latter are fure to return, at, the end
of the given interval by an immutable law. I
fhould think it but a yery petty conceffipn, fhould
I hear an aftronomer fay, that he had made a caV
culation for A. M. 1656, as fituated by this fcheme
of the world's chronology, and was fatisfied that
the Moon wasvin the end of Jhat year, at fuch a
diftance from the Sun, that it might be vifible at
its fetting 11 days before, the autumnal, aequinox.
This is not fufficient, nor faying fo much as the
cafe demands: for the original pofition, and. the
true quantity of the Mofaic Shanah, or folar tro
pical year being granted, it muft neceffarily hap
pen as ftated and recorded by Mofes ; and it is,
im-

• ( 363 )
impoffible in nature it fhould be otherwife. The
conclufion and determination is as fure and certain,
as when from i 5 we fubftradt 4, the remainder
muft neceffarily be 1 1 . I will proceed a ftep far
ther and fay, that the original pofition admitted,
theh in the beginning ofthe 1657th folar tropical
revolution from thence, the 15 th day from the
autumnal new Moon (C) evening muft neceffarily
coincide with the 4th day from the aequinox in
clufive ; and that this conclufion and determina
tion is as fure and certain, as when from 15 we
fubftradt 11, the remainder muft neceffarily be 4.
And thefe calculations (if the grounds of them
were rightly underftood) are alone and in themfelves
confidered, not only a fufficient, but a conclufive
proof of the truth.
The more diligently we examine into and con
fider it, the more we fhall be open to convidtion,
that Mofes's account of the univerfal deluge is a
moft extraordinary record ; not only with refpedt
to the circumftances ofthe hiftory, but alfo to its
chronology and its aftronomy. But I would not
willingly have my dedudtion of the lunar epadt
r 1, nor the grounds of its certainty, to be mifun-
derftood : for the argument was not framed nor
defigned to run thus, viz. becaufe Mofes has re
lated Noah's entrance into the ark, on the 17th
day of the 2d month of one lunar year, and his
receiving the divine command to come out of it
on the 27th day ofthe 2d monthof the next, fol
lowing in immediate fucceffion ; 'that therefore,
in the ydar of Nddh's life 600, in which the de-
•f Zz2 luge

( 364 )
luge began and ended, there mujl have been a co
incidence of the lunar year with the folar,- and
that the epadt in the end of that year muft have
been 1 1 : for the very reverfe of this is fhe truth ;
and the argument is defigned to run thus ; viz.
becaufe, in the beginning' of the year of Noah's
life 600, the firft day of the firft month of the
lunar year fell, by the annual courfes of the two
luminaries, and their various relations to each
other, on the firft day of the firft month ofthe
folar year, and muft by its, frame and ftrudlure end
1 1 days before the folar ; therefore Mofes has
ftated and. recorded the aftronomy of that diftin
guifhed year : nor can the ftile and circumftances
,of Mofes's hiftorical narration be interpreted to re
cord any other difcoverable pofition of the two in-
commenfurate years, but that which was in real
matter of faft the true one.
We are now then to examine into the certainty
of this matter of fadt, and to fift and try, whether
my aftronomical interpretation of Mofes's hiftori
cal record has its foundation in nature, and in real
fadlornot, A. M. 1656, V. N. 600.
It is an allowed, and a fure method of proof to
affume a principle as true, and to argue from it
as fuch j for if all things happen, as they neceffa
rily muft have happened, in cafe the principle
had been a certain truth, then the affumption can
not be falfe.
I affume then thefe two numbers 15 and 11,
deduced from the Hebrew text of the Pentateuch,
according to my interpretation of it, as true aftro- no-.

(365 )
nomicaldata, and I will argue from them as fuch j
afterwards we will examine, and bring to fome
other. teft the conclufions.
From 15 fubftradt 1 1, and then we fhall have 3
numbers, viz. 15 114. Now I defire the affiftance
of no other mediums befides thefe 3 numbers,
1 5 1 1 4, to enable me to adjuft the twofold lunar
year to its correfponding tropical folar, in thofe
5 years, which my own fancy (though perhaps,
not quite without reafon) induced me to feledt.
And thefe feledled years are, (ift) The chaotic
year ; by chaotic, I mean that year which may be
fuppofed to precede Mofes's account of the origin
of time j and this ne-year is neceffary to be con
fidered for the fake of connection, &c. (2dly)
The year of the creation, or A. M. 1. (3dly)
The fecond year before theflopd, or A. M. 1654.
V. N, 598. (4thly) The year immediately prer
ceding the deluge, or A. M. 1655. V.N. 599.
(5'thly) The year of the univerfal deluge, or A. M.
1656. V.N. 600.
I fhall now proceed by thefe feveral fteps.
Firft, I fhall make tables of thefe 5 feledled
years ; with 3 of which the reader is already in
fome meafure acquainted ; but they are now laid
, again before him with a higher view, viz. in or
der to afcertain their reality (excepting only the
firft, which is chaotic and imaginary, but reduced
to a calendar for the fake of connection) and to
demonftrate the aftronomical certainty of their fe
veral

( 366 )
veral parts, aindtigk. Which are to bereckoried the
quadrants, though concealed from the vieW.
Secondly, I fhall make it a^ear, hdW; and in
what particular manner I was enabled add di'redt-
ed to make thefe tables by the alone affiftance of
thefe 3 numbers, 15 114. The two former of
Which are here afiumed as true aftronomical data
of the Pentateuch.
Thirdly, I fhall confirm arid eftablifh the truth
and certainty of every one of thefe charadters, both
folar, lunar and hebdomatic, by a plain, eafy, arid
fimple arithmetical calculus ; independent bf any
known principles of fcience, of any knoWh laws
of aftronomy, or bf any metHbds of computation^
Whatever, but what are founded on the principles
and terms of the Pentateuch, arid the created pofi
tion of the Moon to the Sun, as it is levelled to us
by the author of the fyftem. This, I may pre-
fume, will be a fufficient and fatisfactory anfwer to '
the demand upon me. c
In the firft place, I herd exhibit 5diftindt folar
and lunar tables, from whence we may eafily learn
What were the true aftronomical and primitive
laws of connecting, and jointly computihg by,
the two incommensurate years.

(0

A.M.o.

0
O19 C 4

( a67>
(0

A. M. o.

(2)

A. M. 1

O
11O354O
350 C 15

354011 339C26J

(3) (4)

©.

A.M. 1653? end-
V. N. 597 S ing.

A. M- 1654

A. M, 1655.

A.M. 1656

— ¦

V.N. 59S

Y.N, 599

V.N. 6do

-n_

£b

--fy.

£V

0

©

©

©

C24

6 O S550 4

350 O 15

339 O 26

C 9
346 C 19
WC354 C
354 C 11
f
Secondly, I fhall make it appear, how, and in
what particular manner, I was qhabled and. dicedV
ed to-make thefe tables, by the. alone affiftance of
thefe 3 numbers, 15 11 4. T^he two former, of
which are here affumed as true aftronomical data
of the Pentateuch.
Within the limits of thefe tables, there are 7
full Moon (O) and 7 neW Moon (C) epadts
(reckoning the cypher twice repeated for 2) and of
thefe 14 epadts, the 3 numbers 15 114, as they
occur twice over, make fix ; which may feem,
at the firft view, not a little pr-omifing, as I con
fider them of fuch importance, andr rank them
with fundamentals. But notwithftanding thefe
promifing verifimilitudes, the queftion ftill recurs, and
( 368 )
and muft be fatisfied, viz. whether it was true
in fadt, that in the end of A. M. 1656,* the new
Moon (C) firft appeared at the diftance of 11
entire days from the autumnal aequinox ; for no
one will or can allow that my deduction, with
out farther proof, has afcertained it. But how
reafonable foever fuch furmifes to the contrary may
be thought, I fhall not fcruple to argue from it,
as an eftablifhed conclufion and a certain truth ;
and fhall undertake by its affiftance, and the, ra
dical number 4, to determine, with an aftrono
mical exadlnefs, the twofold feries of 2 years
epadts, i. e. quite back to the end ofthe 3d year,
before the deluge, A.M. 1653. V, N. 597.
In the following determinations then (for I fhall
give 4, exclufive ofthe lunar tables, p. 307, 308.
and a regular arithmetical proof) the calculus pro
ceeds by the continual addition of the 2d radical
number 4, to the Mojaic datum 11, and to its
refult fucceffively, according to the number of
years, which are here computed backwards from
the recorded epadt 11. E. g.
A.M. 1656?^ , , .
V.N. 6oo5Tab-(5> <"+*=
A.M. 1655?™ , , . _ . I
V.N. 59^Tab-(4)=0 i54-4=
A.M. 1654?— , ,
V.N. 598STaM3)= C 194-4= ¦
A.M.1653?™ , , . . ^
V.N. p597^Tab-(3)=234-i=-024. The

(369)
The reafon why one is added to 23 in the'laft
dedudlion is, becaufe the lunaryear, connected with
its correfponding fokr, A.M. 1654, tab. (3)was
of355days> and the additional day is here ta
ken in.
We may obferve, that thefe new Moon (()
and full Moon (O) epacts, or integral diftances
from the autumnal aequinox follow one another al
ternatively, and that thefe 3, viz. CfiOiiCio'
encreafe in arithmetical progreffion by 4; andfo
likewife do O15C19. and $24, excepting the
laft, for the reafon abovementioned. But as A.
are omitted," they may be thris obtained ; only"
premifing_ that, 114-15=026. ' , '
¦ -v; .-;¦• ? ¦ :•-, ;,, .
A.M. 16 56?™, , , . _ , , ,
V.N. 6oo5Tab'(5) 0264-141=30-36=
A.M. 165O , - ¦ ¦
V.N. 599'5Tab-W =C-o_H4|= ..
^N;-j9j|^(3).=b4-H4l=8+i =
A.M. 1655? ,.
V.N. ^J^g, =c9
This is .the firft method of difcovering and fet-
ling the feVeral full Moon "and new Moon epacts
of the given years, by a continual addition of the
2d radical number 4, beginning at the datum c'i 1 j
in a backward computation. The next proceeds
by a continual fubftradlion of the datum 1 1, ftill
computing backwards, in jhe following-manner.
Aaa A.

