An essay towards the recovery of the Jewish measures & weights, comprehending their monies, by help of ancient standards, compared with ours of England useful also to state many of those of the Greeks and Romans, and the eastern nations / by Richard Cumberland ... Cumberland, Richard, 1631-1718. 1686 Approx. 165 KB of XML-encoded text transcribed from 84 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-03 (EEBO-TCP Phase 1). A35425 Wing C7581 ESTC R14108 11914994 ocm 11914994 50948

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Early English books online. (EEBO-TCP ; phase 1, no. A35425) Transcribed from: (Early English Books Online ; image set 50948) Images scanned from microfilm: (Early English books, 1641-1700 ; 813:8) An essay towards the recovery of the Jewish measures & weights, comprehending their monies, by help of ancient standards, compared with ours of England useful also to state many of those of the Greeks and Romans, and the eastern nations / by Richard Cumberland ... Cumberland, Richard, 1631-1718. [18], 140, [4] p. : ill. Printed by Richard Chiswell ..., London : 1686. Reproduction of original in Huntington Library. "Books printed for, and sold by Richard Chiswell" at end. Diagram: p. [17], [18] "A table of the principal measures, &c. herein contained": p. 135-139.

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eng Weights and measures, Jewish. Weights and measures, Medieval. 2003-11 Assigned for keying and markup 2003-12 Keyed and coded from ProQuest page images 2004-10 Sampled and proofread 2004-10 Text and markup reviewed and edited 2005-01 Batch review (QC) and XML conversion

AN ESSAY Towards the Recovery of the Jewish Measures & Weights, Comprehending their Monies; By help of Ancient Standards, compared with ours of ENGLAND.

Useful also to state many of those of the Greeks and Romans, and the Eastern Nations.

By Richard Cumberland, D.D.

IMPRIMATVR. Jo. Battely, R. Rmo. P. Domino Wilhelmo Archi p. Cantuar. à Sacris Domesticis. Ex aedibus Lambeth. Octob. 12. 1685.

LONDON: Printed by Richard Chiswell, Printer to the Royal Society, at the Rose and Crown in St. Paul's Church-Yard. MDCLXXXVI.

To the Honourable SAMUEL PEPYS Esq Secretary of the Admiralty of England, and President of the Royal Society. SIR,

BEcause the Improvement of Natural Knowledg, for which the Royal Society was founded, may be attained in some degree, by recovering some parts thereof, which the Ancients had, but are now unknown; I thought it not improper to present to you, who deservedly preside in that Illustrious Society, this Attempt, to restore those eldest Standards of Measures and Weights, which are mentioned in the most ancient Records, the Sacred Scriptures, as commonly known when they were written. But such hath been the ignorance and carelesness in these Matters, of many intervenient Ages, by whose care these things should have been transmitted to us their Posterity, that most of our late diligent Enquirers have declared their Opinion to be, that tho the retrieving of them be highly desirable, yet that success in such an endeavor is scarce to be hoped.

Nevertheless, being desired by some Learned Divines of our Church, in subserviency to some brief Annotations on the Bible by them intended, to do the best I could in this Affair, I have by this Treatise attempted to rescue this most ancient and useful Piece of Learning, from the Grave of Oblivion and Neglect, into which many despairing Men were casting it, before it was quite dead, or past recovery.

Learning I call this Knowledg of Weights & Measures, because the first Constitution of them, and the Reason, and Proportions contained in their mutual Correspondencies, do import, not only prudent Observation, which is Learning's Foundation, but also some Elements of Geometry, Arithmetick, and Staticks, (which are essential Parts of its Superstructure) thence peculiarly called 〈 in non-Latin alphabet 〉 , or the Learning. And for this cause I have been forced, in the prosecution of this Enquiry, to call in to my assistance some of the easiest Mathematical Notions, which are as old almost as Mankind, associating thereunto some Observations of Nature, whose constancy from the beginning gives reason to believe that they were known early by Men, together with the eldest Works of Art remaining in the Pyramids, Shekels, and other remains of Eastern and Western Antiquity, that from the concurrent Evidence of these Aged Witnesses, I might be enabled to give this my Verdict, which is now brought in before you.

Ancient I may well assert this kind of Learning to be, since it appears by Moses's Description of the Ark by its Measures, that the Cubit was in use before the Flood. And amongst the Kingdoms founded after the Deluge, Egypt will claim very great Antiquity, being by Scripture called the Land of Ham, whose Son Mizraim is found in the eldest Monuments of Time, in the Head of its Kings. But here, Proclus assures us, the Art of Measuring was cultivated in the eldest Times; whence we justly conclude this to have been part of that Wisdom of the Egyptians, in which St. Stephen affirms Moses to have been universally skilled.

The great Difficulty of finding out the exact Truth in this Case, that is perplext between the despair of many; and the contrariety of Opinions of other Authors, will plead sufficiently for the Pardon of such Defects, as after my utmost Endeavour, to clear this matter by decisive Evidence, both a Priore, and a Posteriore, may yet be discovered in this Discourse by your piercing Eyes, or by the curious Examination of the Members of the Royal Society, to whose Censure I willingly submit it.

Nevertheless I cannot but hope, that this Essay of mine will be kindly received by you, even on account of your constant love to its Author. For that good Affection being begun in your Youth, thirty Years ago, in Magdalen-Colledg in Cambridg, you have continued to this day, while you have gradually risen higher in the Favour of our two Great Monarchs successively. And I may justly reckon, that nothing can break that Friendship, which so great Advantages of Preferment, on your side, doth not abate.