037° )
v:N^»<4)^3lo-l-^ .
vIr1^^"4^^^
V.N.I598|Tab- (3) 04+30=34-1101=
A.M.16537 ,. ^
V-N7597fendinS'>024 In the third method we will make ufe of the 3
numbers, 15 11 4, promifcuoufly as peeafiprt re
quires,' but principally and chiefly of 1-5. £, g.
V.'N.I6ooiTab-^ »+l'5i=Q26 ';.
A.M. 1.656 ?Tab. (5X0264-4=39— J15J-Q15
V.N. 600 5 Andj^ii-f- 4=15— j 151= < o
A.M. 1 6557T ab. (4) 3 jo ( +4=34—1 1 5\*F < 1,9,
V-N. 599.5 (19— Li 51=Q 4
V^Uti^' (3)"« 19+5=24-1151= < St
vl1^| < 9+ „51=0,4

(37*)
I have fet down thefe various determinations to
fhew, that thefe 3 fundarriental numbers, and
aftronomical data of the Pentateuch^ 15 1 1 4,
are clotfely conriedled, like the links of a chain with
each other, and are by nature adapted to produce
cOHClufibns foientifieally true, as the fubfequent
calculations Will abundantly and clearly evidence.
Thfe remaining dedudtion arifes from the fub-
ftradtiori of the epadtSj from the days of the corref
ponding folar year, and the days of the lunar year,
which fall Within the cardinal limits of the folar,
from therefidue, Which will carry us back to the
fame conclufion. E. g.
V:N:1£l365-n=354-354^ 16
V:N:l99i365-354=nArid 30- 11=09
V:R1sp8|365-i9=346And355-346=t 9
365— 26=339And,3 54— 339=0*5
365— i5=35©Add,354— 3io=Q: 4
365 — 4=36iAnd,36i — 333= 6 And 30—6
; [=624-
By thefe feveral calculations I have fufficiently
informed the reader, how and in what particular
manner I made thefe tables (excepting the addi
tional unit) by the joint affiftance of 3 of the 7
radical numbers; which is more, I am pretty
confident, than he expected from my engagement ;
and indeed, he had no juft grounds to expect it,
A a a 2 ef-

( 372 )
efpecially. in. fuch a variety/of methods," from any
known principles of > fcience, or any known laws
of aftronomy, which have been taught mankind,
fiaee its firft: rudiments- were imbibed by the
Greeks. r ,
_ I fhall give one more reprefentation of this two-?
fold feries of epadts,* from the full Moon (Q)
and new Moon (C) lunar tahles, p., 351 and 353 ;
firft, begging leave to , make two fhort,, but ner
ceffary, remarks. (1) When, in any calculated
year, we have^occafion to make, ufe of thofe pa
rallel. lines,,' in which the numbers of' the 4th and
(4)' , :-,. w. , ,
5th columns, 1. 34. (index 14) 2. 33. "(index 3)
M • (4) • c
3. 32. (index. 22)4. 31. (index 11) are found, the
30s muft be over looked, and as the primitive folar
year is digeited: into 3 604-5, as well as into 33b
4~35 days, the numbers of the 4th column muft
be read,' the -ift ofthe 5, the id of the '5, 'the
'3d of the 5, and the 4th of the 5 appendent
days. TU~ •* * ' : '.-'*'-
(2) It has been already noted, p. 356, that the
numbers of the 3d arid 4th columns being added
together, are ever equal to the leaft aftronomical
( 'meafure 29 days ; but as a lunar year of 355 days
ever begins and ends with 3b days, the '3 firft
numbers of the' calculated parallel line muft be
transferred tp 'that line, in which the number of
the 4th column, being added to the number of
the 3d, 'fhall' be equal to 30. We fhall have 2
inftances of this in the followingextradt from the
tables. s: .; ;. , ¦. From

( 373 )

From the full Moon (O) table, p. 352.

. ,1 .

(0 <

W (3)

•I

.(4) (5)

Index 24

"O
24
25 H
024
25
29
-,.
3UO
4
., ?5
O 4
5
9
20Q
J5
16
CMS
16
20
90
26
ending.
Index 9
10 293°
From the new Moon (O table.
(1) (2) (3) (4) (5) A.M.
C 9
09 C o
10
20 I
14
24 5
26c 1 6t
9
r9
5<*3°<>
24CI11
It is fcarcely to be imagined by thofe,., who
have not had the convidlion of experience, what
an accumulated congeries of fure and infalli
ble criteria of time (which will. ftand the.teft
of the moft nicely inquifititfe, the moft dili-r
gent andvfkilful examiner) may be collected, and
by irrefragable proof eftahliihed, from Mojes's hi
ftorical account of ;the flood, and his 3 terms, of
computation days, weeks, and years (which are
by this time, I fuppofe, admitted to be both folaf
andlunar) carefully iremembring, thefe two impor
tant obfervations, ( 1 ) that there is no word in the
Hebrew bible to exprefs the hour: and (2) that
the 4 cardinal points pf the aequinodtial Nudthe-
meron are exprefsly denominated.
The fyftem of 7 days is an original and pofitive
divine inftitution, and in the fcheme of facred chrar
nology
(( 374 )
nology is of prime ufe, and of the greateft im
portance. Jt.isan Malhbls difcerion of time, in
union with the folar and lunar characters, and a
juft aftronomical me&irim of proof; hbr can the
diurnal devolution of the Suh meafure one fingle
day of our exiftenae, abftradted from this divinely
appointed fepteriary fyftem, ift a clofe and undi
vided connection with tbe Mofaic Hfexagftieron,
on the 4th of which, the firft .motion of time
commenced: for althbUgh the rotation of the
Earth about its axis fubfif^ed 3 days and |, prior
to the annual ; : yet, in that fingle and linconnedted
ftate, it meafured no part pf a year. , Time began
to be meafured, when God faid-^A/ the'm be for
days and years.. ,.;... j
With refpect to this divine hebdomatic meafure,
the following1 reafonings afe indifputably certain,*y/z.
All chronologifts poftulate the worlds determinate
paft duration, though their C0nclufiort9 have been
various. From hence it follows, by fUfe confe-«
quence, that a determinate number of annual re^
volutions of the' SUn muft include a determinate
and correfponding number bf diurnal ; thefe being
divided by 7, niufl give in the quotient a deter
minate and correfpbrtding numbef of weeks, either
with or without a remainder.
Now then, fuppofe, I wanted to know what
day of the Week was the 6th of September, A. D.
f 750 1 independent of the year of out Lord, a(f*
cording to the vulgar ajra, and ofthe cycle ofthe
dominical letter ; and moreover, of all the me*
thods which are known arid made ufe of by us to
find out the day of the week, in any given Julian
month.

0 375 )
month and year ;•<— Is not this the fame in fa<& ag
aftiogi what 4ay pf the wsek, was the 4th of the,
Mofaic Hexaemeron, when ijhe- annual motion.'
commenced on ^ autumnal ^quippdtial day ? And
likewifel what is the precife fol%? (both amm\ and.
diisrnal) meafo?e, ffbm tJae M$foi& radix, to the,
6th of September A. D. 1750? And thefe twoex-
tremes are as certainly connected by the hebdoma-
tjo,. as. by the fplar* and lunar charadters.
But although it mnft be pwnfed, and it is
too notorious to be dented* that very vofomi-
nous and almoft endlefs controverfies.a-nd^difbHtes
have arifen from the diffentient opinfons of the
learned, concerning the authenticity, (i^. ofi :*h#
Hebrew chronology, (2) ofthe SamariianrPenfafr
teuch, (3) of thefeptuagintveEfipn (4) of J^oJ'ephm*
as if each of them .might claim to be the ftandard*
and had a native, inherent right tp. challengQ the
preheminence ; yet am I riot difcouraged^ and
fhall afUime the Hebrew as the only true chrono
logy. I fhall try (after for many fxuitlefs.and un-
fuccefsful trials) if we cannot adjuft, at laft, its, li
tigated Glajm, and vindicate, the right of its. pre
tenfions. The principal view of this-ffril part of my de
fign being to lay open, affer^ and explain the Sua
and Moon aftronomy of Mbfe£% genealogical and
chronological tables, I fhall riot digrefs from this'
main point, in order to fettle every branch and
period of the Hebrew aftronomical canon : that
is referved for a future work. But fince one
Angle year cannot upon Scripture grounds, and
upon

.(>*.)¦
Upon Scripture authority, he either added to,
or fubftradted from, the following collection of
years (as I am ready to prove againft all oppofi
tion) I fhall diftribiite them into 5 large inter
val's, which were never offered before as I knoW
of, and give tb the whble this denomination and
title. <
The world's chronology collected from the
Hebrew bible, and PtolomyV canon
, of kings.
FROM the 4th ofthe
Hexaemeron (exclu- ]
five) to the death of Jojeph,
and to the autumnal aequi- Mofaic Shanim at '
noftial day of that year, ex- troP^al ?e8's-
dU^Ve* a j 1. r * L ® *36<> ©G«0&.
From the death of Jo
feph, to the uncontefted aera
of Nabonaffar, and to the
autumnal aequinodtial day of Ir- 892 In the reign of
that year, exclufive. 4taAkind of
rrom the aera of 2V^w-
naffar, to the death of An
toninus Pius, A. D. 161,
and to the autumnal aequi
nodtial day of that year, ex
clufive. TrT „ „, , ,
in. 907 /wftayis canon,
A. M. 41&8 Front

( 377 )
From the death of An- ' 4It?8 Brought up.
toninus Pius, A. D. 161,
to the sera of William I.
the conqueror, A. D. 1066,
and to the autumnal aequi
nodtial day of that year, ex- T v ^ v , . .. , ,
, r J J ' IV. 905 Ecclefiaftical and
ClUUve. ciVJl hiftory.
From the aera of Will. I.
A.D. 1066, to the end of
the 24th year of the reign
of his prefent majefty George
II. A. D. 1 75 1, and to the
autumnal aequinodtial day of
that year, exclufive. v. 685 Englifh chronicle.
Sum Total — A.M. 5758.
Of thefe 5 intervals, only the 2d is liable to dif-
pute, which collects 892 years between the death
of Jojeph and the commencement of the aera of,
Nabonaffar : but without flaying, at prefent, ei
ther to fupport this colledtion, or to examine,
compare, and judge ofthe different accounts Which
have been, and probably may be, given by others ;
I fhall affume 5758 folar tropical revolutions as
the true adequate meafure of the world's paft du
ration, from the 4th of the Hexaemeron exclufive
to the laft autumnal aequinox, in this current year,
A. D. 175 r: I fhall calculate from it as true, and
let thofe overthrow or invalidate the truth of the
affumption, by aftronomical arguments, who can ;
I fhall hereafter afcertain the feveral particulars of
this collection againft any opponent.
Bbb Ii

(37«)
Iwas obliged to fetch this compafs to enable
me to anfwer this fingle queftion, viz. What
day of the week was the 6th of September, A. D.
1750? But in the difcuffion of this point, I fhall
take occafion, not only to lay down and illuftrate
by example the rules of the integral calculation (for
a full explication of the ratio of every particular
will require not a few pages, and muft be poftponed
to the clofe of the whole) but alfo to make good
that, entirely new and all-cementing propofition,
which is emboldened to affert,
IX. That there can be no chafm in the (Hebrew)
Scripture chronology, becaufe it may be demori-
ftrated that there is no interruption in the Scrip
ture aftronomy.
For the bafis of this demonftration we have
thefe two exprefs aftronomical data. (1) The
created pofition ofthe Moon to the. Sun, as ftated
and recorded by Mojes in the firft chapter of Ge-
nefis, and explicitly in the Levitical 'law. (2) A
continued feries of 5758 folar tropical revolutions;}
from hence fubftradting 1 , remains A. M. 5757,
which will terminate at the autumnal aequinox,
A. D. 1750.
Now I fay, that thefe two exprefs aftronomical
data, are fufficient for a full and fatisfadtory folu
tion of the following
Problem.
If, in the beginning, the Sun croffed the Mofaic
cardinal, or autumnal aequinodtial point, on the
5th

( 379)
5th day of the week (for that day of the 7 wass,
as will be proved, the 4th of the Hexaemeron)
and on the 15th day from the new Moon (() even
ing, then in the end of the 5757th folar revolm-
tion from thence, it is required to determine, ( 1 )
At what diftance, in entire days, from the new
Moon (C) and the full Moon (Q) evenings re
fpedtively, did the Sun again crofs the fame car
dinal point of the year,? (2) On what days ofthe
1 2th 35-day,mqnth ofthe patriarchal folar year,
brought down to the prefent times, did the hew
Moon (() and the full Moon (O) evenings fall
refpedtively ? Here it is neceffary to remember,
that the primitive new Moon (() eveniug is the
fecond from the conjunction, and the primitive
full Moon (O) evening is the fecond from the
oppofition. (3) On what days of the Week re
fpedtively I (4) In what Julian months, and on
what days of the month refpedtively ?
It is obvious to infer, without the help of a
comment, how much a true aftronomical folution
of all the particulars of this problem, will contri
bute towards the completion and the full confir
mation of my fcheme. When we return back to
the Mofaic tables, the reader will be enabled from
hence to form a truer judgment, and will have a
more ready conception both of the calculus and the,
conclufion, in the remote ages of the world.
From hence he, will be made quite fenfible, that
the charadters, by which every given Scripture
year is diftinguifhed from another, are the day of
the month, the day of the week, and the cardinal
B b b 2 point

(38o)
point of the day (with refpect, I mean, to that
meridian in which the folar year and the folar day
begin together, which they annually do by an
uniform law) in which the Sun makes its tranfit
over the Mofaic cardinal point of the year : which
are the moft perfedt laws of connection in na
ture, between the two incpmmenfurafe years,
the folar and the lunar, vide Prop. V. From
hence he will gain as true a knowlege of the
^original antient year, as he has of the Julian;
and alfo, of t the primitive laws of- computing
the times, by -folar, lunar, and hebdbmatic cha
racters; and he will be able to judge too, wheidher
the antient or the modern computation deferves
the preference. Laftly, from hence he will be
thoroughly inftrudled, that the civil praecefiion of
the aequinodtial points, and the lunar, anticipation,
graece, <riMvi*.Kn Tfow^wa-/?, (which I may venture to
reckon amongft the T^m<ni-iLa.ra. or flumbling blocks
of modern fcience) have no foundation in nature.;
.but are equally owing to, and equally arife from,
not only a miftaken method of computation, but
more immediately, to the not apprehending one
of the moft curious, and the moft ufeful practical
laws in Sun and Moon aftronomy, in our allot
ment in the folar fyftem-
Thefe feveral advantages, and perhaps more
than thefe, will accrue from a juft folution ofthe
precedent problem. What remains now then is
to reduce thefe 5757 folar tropical years to days ;
then to lunar years, and thofe lunar years to days :
for though time be meafured in a circle, yet being mea-

< 3*i )
meafured, it ftretches out into a line ; and Orech
Jamim, length of days, is a fcriptural expreffion of
peculiar aptnefs and propriety.
¦'. Should any- one with confidence affert, that
the ftile of Mofes alone, and the very terms in
which he records the ; circumftances of his plain
hiftorical narration, fpontanebufly fuggeft; and
with the powers of a true and faithful' index,
immediately direct us to a difcovery, bf the gene
ral rules, of the neceffary and fundamental laws,
both of the* folar and the : lunar computations,
and aU within the, compafs of the 4 primary ope
rations of common arithmetic, who would iriipli-
citly credit the affertion ? But there is nothing like
appealing to matter of fact: thus <then Mojes
writes ; God made two great luminaries, and God
fjud, — let them be for days and. years. , Thefe
words are our diredlory : we are from hence, ex
prefsly taught to calculate the diurnal and the an
nual revolutions, and to compute the fucceffions
of ages by days and by years. So that inftead of
complex diagrams, an operofe algebraic procefs,
and the continual folution of geometrical problems;
the fum and fubftance, and the whole praxis of
Sun and Moon aftronomy, may be clearly and
fully exhibited by the primitive fimplicity of the
following redtilineal fcheme ; which like an uni
verfal algebraic theorem comprehends all fubbrdi-
pate rcafes.

( 3^ )

."\_

jy. «  ', -. .".-I ¦¦ &— — -<r  <^! ;"
»,; e — f—  ¦ >¦ g-  ^-^.h-^^-iM-k
tfhm-vi *s>afl;t>«; v.-iuh- i^f!:^ t>.) ;j>iiA o^i
«i Here are 3 flrait lines, maVked ar^jz. xvepr6-
fents the collected fum of folar ¦tropical' years(fdl-
lowing'one another in a^continued'feries, andiih'fc
formly beginning and -ending at the autufrifial
aequinox) reduced to days. '* *^t .,»-, t* kn i; i
(,,The flrait line- ' marked {y, dfeneiteS*' the?' Tdttifci.
tion of full Moon (O) years to daysi '*"''' •'*• 'Jf,K
The flrait Kne marked #, ireprefents, on the
crifitrary, the redudtioti of new Moon {€)-y£ars
to ".days, (which-1 by the charadters1 bf the ''ori
ginal pofition of the two luminaries, begin arid
end i 5 days before the other) within the- cardinal
limits of the current folatf year, whenever tbefiYll
Moon (O) evening comes immediately before the
aequinox.:* And when this happens, as it necefia^
rily.muft 1 1 'limes in the fpaee of 30 years, then
the full Moon (O) epadt, of whatever quantity j
becomes the aftronomical regulator of the facred
and ecclefiaftical lunar year, which invariably con^
fines the Moon, or more properly fpeaking, the
15th ofthe 30-day month, to the law of its ori
ginal pofition. And the feat of chag haafiph will
be found after the aequinox, and may be deter
mined by fiibftradting the new Moon epadt,) of
whatever quantity, from 45, by a perpetual law. a

( sh )
a Denotes and expreffes the coincidence ofthe
original full Moon (Q) day with the 4th of the
Hexaemeron j and- the Mofaic Tekupha, or the
autumnal aequinox.
a b The collected fum of full Moon (O) years
reduced to days. <
b The full Moon (O) evening coming imme
diately before the aequinox.
b c Its diftance from it.
c Its coincidence with it.
c d The diftance of the Mofaic Tekupha from the
new Moon ({) evening.
e Reprefents the chaotic and imaginary new
Moon(C) evening.
ef Its diftance from the 4th ofthe Hexaemeron,
and the original Tekuphd-
fg The colledled fum of new Moon (c) years
reduced to days.
g h The diftance of the new Moon (() evening
from the aequinox.
h Its coincidence with it.
h i Its diftance immediately1 after it. • And
when this happens then the feat of chag haafiph
will be on the 1 5th of day from thence, viz. ink.
if the aftronomical meafure be of 30 days ; but if
of 29 days, it will be the 1 6th, becaufe then the
political 30-day month will be divided in this
manner, 1 5—^—1 4C— ^— r ^
To finifh this general explication ; it is the of-
fice and adequate property ofthe integral calcula
tion, to difcover and determine the precife mea
fure, in entire days, of thefe feveral diftances. And

(3«4)
And how plain and fimple foever, the Mofaic and
primitive laws of the folar and lunar computa
tions may appear at the firft view, to a phyfical-
ratio philofopher, and to a fcientific genius, the
praxis will moft furely approve itfelf, not only to
the curious in general, but to the moft acute, and
the moft expert mathematicians, without entring
into depths. The uniform truth, the unerring
certainty, and the perfedlion of the conclufions,
beyond what invented fcience could ever attain
to, will gradually lead us to acknowlege that they
are truly admirable ; that there is fomething in
thern fuperior to all the moft ftudied rules of art ;
that they lie out of reach of fcience founded upon
obfervation, and are evidently flamped and im-
preffed with the fignatures of divinity.
It will foon appear, upon a clofe examination,
that there are 3 feveral caufes concurring, to ren
der every aftronomical calculation by the tables,
efpecially in the remote and far diftant ages ofthe
world, more or lefs precarious and uncertain. And
they are, ift, The meridians. 2dly, Theprofta-
phaerefis. 3<ily, The affigned quantity of the
folar tropical year. Now, in every calculation,
all thefe 3 are affumed as true, and yet who can
be faid to have afcertained the exact truth of any
one of them? Whilft the integral calculations,
founded on the principles, data, and terms of the
Pentateuch, are attended with no adherring im-
perfedlions ; they are not fo much as liable tp
produce erroneous conclufions in Sun and Moon aftro-

(385)
aftronbmy; if they are, then, I repeat it again,
they cannot be, Mofaic.
; But frbm a general explication of this rectilineal
theory,, we muft now defeend- to a minute and
circumftantial praxis ; we muft take no fmall
pains^ and exert our beft endeavours, to obviate
the farcaftical reproach which will be fure to at
tend a failure, and it may perhaps be already faid,
;'. Projicit ampullas & fejquipedalia verfia.
In the following demonftrations, which will
put an end to this book, I fhall include the whole
contents, of my feveral proportions (which fome,
as I am informed, have pronounced to be impoffi
ble) arid illuftrate by examples the ufe and appli
cation, of my aftronomical table, both folar and
lunar, Mojaic and .Julian ; whofe fimple con
struction, and yet complex properties and powers,
will, caufe, as I apprehend, no fmall fpeculation
amongft the connoiffeurs in fcience.
1 My 2d proppfition is indifputably fundamental ;
for it offers to determine what day of the week
was the 4th of the Hexaemeron, which, in the
fcheme of facred aftronomical chronology, is a
moft ufefiil and a moft neceffary firft principle.
Mojes, in the 1 ft 'chapter of Genefis, hiftorically
.relates, in what manner the creator finifhed
the operations of his hands, in the fpace of
fix fucceffive natural days ; I call them natural,
becaufe each of them had its Gnereb, i. e. its
C c c aequi-

( 3?6 )
aequinodtial time of Sun-fetting ; and alfo its
Boker, i. e. its aequinodtial time of Sun-rifing.
Iri the 2d chapter, which may be confidered as
a fupplerrient to the ift, it is revealed to us, God
bleffed the yth day, and fanftified it, becaufe in it
he refiedfrom all the work which he had made.
From this hiftorical account of Mojes, itis plain,
that 7 is refolvible into 6-f-i. Now then quaery^
what day of the week does this detached unit ex
prefs ? To which I anfwer, the very day of the
week in real fact, which correfponds with its va
lue ; and that is the ift, or our Sunday.
But the deduction does not reft here ; we may
draw the fame conclufion feveral different ways,
and all of them equally true. For, ift, the 3
Mojaic terms of computation are years, weeks
and days. But years may be reckoned, in fome
fort, as a fyftem of days; therefore reduce them
to weeks and days ; then to one week and one
day ; exprefs thefe in numerals, and we have, 1. y.
But 7 is refolvible into 6-j-i, fo that thefe num
bers, placed in this order, 1. 6. 1. reprefent the
true pofition of the Hexaemeron.
2dly, In the 7th chapter of Genefis, in the ift
and 4th verfes we read, ver. 1. And the Lord Jaid
unto Noah—>ver. 4. For yet Jeven days, and I
will caufe it to rain upon the Earth 40 days and
40 nights. The day in which God fpake unto Noah
muft be one day, fo that we have again the nu
merals 1. 7. and confequently the fame order as
before, 1. 6. 1. But what I would principally re
mark here is this, viz. Thefe two laft units on
each

(387)
each fide of 6 denote the very days of the week,
in which God revealed his intentions to Noah,
and in which Noah and his family entered into
the ark; fo that all the days of the week through
out the year of the deluge, and quite back to the
end of the 3d year before it, viz. A.M. 1653,
V. N. 597, may be determined from hence with
a demonftrable certainty, as will be evident in the
calculations. The remaining deduction is more unexpected,
and much more furprifing ftill ; for the laft num
ber, viz. 4. which arifes from this next calcu
lation, of itfelf expreffes (fee the beginning of the
chaotic calendar both folar and lunar at the end of
this book) both the day of the month, and the
day of the week, as the aftronomer would find it ;
fo that by the number 4, (which is alfo the diftance
bf the (fuppofed) new Mbon evening from the
aequinox) the true aftronomical feries of the days
of the week, down to thefe times, are from hence
fettled and determined from before the foundations
ofthe world.
The dedudtion confifts of thefe few particulars:
15 is the original new Moon (() epadt. But
365—15=350. And 354^35o=c 4. Again,
15 is refolvible into 4. 7. 4. From 354 throw
off 3 50, and we have thefe numbers, 4. 4. 7. 4.
The two firft of thefe numbers being added toge
ther conftitute an octave^ viz. 4+4= 8 . Bu t 8 —
'7= 1 , we have now thefe numbers, viz. 1.7.7.4.
But each of thefe feveris is refolvible into 6-j-i, fo
C c c 2 that

('388.)
that now they will ftand in this order, i .' 6. i . 6.
i . 4. This laft number 4 is the 4th of the Mojaicb,
in its original and true aftronomical pofition. And
1 -j— 4= 5 is the correfponding day of the week.
From the 4th entire day fubftradt 4, remains 3
days-]-!, or the time which the diurnal motion
fubfifted prior to the annual. Vid. p. 56.
Refolve 7 into its days, and alfo 6 into its daysi
and then fet the latter under the former in this
manner. Days of the week.
1 23 45^7 I 1.
1 2 3 456 I 7-
From hence we may obferve, that the 4th of
the 6th falls upon the 5th day of fhe week, and
the 6th upon the 7th ; and that the original 7th
falls upon the ift, as ftated before. I fhall con
clude thefe determinations with this table :
1 6 1
262 3^3
464 5P 5
6 6 6
7 6 7
We have expreffed here the whole variety of
every poffible pofition of the Mojaic fix days j
but I affume the firft as true, arid fhall argue from it

C 389 )
it as fuch. And fhould its truth be doubted, J
am able to offer more than 100,000 over and
above two millions of proofs, and an objector
may chufe where he pleafes.
' Having laid this foundation, I can now, by
the help of the only proper medium in nature,
readily determine what day of the week was the
6th of September, A. D. 1 750 ; and this, with
out being under the neceffity of making any ap
peal either to the Julian period, or to the years of
our Lord, according to the vulgar aera, or to the
cycle of the dominical letter ; which privileges the
aftronomer would not willingly be debarred
from. , I am now to reduce the collected number of
5757 Mojaic Shanim or folar tropical years to
days ; which might be readily done by the table
p. 263, but I rather chufe to calculate by the ra
dical numbers upon the account of the entire qua
drant pr quadrants, which, by this method, will
remain over and above the complete days ; and as
I have no occafion to be follicitous about the me
ridian, I will, after the ift divifion by 15, take
in the remainder, which is the only alteration I
fhalj make in the rules of redudlion. p. 254,

The

( 39° )
The reduction of ^y^y folar tropical years todays.
Ralel. 57^ years -4*15=^=383 femainder 12.
Rule II. 38354 n-t-iz=42.2 5.
Rule III. 4225 -=-24=176 quadrants to be fabftralfted. D'. h.
RulfelV. 5757yearsxH*I^ua^,:=^4,09771u?<l,^"'l-==2IO27++ 6 Jul-freflufl.
RyleV: 176
?4lo8oiquad. -$-4=2 102700 6 fol.reduift.
Julian excefs 44 o
From this reduction of years to days, I am to
find out what day of the week was the 6th' of
September, A. D. 1750 ; but firft we mrift deter
mine the Julian ftations of the autumnal aequihox
in this age. In order to this, from the Julian ex
cefs of 44 days, fubftradt 30, and with the re
mainder 14 enter, either of the 2 tables, p. 351,
353, and look for it in the 4th column, then
fet down the number of cbl. 2. in the fame pa^
rallel line. E. g. CO ,® (3) (4)
Index 21 | |n[ j J14I. Now I fay,
that the number 14, col. (4) becomes the au
tumnal aequinodtial Julian index to the oppofite
number 1 1 , which ftands in that column at the
head of which is placed the fymbol of the Sun's
entry into Libra. If from 14 we fubftradt 1,
apd look for the remainder 13 in col. (4) we fhall -ru
find over againft it in col. (2) the number 12;
to find out the month, from 29, fubftradt men
tally 1 1 , and to the remainder 1 8 add 6 1 , (the
reafon will be given hereafter) the fum 79, in
the

( 39* )
the table annexed will be found over againft Sep
tember ii. .Confequently the nth and 12th days
of September are, in this age, the Julian ftations
of the autumnal aequinox. <. •¦:....; _¦>
-. In the next, place, from September 11, fubftradt
September 6j the difference will be 5. We have
but two eafy fteps mote to. bring us to a conclu
fion; (1) from the fum total of folar days fub
ftradt thefe 5 ; and (2) divide the refidue by 7.
Now I fay, if there remains o after this divifion,
then the 6th of September was Thutfday, or the
fame day of the week as was the 4th of the Hex
aemeron, i.e. the 5th. But if after the divifion
by 7, there be a remainder, add 5 to it, and the
fum, if 7 or under, will be it; if more than 7,
the difference will be the day of the week re
quired. E.g'.
From 2102700 folar days.
, l( Subftradt 5 , . ., . ¦_¦•:
.,  ,, >
7(2102695(300385 eompl. weeks,
, Remainder o
Now becaufe there are no remaining days, the
6th of September muft neceffarily be Thurfday, or
the fame day of the week as was the 4th of the
Mofaic fix, from whence exclufive the computa
tion is dated. The

( 39* )
The dominkaLletter-for A. D. 1750 Was Gj
therefore D muft be-the character, or calendar let%
ter of September 6, ,and fo it is. % E. P.Z~? k>
The being able to determine, .iwith an aflro*
rioniical- certainty, the day ofthe week, asodca-
fion requires, from the Mofaic radix to the curcerit
day, is a fundamental .point: feciired; and; Dr.
Halley'% fanguirie phyfical hopes, of which. • Mr.
Wktfion has informed the public may, poffibly}
in due, time, according to my fariguine Scripture
aftronomical hopes, be defeated. 1 0 t,, v.. ;
But now the inquifitive reader . Wants- to be let
into the fecret of fome particulars} an$ will be
ready to afk, I fuppofe, why is the 6th of Sep
tember, A. D. 1750 culled out, and a preference
given to it before all the reft of the days of the
Julian calendar, of which,, as every body knows,
there are 365 ?
But an anfwer to this enquiry is ready at hand.
The 6 th of September A. D. 1750 was made
choice of, becaufe it is linked, in a clofe aftrono
mical connedtion,' with the Mojaic radix in a
double refpedt; ift, as has been already proved,
by the hebdomatic ; and 2dly, as I am going to
prove, by the full Moon charadler. For was
the 4th of the Hexaemeron the primitive full
Moon day, or the fecond from the oppofition ?
So alfo was the^6th of September, A. D. 1750.
Again, was the 4th of the Mofaic fix, the 5th
day of the week, or our Thurfday? So alfo was
the feledled 6 th of September. Thefe two cha
radters united, at the diftance given, from the
He-

( 393 )
Hebrew bible, and Ptolemy's canon of kings,
jointly concur to the eftablifhing the truth of,
Prop. IX. viz. That there can be no chafm in
the Scripture chronology, becaufe it may be de-
monftrated that there is no interruption in the
Scriptureaftronomy. Here- it mhft be carefully obferved, and as care
fully remembered, that this famenefs and union
ofcharadters entirely depends upon, and immedi
ately arifes from, a fure aftronomical and uninter
rupted connedtion with the original pofition of the
two great luminaries, as ftated and recorded by
Mofes in his Pentateuch. An<^ fhould any one
object, that the interval of $ysy years may be
changed , and that many will contend for a change ;
yet ftill I fay that fuch a change, be it more or
lefs, can never be authorized by the Hebrew bible',
and Ptolemy's canon of kings : befides the Mojaic
radix is unalterable, becaufe fixed by a divine ori
ginal law. And therefore, fuppofing a correction
of the interval fhould be attempted, it muft be,
either by fubftradlion or addition ; if by the for
mer, then, as the radix is immutable, the calcu
lus by reduction would produce in the conclufion
the charadters pf fome one year which came before
A.D. 1 750 ; if by addition, then of fome one year
that would come after it ; and each of thofe cha
racters would be in exadt correfpondency with the
number of years added or fubftradted ; whilft the
charadters of the current year would never be ad-
D d d jufted,

( 394 )
jufted, which is a point that was never yet confi
dered ; becaufe the method of calculation by days
and years from a fixed radix, as clearly taught by
Mofes, has never been known or practifed by Us.
Not to pufh this conclufive and unanfwerable
argument any farther, I fhall go on to prove that
the 6th of September, A. D. 1750, was the pri
mitive full Moon (O) day, or the next after the
oppofition. In the courfe of this calculation, I
muft reduce the collected number of 5\y§y folar
years to lunar, and thofe lunar years to days,
But I have a mind, antecedent to a regular caU-
culation and independent of it, to let the reader
fee the powers of thefe primitive folar, lunar and
hebdomatic charadters ; and how they are adapted
to produce aftronomical truths : fo that, in any
year, if one lunar, and one hebdomatic charadter
be determined and known, feveral others, like
the links of a well compacted chain, immediately
follow together with it, and from hence likewife
may be eafily determined and known. I have
given fome proof of this already, from the Mo
faic datum, or new Moon (C) epadt 11, difcover-
able from '. the hiftorical account of the circum
ftances of the deluge ; and am now able to en
large it from the hebdomatic charadter, which of
fers itfelf to our view, in the deduced pofition of
thefe numbers 1. 6. 1.
I fhall, at prefent, give another diftindt proof
of this, from the number 5, which in the fore
going arithmetical operation we fubftradted from
the fum total of folar days ; and I fhall confider this

( 395 )
this number 5 as a datum, becaufe it did not arife
from a regular calculation, terminating upwards
in the Mofaic radix ; although fuch a calculation,
as we fhall foon fee, will confirm it.
Now fuppofe fome one fhould be prorripted to
argue with me in this manner ; A. D. 1750, the
primitive full Moon day, which immediately fol
lows after the oppofition, was at the diftance of 5
entire days from the autumnal aequinox ; from.
this number 5, it is required to afcertain the Ju
lian month, the day of the month, (and alfo by
calculation to fix the day of the week) on which
this primitive full Moon fell. And farther, from
this datum jn union with the calculated day ofthe
Week (fee t}ie above arithmetical operation) it is
required to determine the refpective diftances, in
entire days, both of the primitive full Moon (O)
and pf the primitive new Moon (c) evenings from
the original Tekupha, or cardinal point, in the
head or beginning of A.D. 1750, carried back
to the autumnal aequinox, in the end of A. M.
5756, A. D. 1749. And alfo, the Julian
months, the days of the month, and the days of
the week refpedtively. And laftly, the refpec
tive days ofthe 1 2 th 35-day month of the patri
archal folar year, brought down to thefe times.
Thefe feveral points are to be fettled and ad
jufted by the affiftance of the given number 5,
and its coadjutor the calculated day of the week,
which was found to be our Thurfday, or the 5th
day. But how eafy, and how ready is the true
aftronomical folution of all thefe demands ? In
D d d 2 the

( 396 )
the firft- place, it appears by the precedeht calcu
lation, p. 3 5 1 , .that the Julian excefs of 5757 years,
over and above the correfponding number of true
folar reduced to days, was 44. From thefe fub
ftradt 30, and to the remainder 14, add the given
number 5; then look in the full Moon (O)
table, p. 351, for that parallel line in which the
. (*). (si (4)
mm 1 9 ftands in col. (2) index 19 : 19. 23. 6. Q,
to the middle number 23 add 61, and the fum
84 will be found in the table of redudlion to the
Julian calendar (which remains to be explained)
over againft September 6 Q, with the fymbol
of the full Moon affixed to it. Therefore, by
this medium 5, and by this table, the felected
6th day of September, A.D. 1750, was connec
ted with the 4th of the Hexaemeron, as it was
the 5th day ofthe week, and as it was the primi
tive full Moon day. I now look into any com
mon almanac for A. D. 1750, where I find this
notation, September. Full Moon 5 dav at 1 morn,
%.e:p.
The next folution ofthe required diftances, &c.
is eafier ftill ; for we have only to fay, 05+4
=C 9. and we have one determination at the end
of A.M. 5756, A.D. 1749. Again, 54-15=
204-4=024. This laft calculus limits the di
ftance, in entire days, of the primitive full Moon
evening, and the former (C 9) of the primitive
new Moon evening, from the autumnal aequinox,
A. D. 1749. The one being the 2d from the
conjundtion ; the other, from the oppofition : only h

( 397 )
it muft be obferved, that if either the new Moon,
/. e. (conjundtion) or the full Moon, i. e. (oppofi
tion) happens after fix o'clock in the evening, and
before 12 at night, another day both ofthe month
and of the week is begun, in primitive account.
Having obtained, what I chiefly aimed at in
thefe concife calculations, I mean a fimilarity of
primitive full Moon (O) and new Moon (c) cha
radters, or equal diftances from the autumnal
aequinox, in the end^f A.M. 1653, V.N. 597;
and in the end of A. M. 5756, A. D. 1749;
which are diftant fromNeach other 4103. Mofaic
Shanim or folar tropical Y?ars, as appears by fub-
ftradtion, I fhall fet down their folar and lunar ta
bles, one after the other, &->d feparate them by '
the interval,

A.M. 1650
V.N. i9J

A.M. 1654
V.N. 598

O24 t 9

-TU
O
6035504 346 C 19

Interval. 4103 Shanim or folar tropical years.

0

Who,

A.M. 5756
A. D. 1749

^^¦S7sy A. D. 1750

O24
' * 9

-n.O 6035405 345 C 20

(398)
, Whoever will look over and compare the feve-
ral ••characters pf thefe two tables, as they are placed
in the fame view, will fooa perceive that the
only obfervable difference betwixt them arifes
from the different quantities of the two complete
full Moon (O) years, which fall within the
cardinal limits of their correfponding folar ; the
former, under A. M. 1654, confifting of 355
days, and its attending epadt of 4 ; the latter, un
der A. M. S757i °f 354 days, and its attending
epadt of 5 ; I need not carry thefe remarks any
farther, becaufe they are needlefs in things evi
dent, to fenfe.
The difference of an entire day between the
quantities of thefe two lunar years, and of their
attending both full Moon (O) and new Moon (C)
epadts, will afford the aftronomer an opportunity
to form a proper judgment of the truth or falfity,
the accuracy or inaccuracy of thefe tables; and
likewife, of thofe calculations, which, by their
conclufions, will fupport and eftablifh every par
ticular exadtly ask is here fet down.
Another very confiderable advantage may be
gained by the joint calculations of thefe two dif
tant years ; the one lying in the remote ages of
the Antediluvian world, the other in the prefent
times. For from hence we fhall be certified by
demonftration, that what we call and confider as
the civil praeceffion of the aequinoxes, and the
lunar anticipation, is a miftake in fundamentals.
And they muft? each pf them, be afcribed a-
mongft other caufes, to an erroneous method of
• •¦'-'¦" com-

( 399 )
computation : from hence and the annual defect
of 3 feconds of time, it has come to pafs that we
have never been able to apply the folar tropical
year to civil ufe.
In the front of each table, we have thefe fimi-
^ O
lar characters, O 24O O 24, which may be thus
expreffed in words, viz. In the end of A. M.
1653, and likewife, of A. M. 5756, at the di
ftance of 4103 years, the primitive full Moon
evening fell 24 entire days before the autumnal
aequinox, and on the 5th. day of the, week, in the
firft cafe, and on the 6th in the latter. But
how does the certainty of thefe hebdomatic cha
radters appear, may one fay ? Now fince the cal
culations will require me to adjuft this fomewhere,
I will take occafion to do it here ; and fhould it
be reckoned amongft my digreffions, fure I am it
is no impertinent one.
The particulars on which a backward computa
tion from a given or calculated day of the week
depends are thefe, viz. If 354 or 355 days be
divided by 7, the remainder, in the firft cafe, will
be 4 ; in the .latter, 5. If 30 be divided by 7,
the remainder will be 2 ; if 1 5, 1 . To apply
thefe rules; the 6th of September, A.D. 1750
Was, by calculation, the 5th day of the week, or
our Thurfday. Therefore 5 — 4=1 — 1=0=7 —
1=6, which is the day ofthe week fought.
On the other hand, this pofition of thefe
numbers, 1. 6. 1. expreffes the day of the
week

{ 4°° )
week on which Noah entered into the ark ; the
full time of his abode there was 365 days, which
being divided by 7, the remainder 1 again de
notes jthe true day of the week, on which he was
commanded to come out. He was commanded
to come out on the 57th day from the new Moon
(C) evening neareft to the autumnal aequinox. But
57-^7=56. And §y — 56=1. Then com
pleat the octave, and fay, 1 4-7=8 — 7= 1 . Now
I fay, the unit afcertains aftronomically the day of
the week on which Noah received the command
of God to go^orth of the ark, and the number 7,
ofthe new lV»on (c) evening. Therefore, 7 — 4
=3+7=7 1°— 4— 6— 2=4-}-7= 1 1— 5= 7—1
=5, which is the day of the week fought. And I
will venture to pronounce before hand, that when
1653 folar tropical years are reduced to lunar, and
thofe lunar years to days, that, after the divifion
of thefe by 7, the remainder will be o; if not,
the deduction and backward computation found
ed upon it is falfe ; but if it fhould be o, both
are eftablifhed beyond the reach of confutation.
I fhall now undertake to prove, by an arithme
tical calculus, that thefe lunar and hebdomatic
charadters, as ftated above, are true in fact ; and,
fhould they be found, by calculation, to be true
in fact, then it will be undeniably certain, that the
number 1 1, in the end of the year of the flood, is
a Mojaic aftronomical datum, and muft have, as
they mutually infer and confirm each other, a fure
conriedtion in nature. With-

(4oi )
Without any farther remarks, I am now to re
duce 1653 an^ 575° f°lar tropical years to days,
and by this reduction to fettle the exact meafure
ofthe flrait line x, in both examples.
Thefe exadl meafures may be readily obtained
by the table of redudlion p.277, as noted in this
fcheme, r6^3 years.
^=603745 Days 14 h. 57' =o=
x.O-  ¦ —  O
5756 years.
i± 2 102335 Days ooh. 44' =£=
x. O  —  O
r , , , ¦
.But fince it is not required to adjuft the prefent
calculation to a fixed meridian, but to that in
which the folar year and the folar day begin toge
ther, we muft complete the 14 h. 57' into a day
in the firft cafe, and throw off the 44 in the other;
and then they will ftand in this form.
I. II.
Solar days 603 746 2 10 23 3 5.
The next ftep of our enquiry is, how many.
aftronomical meafures of 30 and 29 days are in
cluded in thefe folar years ? And then, how many
moveable lunar years, each confifting of 12 of
thefe meafures ? Laftly, how many days ?
Eee The

( 402 .¦))
The, arithmetical operation I. , „•,:•;
I. 1653-^-30=55, remain 3 years, which re-
ferve.
II. The quotient. 55,)^ 37,1 (by a perpetual law)
=20405 aftronomical meafures. |.
III. The remainder 3 years )fj 2=364-1=37.
IV. i653-f-63o=;2, remainder reject.
V. 204054^374~2=20444.. aftronomical mea
fures of 30 and 29 days.
VI. 20444-^12=1703 moveable lunar years,
remain 8 aftronomical meafures.
VII. 1703 lunar years, -^30=56, remains 23,
for which add 8. <o ~
VIII. 56X 11=6164-8 (for the remainder 23)
=624 lunar years of 355 days,
IX. 1703X354=6028624-624=603486 days*
in 1703 lunar years..; D.
IX. 603486 (1)
X. For the remaind. 8 ( VI) add 236 days. 1
To the fum total. O 603722 0(2)
XI. Add  i5
*rrr , , T° ^ ^ ' 6°3737 < (j)
XII. Add,  ¦  1 j
The fum total. O 603752 0(4) If,

(t4°3 ) '
If, for brevity's fake, we take the two laft fi
gures bf the folar days, which are 46, and the
two laftofN0. (-2) which are 22 0,Wl;of N°.
(3) which are 37 C3 and-of N°. (4) which are
52 O, and then compare them together, we fhall
foori perceivie, that the two firft fums of the lunar
computation are lefs than the folar, whilft the o
laft is greater. Subftradt then 22 O, from 46
and the remainder will give the integral diftancd
of the primitive fulf Moon evening from the au
tumnal aequinox, which by the table, and by a
backward computation from the Mojaic datum
11, has been predetermined to be 24 days, and
fo it is; for 46 — 22=024. ^o %' &•
o
Again, 46— 37=C 9, £>. E. D. Laftly, 52
-n. o
— 46=60, which is the feat of chag haafiph y
and it fell A. M. 1654, on the 6th day of the firft
month of the folar tropical year, as in the table.
Now We are able to exprefs the meafures ofthe
2 flrait lines, y and z, and of their feveral diftindt
parts, with an aftronomical and mathematical ex
adlnefs, as in this fcheme,
E e e 2 y

( 404 )
==v D. =& P.
O 603722 days , 24 O 6
y O  ¦ '-.*0<  — A— r-0
D.
o 603737 days 9
z C  *  :  ¦  C  /
As to the days of the week, it has been already
predetermined, by a backward computation from
the new Moon evening, (in the end ofthe year of
the flood) which was tlie 7th day of the week,
or pur Saturday, that the full Moon evening,
neareft to the autumnal aequinox, A. M. 1653
ending^ "fell on the 5th day pf the week, or on
our thurjday, and the new Moon evening next
following, on the 6th, or our jFWVtfy ; and con-
fequently, the original feftival chag haafiph, which
was the 15 th day from thence, muft be the 7th.
If thefe praedeterminations are true, then if N°. (2)
be divided by 7, the remainder muft necefiarily be
o ; and, if N°. (3) be divided by 7, the remain
der will be 1 ; laftly, if N°. (4) be divided by
7, the remainder will be 2 f I fay farther, that
if thefe feveral fums of collected days being feve-
rally diyided by 7, do give thefe remainders, o. 1,
2. then thefe praedeterminations and calculations
will never be convicted of error. Let us try,

f

( 405 )
7) 603722 (86246
41342 o. %, E. P.
7) 603737 (86248
4I3J6 1. ^ E. P?
7) 603752 (86250
4135 2, ^ £. P.
Having calculated and adjufted the neareft di^
ftances of the primitive full Moon and new Moon
evenings from the autumnal aequinox jn the end
pf A. M. 1653, together with the refpedtive
days of the week, and the feat of the original fe
ftival chag haafiph, we muft now determine the
correfponding days of the month, firft in the pri
mitive aftronomical calendar, whofe 12 th month
was of 3 5 days ; and fecondly in the Julian, con
fidered under a twofold view: ift, As rendered for
ever commenfurate to the tropical folar, which
excludes the civil praceffion of the aequinoxes,
a.nd the lunar anticipation : And 2dly, as ufed by
us, under the quantity of 365 di 6h. which in-
pludesand carries alopg with it both. The

( 406 )
The firft enquiry will be very fhort ; for as the
1 2 th month is of 3 5 days, the epadts being known,
the correfponding days of thp month are known
by fimple fubftradlion, viz. 35 — 24=1 iO- And
35— 9=26C.
But they may be alfo fixed by an eafy arithme
tical calculus in this manner. To the two laft
figures 22, N°. (2) add 35, and from the fum ^y,
fubftradt the two laft figures in the collected fum
of folar days, viz. 46, remains 11O, or thus,
35—15=20. Then 37, N°. (3) +20=57—
46=1 1 0 as before. Again, ^52, N°. (4) 4-20
=72— 46=26 C. ^ E. P.
But in order to make an immediate tranfition to
the correfpondirig month and days of the Julian
calendar, rendered for ever commenfurate in the
folar and lunar table, p. 351, 353, to the primitive
tropical folar, we need only fubftradt 10 from the
calculated days. E.g.' 11 Q — 1 o=Oftober 1 Q.
And 26c — io=Oftober 16 C And we cannot
be at a lofs to underftand the reafon of this ; for
if we look into the calendar at the end of this
book, we may perceive in the clofe of it, that the
number 35 ftands over againft Oftober 25, but
-n- 0
35—2 5=10, and vice verfd, 35 — 10 = Oftober
0 ,-¦ -
2-5. •'-¦ . ¦¦'
In order to find out the original Julian ftations
of the Sun and Moon at the creation from my
table.

( 407 )
table, p. 351, look for the chaotic epadt 15, in
dex 5, columri 2, arid fet Jdown the numbers of
column 2, 3, and 4, which are thefe index 5,
(i) (3) (4) ¦•:¦•¦• ' -
15. 19. 10. Now then to the middle number
19, add 31, "the fum 50, in the table of reduc
tion, will ftaridpver againft Oftober 10 C. Oftober
to then, is the original ¦ Julian-Ration ofthe Moon,
and the integral epadt 15 exprefies its diftance
from- the autumnal aequinox. .., But October 1 o C
r, -:-.. ' ¦: -: ..O. ,. - ^ '.'.¦'¦
4I.1 5= Qftobef 2, 5, Look for index 20, a^d fet
down the numbers of column 2, ,3, and 4. in-
'6) (3)' ti) " '' , . - ..,,.,
dex 20 : o 4. 25. To the middle number add
31, and the-funr 35 Will be found over againft
Oftober 25, Wfiich Was the original Julian flatioq
of the Sun at the aUtUmnal asquinox, the cypher
cbldrhn 2-, denotes its no departure from it ; nor
will there ever be a departure from it to the end
of time. ' c ' ,
So then, whenever we adjtift the epacts to the
primitive calendar,1 We muft look for them in cb-
Irimn (5)1 and the correfponding days ofthe month
will be over againft them in column (4). In-like
manner, when we adjuft the epacts to the aftto-
nbmico-julian calendar, we muft look for the'rii
in column (2) and the correfponding days of the
Julian month will be over againft them in column
(4) at ten days diftance from the former. E. g. table
(4) (5) ' ", TT
I. P« 35i> m^ex 24. HQ24. And table II.
*'.. P-353>

X 408 )
. < (4) (5) '¦¦• - f4'.
p. 353, mdex9. 26C9. But 11O— io=Cfc>
iober a O- We have here an immediate tranfit,
tion to the Julian calendar. Now look for index 14,
' - w , (3) (4) oa. " = .-,
and we have, 24; 38. : : iO H, here tne ePa&
is in the 2d column, and the day of the month
ftill in the 4th, at the diftance, of ten days, by an
. . .... (2) .(j) WOa.
invaiiable law. Again, index 29 :'g 13: 16 C. Brit
farther, as the numbers of column 4, 5, being
added together, are ever equal to 3 5 ; fo the num
bers of column 2, and of column 4, being added,
are ever equal to 25. And as the two former are
aftronomical indices to each other reciprocalryj;
throughout all ages^of therworld ; fo alfo are the,
two latter, , which/merifs opfervation. , . ,
Having fettled the original, Julian ftations, pf
the Suri and Modn, the Julian month andpdays
may be known by the fame eafy arithmetical cal
culus, as the other, E. g. 22, N°. (2) 4-25=
47 — /\.6=Oftober 1 O; or thus, ^y N°. (3) -f-1©
=47 — 4.6=0 ftoberiQ. Again, 524-10=62
— 4.6=0 ftober 16 C. % E. P. ",..'"¦
Having determined the ftations of the primitive
full Moon and new Moon evenings, in the months
of the Julian calendar, as agreeing in quantity
with the patriarchal folar tropical year ; I fhall
now confide^ it as including and carrying along
with it the civil preceffion of the aequinoxes, and
the lunar anticipation; and the prefent enquiry.
may be propofed in this form ; viz. Suppofe foihe
one aftronomer, fhould make a calculation back wards

( 409 )
wards 4103 years from the autumnal aequinox,
A. D. 1 740, this backward computation would
terminate in the head or beginning of the year of
Noah's life 598, A. M. 1654. Then, quaery, in
what month and day of the month Julian would
he calculate the day after the conjunction, and
the day after the oppofition, neareft to the autum
nal aequinox ; . which is the fame as afking, how
many days the Sun would have departed from
fiftober 25, and the Moon from Oftober 10. (.
And fince, if 1653 be divided by 19, the quotient
will give 87 decennoval cycles, and the remainder
o ; confequently 1653 years will be a proper in
terval, by which we may eftimate the quantity of
the lunar anticipation.
Firft then, the quantity of the Julian, excefs
may be readily known from thefe few eafy fteps,
£„••.,? Q.
1653 XII = J8 183-^-360=50-^-4= 12 days.
, Now then O 244- J 2= 3 6 — 30=6. Look for
index 26, table I. p. 3 5 1., and fet down the
* - ¦ '(*) (3)
numbers as directed above. Index 26. 6. 10.
19O. to 10, add 61, and the fum 71 wijl be
found in the table of redudlion over againft Sep
tember 19. But September 19 0> as well as Oc
tober 1. 0> is 24 days diftant from the aequinox;
rfV. O
for Oftober 25— 12=13, + September 30=43
— 19=024. Fff Again,

< 4*o ) .
Again, C 94-12=21. Look for index; 11,
table JI. p. 353, and fet down the nwnbers as
(*) (3) (4,)
before, index 11:21. 25. 4. C. To 25 add 31*
the fum 56 will be found in the table of redudlion
over againft Oftober 4. *.. But Oftober '4. C. is
at the fame diftance from the autumnal aequjno*,
oa. oa.
as Oftober 16. C. for 25—^12=13. And 13-w
4=C 9. .- • < v>
Here Imuft not omit to remark^ that in the firft
Julian rediidtion the full Moon evening fell on
Oftober 1 > Q, but in this laft on September 19. O 5
whilft both of them are at equal diftances from
the aequinox. But. if to; Oftober 1 we add the
new Moon epadt 9, the calculation will terminate
in Oftober 10'. c. which was the Mpon's original
Julian Ration. On the contrary, if to Sep&mbm
19. p,. we add the fame new Moon epadt. 9, the
calculation will terminate* in September 2 8 at 12
days diftance from it. Therefore 12 is the quan
tity of the civil' preceffion -in cornplete days, re
jecting the odd hours and minutes; and Oftober
10. C — Oftober 4. C=6 is the quantity of the
lunar anticipation in 1653 years, completing the
odd hours and minutes into a day.
Thus I have in fome meafure (hewed the ufe
arid application, and illtlftrated by example, the
threefold property of my aftronomical table, con-
ftrudled from the inverted pofition of the Sun and
Moon, in the beginning and conclufion of the an
tediluvian world.
My

(4H )
My 5th Prop, afferts, that the feveral charac
ters, by which any given Scripture year is diftin
guifhed from another, are (1) the day of the
month, (2) the day of the week, (3) the cardinal
point of the day, in which the Sun crbftes the
Mojaic cardinal point of the Heavens. The 3d
and laft of thefe is the only point Which remains to
be fpo&e tb ; excepting the meridian of the garden
of Eden, which will neither be eftablifhed nor
overthrown by a fingle calculation.
The 3d particular, which I am now to fpeak
to, depends upon thefe few principles. (1) All
thefe computations are dated from the autumnal
aequiriodtial day at noon. (2) The days of the
lunar year begin and end invariably at 6 o'clock in
the evening, or the time of Sun-fetting at the
aequinox. Confequently (3) the days of the folar
year and the days of the lunar year are never co
incident, but when the Sun enters libra at its
fetting, which it conftantly does in the end of
every ift, or the beginning of every 2d year,
in the feries of quadriennial revolutions, but not in
a fixed meridian.
To give the reader a clear view of this, we
will here fet down again the 4 aequinodtial qua
drants, together with their correfponding cardinal
points and their appendant indices, as in the folr
lowing table.

Fffa The

( 4^2 )
T, Solar $ Indices of the cardinal
Lunar j? points of the day.

o

4 3
— i
— o^ —
— — j. • •
 1 —
3
 2 
—-4 ¦ 3
Noon. Sun-fetting. M.N. Sun-rifing. Noon.
We may perceive from this table of indices,
that on the 4th of the Hexaemeron, the ift day
of the folar year anticipated the beginning of the
1 ft day of the lunar year by one whole quadrant j
the folar index being 4, and the lunar index 3.
In the end of A. M. 1, they were coincident, and
there the lunar index is o, the note of coinci
dence; I need not mention any more parti
culars. . ..
Now then,, in order to determine the cardinal
point of the day ofthe Sun's entry into Libra,
divide the given number of years by 4 (having
firft fubftradted 1) and the remainder will be the
index of it. E. g. 1653—1 = 1652-^-4, remains o,
which correfponds with Sun-fetting ; therefore in
the end of A. M. 1653, the Sun entered Libra at
6 o'clock in the evening ; and at that point of
time the folar year and the folar day began toge
ther in a correfponding meridian.
I will now collect together and enumerate all
the particulars, which have been hitherto ftated
and explained in the precedent calculations ; that
the reader may have an entire view and a clear
con-
( 4i3 )
conception what kind of aftronomy may be dif
covered, by a diligent and attentive perufal of the
antient facred records, according to the Hebrew
text. I fay then, that towards the end of the year of
Noah's life 597, A.M. 1653, (1) the primitive
full Moon evening fell on the nth day of the
1 2th month ofthe folar tropical year. (2 ) At the
diftance of 24 entire days from the autumnal
aequinox. (3) On the 5th day of the week, or
our thurfday. ' (4) The primitive new Moon
evening fell on the 26th day of the 12 th month
of the folar tropical year. (5) At the diftance of
9 entire days from the aequinox. (6) On the 6th
day of the week, or our Friday. (7) In the be
ginning ofthe year of Noah's life 598, which runs
parallel with the folar tropical year of the world
1654, the Sun croffed the Mofaic cardinal, or
autumnal aequinodtial point, (7) On the 25th
day from the primitive full Moon evening. (8)
On the 10th day from the primitive new Moon
evening. (9) On the 2d day of the week, or our
Monday. (10) Cardinal point ofthe day pf the
Sun's tranfit, in the ruling meridian of the year,
Sun-fetting. (n) The civil preceffion of the
aequinoxes, in the fpace of 1653 years, o. (12)
The lunar anticipation, in the fame interval, o.
Submitting, thefe conclufions to the examination
of the aftronomers, I proceed to the reduction of
5756 years to days ; but as I proceed by the fame
rules, with only one addition, this work will be
fhort-

( 4«4 )
fhortened, as I have ' nothing more to do, than
to make a calculation in the fame form and me
thod. The arithmetical operation. II.
I. 5756 years -^-30=19 1, remainder 26, which
referve.
II. The quotient 191 X37I=7°86i.
III. The remainder, 26 X i.2=p3if4"9 (f°r ^
remainder 26) =321. .
IV- 57^^630=9.',
V. 708614-3214-9=71191, aftronomical mea
fures of 30 and 29 days. ,
VI. 71191-^12=5932 moveable liinar years,
remains 7 aftronomical meafures.
VII. 5932 lunar years-f-3o= 197, remains 22.
VIII. 197X 1 1=21674-8 (for the remainder 22
(VII) =2175.
IX. Becaufe A, M, 5756 follows after A. M.
3300 add 1, which makes 2176 lunar years of
355 days, > D.
X. 5932 lunar years X 3 54=20999284-2 176=
2 102 104 D.
XI. To the collected fum 2102104 (1)
Addforyaftronom.meaf. . 207
The fum total. O 21023110(2)
XII. Add  I5 W
The fum total. C 2102326 cfaY
XIII. Add .   jr5
O 2 1 0234 1 0(4) As

(4*5)
As I am only directed by the Hebrew text to a
redudlion in general, but am left to find out the
rules as well as I can, I have not troubled the rea
der with a particular explication of my i^iles, be
fog chiefly fplUcitous about the truth and exadlnefs
pf the CQneluJiPns; and fcruple npt to fay in the
words of Horace — r —
 Si quid novifii reftius iftis,
Candidus imperii yfinon, his utere mecum.
¦ — - •£
Having completed the redudlion, in order to
determine the primitive full Moon and new Moon
integral epacts, we muft proceed, as before, by
the plain eafy tules of common arithmetic, firft
throwing off the fimilar figures from the refpective
films ofthe coliedteddays. E. g.
" X ( I .
, ^) 3j— UN0. (2)=024- Here the epad 24
irieludes the firft folar quadrant of the aequinodtial
day, which meafures from noon to Sun\fetting.
For the cardinal point of the; day of the Sun's
tranfit is, in this cafe, noon ; and may be known
by fubftraaing 1 from 5756, and dividing 5745
by 4, the remainder 3 will be the index of the
quadrant ; and from Sun-fetting to noon mere
are 3 quadrants*" : "".. ¦ ;.Al '«
T • , ¦
¦- O ...
(2) 35— 26N0. (3)=C9. The primitive
new moon epaa. (3)

(4*6) -n-
(3) 41 N°. (4) —35=06. The feat* ofthe
original feftival chag haafiph.
(4) By thefe calculations the exaa meafures
of the 3 flrait lines x, y, z, and of the feveral
parts ofy and z, will ftand exprefied thus.
A. D. 1749.
Years 5756.
^ Days 2102335. . —
x. O  O
21023 1 1 24 6
y 0  0~  C  O
o 2102326 9
zC  e-  — C  /
(5) As to the.refpeaive days pf the week, it
has been predetermined by a backward computa
tion from September 6, (which was calculated to
be the 5th or our thurfday) that the full Moon
evening fell on. the 6th ; the new Moon evening
on the 7th ; and confequently the 15th day from
thence, or the feftival day, muft have been the
firft. Now I fay, if thefe praedeterminations are
true, then divide N°. (2) by 7, the remainder
will be 1, becaufe 6 — 5=1. if N°. (3) be divided
by 7, the remainder Will be 2, becaufe 7 — 5=2.
Laftly, if N°. (4) be divided by 7, the remainder
will be 3, becaufe 34.5=8 — 7=1. and vice
versa-, 14-7=8 — 5=3. E.g.

The

( 4i7 )
7) 21023 n (300330
00221

i. ^ E. P.
7) 2102326 (300332
002214 2. ^. E. P.
7) 2102341 (300334
002238
3' % E. P.
(6) The rules for afcertaining the correfpond
ing days of the month both in the patriarchal ca
lendar, and in the Julian, confidered under a two
fold view, are fo extremely eafy, as to require no
explication; E. g. 35— -24=110— io=Ofto-
ber 1. O.
(7) 35 — 9=260— io=Oct,ober 16O.
(8) 11-1-35=46— 35= nO, or thus, 35—
15=20, and, 264-20=46 — 35=110.,,
=(9) 414-20=5:61 — 35=26*. Videtah. p. 351.
f(io) 114-25=36— ~2,5=Oftober 1 0-
(11) 264-10=36 — i$=.Oftober iO-
(12) 4-\-\-Oftober 10=51 — 3 §=Oftober 16 C.
Vide table p. 353, index 29.
(13) The Julian excefs in 5756 years, 44.
Then 44—30=14, and 024-}-I4=38 — Aug,
Ggg 31

( 4i8 )
31=7. Look for index 7, and column 2, 3, 4,
W ' (3) (4)
where are thefe numbers, 7. 11. : : 18. To
the middle number 1 1, add 92, and the fum 103
in the table of reduaion will ftand over againft
Auguft 18, But Auguft 18 is 24 days before the
aequinox; for September 114-31=42 — Auguft
18=024. Ilook into an almanac for A. D.
1749, where I find it thus fet down.
Full Moon the 1 6th day at 1 2 at night.
But this being paft fix o'clock, it muft be
reckoned Auguft ly, therefore Auguft 18 is the
day after the oppofition.
The calendar letter isf, and the dominical let
ter A, therefore it was the 6th day of the week.
(14)44 — 30=14. Then 14-1-9=23. Look
for index 3 in table II. p. 353, where are thefe
(*) (3) (4)
numbers, 23. 27. : : 2. C. To the middle num
ber 27, add 61, and the fum 88 in the table of
reduction will ftand over againft September 2. But
September 1 1 — 2=C 9.
I look into an almanac for A. D. 1749, and I
find it fet down thus, new' Moon the 3iftvday of
Auguft at 8 at night; —
But becaufe it was pafl 6 o'clock, therefore in
the primitive accourit it muft be reckoned Septem
ber i,- and confequently September [2, 'is. .the day
after the conjunaion. * ' -
The calendar letter for September 2, is g, the
dominical letter A, and therefore it'Wasthe^th
day of the week. (15)

(4^9 )
{ Us) 44—30=14. Then 24-1-14=38—30
'=0. Look into table I. p. 251, for the index
10, where are thefe numbers, 8. 12. :: 17. O-
To the middle number 12, add 61, and the fum
73 will be found in the table of reduaion over
againft September 17. Now fays Mofes, Levit.
ch. xxiii. ver. 39. on the 15th day of the 7th
month, when ye have gathered in the fruit of the '
land, ye fhall keep a feaft unto the Lord. But
September ly — September 2, (=15, and Septem-
O
ber 17 — September 1 1=6.
The calendar Letter of September 17 is A,
which is dominical.
I will now enumerate all thefe charaaers, and
lay them before the reader in one entire view.
In the end of A. D. 1749, A. M. 5756, the
primitive full Moon evening fell, (1) On the nth
day of the 12 th month in the patriarchal calendar.
(2) At the diftance of 24 days before the aequi
nox. (3) On the 6th day of the week. (4)
The primitive new Moon fell on the 26th day of
the 1 2th month of the patriarchal calendar. (5)
At the diftance of 9 days before the aequinox. (6)
Qn.the 7th day of the week. (7) In the begin
ning of A. D. 1750, A, M. S757, the Sun
croffed the Mojaic cardinal, or autumnal aequi-
noaial point, on the 24th day from the primitive
full Moon evening. (8) On the 9th day from
the primitive new Moon evening. (9) On the
GZ£2 2d

( 420)
2d day?of- the week. (10) Cardinal point of the
day, noon ; with refpea, I mean, to that meri
dian, in which the folar year and the folar day be
gan together; beginning the computation from
noon, (i i ) The civil praeceffion of the aequinox,
in the fpace of 5756 folar tropical revolutions==o.
(12) The lunar anticipation in the fame fpace of
time=o. Here I fhall reft at prefent ; and muft now fiib-
rriit it to the judgment and determination of the
reader; whether, in thefe calculations, I bave^ln-
cluded or not the whole contents of my feveral
propofitions, excepting the certainty of the firft
meridian, which will require fome time and pains
tb adjuft. But the more immediate points to be
examined into and confidered are, (1) Whether
as a Scripture chronologift, I have made it appear,
in a fatisfaaory manner (however new and unex-
peaed the proofs may be thought) that Mofes
meafures by the true folar year, and computes by
the months and days of the lunar? (2) Whether
the1 Hebrew chronology of the antediluvian world
(to which period I confine my prefent enquiries)
is undeniably afcertained in a method a priori, by
data which are true in nature ? By folar, lunar
and hebdomatic charaaers, which exaaiy cor
refpond with the Hebrew computation, and not
poffibly with any other ? (3) Whether the ages
ofthe patriarchs at the birth of their recorded fons,
according tb the Hebrew verity, conftitute an un
interrupted fucceffive chronology, and aftronomi
cally afcertain the true extent of the World's paft du-

( 42 1 >
^ration ? (4) Laflly, whether it muft be impli
citly admitted, as a late great and eminent author
has taken. the freedom to poftukte (Letter III. of
fecred hiftory, p. 102) " That he who expefts to
" find a fyftem of chronology, orfujficient materials
u for it, in the Pentateuch, and the other Books
" of the Old Teftament, expefts to find what the
" authors of thefe books never intended?" I fhall
venture to add, (5) If my 9th propofition is al
lowed to be eftablifhed, then it follows, by fure
and certain confequence, that the purity of the
original Hebrew text has been conveyed to us and
preferved entire, " by a perpetual ftanding mira-
iC cle." Since in the fpace of fome what more
than 3200 years from the death of Mojes to the
prefent times, amidft an indefinite variety of tran-
fcripts, not one error has crept in, to give any the
leaft difturbance to its chronological feries of years,
from the creation to the burning of Solomon's tem
ple, where Ptolomy's canon comes in as an auxili
ary, and by its uncontefted authority, completes
the interval. Now the excefs or defea of a fin
gle year, arifing from the miftake of a fingle nu
meral, muft have occafioned a diflocation of the
parts, and confequently, an interruption in the
aftronomy. But there is no interruption in the
aftronomy, and therefore no chafm in the chrono
logy, and no error in the Hebrew numerals, which
confiitute the Scripture fcheme. On the con
trary, let fome one try to apply this argument ei
ther 'to the Greek tranflation, or to the Samaritan
Pentateuch, he will foon become fenfible of the
dif-

( 422 )
difference between the authenticity of the former
and of the latter.
Letter III. of facred hiftory, p. 94. It has
been faid by Abbadie, and others, " That, the ac-(
cidents which have happened to alter the texts of
the Bible, and to disfigure, if I may fo fay, the
Scriptures in many refpefts, could not have been
prevented without a perpetual ftanding miracle, and'
that a perpetual ftanding miracle is not in the order
of providence." " Now I can by* no means fubfcribe to this
" opinion. It feems evident to my reafon that the '
" contrary muft be true ; if we fuppofe that God
" aas towards men according to the moral fitnefs
" of things; and if we fuppofe that God aas ar-
*' bitrarily, we can form no opinion at all. I
ct think thefe accidents would not have happened,
" or that the Scriptures would have been preferved
" entirely in their genuine purity, if they had been
" entirely diaated by the holy Ghoft : and the
" proof of this probable fuppofition, according
" to our cleareft and moft diftina ideas of wif-
" dom and moral fitnefs, is obvious and eafy."
I heartly join iffue with this fine theological re
mark ; and, with no fmall pleafure obferve, that
this reply to Abbadie and others, is penned with the
true fpirit of a zealous and difcerning Scripturift.
It is animated with a fentiment which plainly informs
us, that the acute and penetrating author (though
ftrongly biaffed with an unbecoming prejudice) had
exaaiy weighed and maturely confidered the necef
fary refult, the uniform truth and providential incor
ruptibility

( 423 )
ruptibility of a book, which was entirely diaated,
influenced and direaed by the infallible fpirit of
,God. And I wifh I was qualified to tranfmit fo
jufi and well grounded a jentiment of revelation
down to the lateft times.
To draw to a conclufion ; there are many ex
cellent and , ufeful, though, alas, latent truths, in
the Hebrew Scriptures ; a clear evolution and full
•explication of which cannot fail of giving a pro
portionable fatisfaaion to every Chriftian reader.
Jiventhe ftiff-necked and obdurate Tyndalifis, who
have eyes and fee not ; who have ears and hear
not; whofe hearts are waxed grofs, and under-
ftandings darkened, will find themfelves compel
led to acknowlege thus much at leaft ; that the
prieft j of Midian's fon-in-law, the /Egyptian fu
gitive, was, in troth, a notable clever fellow, and
learned in all the wifdom ofthe Egyptians.
Upon an attentive perufal and the clofeft , exa
mination of this moft antient record, this venera
ble code, it would be injurious to it not to fay, if
Sdnconiatho's Phoenician annals, tranflated into
Greek by Philo Biblius ; if the Egyptian dyna-
fties of Manet ho the Sebennyte; if the Chal
dean dynafties of Berojus, a prieft of Belus ;
if the Laterculus of Eratofienes ; if the Septu
agint verfion, the Samaritan Pentateuch and Jo
fephus; if the accounts of Herodotus the moft
antient Greek hiftorian, of Diodorus Siculus,
and of Strabo ; if Ptolemy's canon of kings ; if
Georgius the Monk, and the colleaions of Julius
Africanus and Eufebius ; if the moft ftudied at
tempts

( 4H )
tempts and labours of the moderns, can offer any
fcheme or plan of chronology, which may ftand
in competition with the antediluvian arid poftdilii-
vian genealogies, then doubtlefs thefe Mofaic both
folar and lunar tables, cannot he juftly placed at
the head of things, nor, like an univerfal monarch,
claim a prerogative fupreme.
Purfuits after aftronomical improvements have
been for fome time negleaed, checked, and, I
had almoft faid, entirely fuperfeded by the fole in
fluence and authority of Sir IfaacNewton ; who was
profeffedly, in fcieritific fpeculations, fo eminent
a genius, fo profound an adept, that Mofes^ the
writer of the Pentateuch, can alone upon Earth,
with refpea to praxis, be entituled'to a fuperiority,
and challenge the right hand of preeminence.
And methinks I fee the Jewijh legiflator, Ijh Elo
him, feated on his glorious throne^ and beaming,
from his fhining countenance the imprefied rays of
divinity, with this motto infcribed over his head,
Magna est verity, et pr^evalebit.
Hail ! jimrdm's fon ! aftronomer divine,
Offspring of Jacob's loins, of Levi's prieflly line y
What heavenly treafures does this world below,
To flags, and the Nilotic papyre, owe!
Mofhe ! extracted from the flood of Nile,
Infpired Mofhe ! born to blefs our ille.
Born to inftrudt a philofophic age,
Give knowlegeto the' leaned, and wifdom to the fage.
To thee 'fhall fons of art and fcienCe flow,
To thee fhall cultivated nations bow ;
Thy, Pentateuch all father progrejjs bars,
This the enlightening Sun, and arts the twinklingflars.
POST-

(42; )

POSTSCRIPT.
UPON a review of the whole, I am fenfible
of fome miftakes, which are of a different
nature from thofe that are inferted in the table of
errata ; and I think it incumbent upon me to take
notice of twp.
Firft, p. 19. in the bottom paragraph, inftead
of — : between the poles and the polar circles —
it fhould have been wrote, at the pies ; for what
I there fay concerning the fix-month day, and the
)$x- month night, is ftriaiy true only at thofe
joints. , > Secondly, p, 251, I enter upon the explication
of prop. 8. and there, inftead of the 969 years
of Methujalah, I have fubftituted the age of
Enoch, who lived juft as many years as there are
days in a folar year. Thefe 365 years of Enoch's
life, I have miftakenly called the fquare of a fo
lar revolution, and have repeated it in the reduc-
I tion. But there is no occafion to regret an emen-
ij dation of this form of expreffion, fince, inftead of
, weakning, it ftrengthens and enlarges my argu
ment ; for, upon reconfidering the Mojaic table
of genealogies, I now find myfelf able to afcer
tain the true meafure of the Sun's year, from the
H h h age

(426 )
age of Adam, or of any one of the Patriarch's
indifferently, throughout the table, which did
not occur to me at firft : And I now perceive by
my own experience, that long fecreted and un-
fufpeaed truths open and difcover themfelves by;
degrees. . w
Before I draw up and publifh any more propo-
fitions for the fubjea of another book, I fhall wait
to fee what material objections may be urged againft
what I have advanced and endeavoured to eftablifh
in this firft part of my undertaking. I am far from
being puffed up with a conceit that I have donp.
due juftice to, the important fubjea^ in my mer
thod of treating it ; on the contrary, I am hum
ble enough to rank myfelf amongft the number
of thofe who would be extremely well pleafed to
fee a fatisfadiory folution of the following queries,
from any one who has taken fome pains, in the
ufual methods, to acquaint himfelf with the folar
fyftem. Firft, For what particular ends and purpofes,
With refpea to us the inhabitants of the earth,
has the great Creator (all the operations of whofe
hands are direaed by infinite wifdom, which is
glorioufly difplayed in the eftablifhment of final
caufes) Prdained a folar tropical year to confift of
one fourth part of a day, over and above 365 ?
Secondly, How much lefs than one fourth part
of a day exaaiy ? and likkewife,
Thirdly, For what particular ends and pur
pofes, with refpea to us ? Fourthly,

( 427 )
Fourthly, By what fettled and determinate
rules may the feparate quadrarit be annually com
puted, as well as annually meafured, and ftill the
day, in civil reckoning, fhall ever have an im
mutable epoch ?
Fifthly* By what law of computation may we
avoid the numeral denomination of a 13th month
in the lunar year, which the Jews call Emboli-
maan, and in the altered year, Ve-Adar ?
Sixthly, Should it be alledged that, in the lu-s
nar computation, I have not obferved the exaa-
nefs of minutes and feconds, I would, in my
anfwer,' propofe it as a nice and juft matter of
enquiry, whether the author of the fyftem did
not originally intend the cardinal points of the
day for the perfea terminations of the aftrono
mical calculus, which an adherence to minutes
and feconds can never attain to ?
Laftly, Should any one be defirous tb know by
what authority, and by the direaion of what
vlaw, I have placed two feparate artd two inter-
feaing circles, in the front of the patriarchal ta
ble; my anfwer in general is this : I was direaed
to this fcheme, by contemplating the circum
ftances, charaaers, and appendent proportions^
of the created pofition of the Moon to the Sun ;
and to evince the reality of this, and its true foun
dation in the primary conftitution of' nature, I
here lay before the reader, Hhha d

§ J'!N

Ui -f». U> tO »-. © \Q OOVJ Oss>, 4V. ^ M

NN

1

1 -

*' 400000000000000

O

NN 1 ^H NN NN NN k*«
s*i 1 w MW ^o, CSV! OCSO O x MW^.

£

OH HHHHHHHHHHiiHiiH

^ H n*»

|s^ W N m O sQ OOVJ Ostn •$»• \*» tsl m

4*

<-r»

.

¦

Ol

M HH 11 HH HI
- NW^O, OsVj OOsO O » U v»4i

j: M

*o lf>

\> fr \> l> !> 1? I> l> l> l> l> l> \>\>

00 ti h

1— 1 t-H m-4 w t— (
^^» w h OVO OOM Gstn 4>OJ t) H

1 ^®!

,.._.,

OOOOOOOOOOOOOO

jvoi

I

ft

^ -?s»
5:;$ «
S" ?st. 8
i- *"• «.
i *
-8 <S |
§• §: 1?

to OO

< 429 )
If we poftiriare the firft parallel line ©f this ta
ble with the laft, we ffeafl find that the pofitiofls
of the luminaries are inverted, and that the new
Moons and full Mpons have changed their places
in fuch a manner, as to be fituated in each other's
centers, as, by infpeaion appears. Thus they
were fituated in the beginning, and in the end of
the old world ; and here we have a femiperiod of
thefe proportional variations from the original cen
ters : Therefore, in order to its completion, we
muft make the laft pofitibn the firft parallel line
of another table.

I

:
4

2
IS

3
O

4

5

6

7

8

9|

*5

©

2 3
4 56
i 9
10n
X2 i314
C
<L<L <LH
'« «<L ««
*4 *312 11 10 I I5
41 32 1
*•
X X X
X X
X
1
234 5
6 7
8
ron. 1.4.13»4
O
O O O O0 0, 0
§ O0
O
14. r31211 10 9 8
76 S
4 3 2 1
1
2 3
456
i 9
10 1112 13
i
<L« «
o
15
X
c
*5
© O
The
(43° )
The fame table without the fymbols of the
full Mpons <D, new Moons C, x, and =a»

I

0

ij

0

15

2

¦

H

1

14

1

3

»3

2

*3

2

4

12

3

12

3

5

-

11

4

ii

4

6

10
5
10
5
7
9
6
9
6
8
8
7
8
7
9
7
8
7
8
io
6
9
6
9
ii
5
10
5
10
12
4
11
4
11
¦13
3
12
3
12
"4
2
J3
2
13
15
1
H
1
H
1
0
J5
0
ii
Thefe may be juftly reckoned valuable, becaufe
they will approve themfelves, in the praxis, to
be very ufeful, tables ; for they exprefs, with the
integral exaariefs, the whole variety of theepaas
both full Moon and new Moon, which come
immediately before the aequinox, through the fuc-
ceffions of ages. Now,
( 43i )
Now, I fay, *hat whilft our aftronomers con
tinue to calculate conjunaions, dichotomies, and
oppofitions, they will never be able to difcern
thefe divifions of the thirty-day month ; much
lefs will they be able to afcertain thefe propor
tional variations of the primitive full Moons and
new Moons from their created centers, and re
turns to them, in determinate times ; with which
remark I fhall conclude this firft book.

FINIS.

*&tfat4sr