Besides, I believe this Book will be the more welcome into your choice Library, because the Subject of it, is not any quarrelsome Interest, or distinguishing Tenet of a Party of Men, but the peaceable Doctrine of Measures and Weights, which in their General Nature, are the Common Concern of all Mankind; as being the necessary Instruments of just Dealing, and fair Commerce between all Nations; which the Admiralty of England (wherein you are so highly trusted) doth promote in Times of Peace, as it secures our Safety in Times of War. For I may without any arrogancy affirm, that not only the Principles and Method of this Discourse, do give Light to that General Doctrine, but also that the particular Measures and Weights therein stated, have an universal influence thereupon. Because these being the most Ancient and Sacred Examples of that kind, and the Rules of that Righteousness, whereof Noah, the Father of all Men now living, was a Preacher, it's highly probable that all Nations did derive as their Pedigree from him; so their Measures and Weights from the imitation of his, (although length of Time, neglect and corrupt Customs, have made great Alterations) which I have briefly proved by the Examples of those used by the most Learned Nations, the Greeks and Romans.

But whatever the Success of my Labours may be as to the Subject or Matter of this Tract, I am secure, that the calm manner of my writing it will be very agreeable to the known Candour and Serenity of your Temper: For I have industriously avoided all appearance of Contention against any Man that may herein differ from me, so far as not to name the known Diversities of Opinions of Men about this Matter, and have employed all my Diligence to prove mine own Assertions, either by Arguments peculiar to them, or by shewing the Approach of Others of the best Reputation to agreement with me.

By this means, and by refusing to make special application of the Generals here stated, to the many Texts of Scripture whereunto in the Annotations they must be applied, I have contracted my Thoughts into so small a Book, that it may seem incongruous to present it to a Man of such great Worth as you are: For which I shall add no other Apology than this, That if in this little Room mine Vndertaking be not well performed, the shorter Follies are the better; if it be, I know you will not think the worse of a Book, because in a few Sheets it determines many and great Difficulties. However, if it were never so great, and never so well written, I should think it insufficient to answer those great Obligations under which I am to be,

Honoured Sir, Your most humble Servant, Ric Cumberland. Octob. 28. 1685.

Appears to be a two vertical page fold-out showing a rule with measurement labels.

The side of a Cubic Epha

Inc: 10.944 A Span or half Cubit

Inc: 3.648 A Palme 3 of them in the half Cubit

dec: Inc. .912 A Digit 4 of which make a Palme

an illustration of two sides of a coin. A Shekell with Samaritan Characters.

OF Scripture-Weights and Measures.
CHAP. I. The Reasons, general Principles and Method of this Enquiry.

THE knowledg of Jewish Measures and Weights, hath been so much neglected by most Men; partly, as exceeding difficult, if not impossible to be attained; partly, as not necessary: that I cannot hope to persuade the generality, even of Scholars to study it; but find it needful rather to give an Apology for this attempt to search them out.

I observed a considerable part of the old Testament to be employed in describing carefully the Measures of Noah's Ark, of the Tabernacle; and the Ark of the Covenant therein kept; of Salomon's and Ezekiel's Temples, with their several parts, and sacred Utensils thereunto appertaining. I perceived therein the most antient, beautiful, and magnificent proportions of Architecture to be recorded; and the usefulness of such Buildings to maintain God's publick Honour and Worship to be suggested. I could not but observe, that near a thousand Years distance from Moses, Ezekiel requires the true old Cubit, Epha, Shekel, and Gerah, to be used at the Restauration of the Church and State, by him prophesied of.

These appearing in the Text to have been so long kept unaltered; I thought they, or some of them, might be spread into other Places, and by the careful methods of God's Providence, or the diligence, of the Learned, especially Teachers of his Church, among the Jews or Christians: that the memory of them might be preserved above 1000 Years more, in order to our more satisfactory understanding of the old Testament, which was written for the use of the Christian Church to the end of the World, Rom. 15.4. 1 Cor. 10.11.

I was confirmed in these hopes, by considering that the Roman Foot Quadrantal and Congius in Measures, and their Ounce and Pound (as Villalpandus proves) in weight, have continued near 2000 Years. And I saw reason to believe, that the Egyptian Cubit had been preserved there, from the utmost Antiquity of the Pyramids unto this day.

Moreover, I considered, that this Enquiry was the fitter for a Minister of God's Church; because the Priests were antiently appointed to be Keepers of the Standards or Overseers of all Measure and Weight, 1 Chron. 23.29. Wherefore, for exercise of my Arithmetic and Geometry; I resolved, in my younger days, to try what service they could do me in this Search: and having made then some progress in this Study, I have been persuaded now to add my riper Thoughts thereunto, for the service of a Commentary on the Bible, designed by some Learned Clergymen of our Church.

The Principles on which I proceed are,

I. Standards of Length and Capacity, that may still be seen, and compared with ours: to which I joyn Antient Shekels, which being both Weights and Coins, are presumed to have been tried and found agreeable in the Ballances with Standdard-weight; and therefore are to our purpose equivalent to Standards: all these attested by credible Persons, who have seen them, and compared them with ours.

II. Arithmetical Principles of Reduction, which are demonstrable, and acknowledged true by all competent Judges. The first Principle bears upon Sense, assisted by Mechanical Geometry; the second upon Reason, used in the most simple and abstract Objects thereof, viz. Number and Measure.

The Method I have taken is most natural.

1. To consider the Measure that relates to meer Length, the first or most simple Dimension which determines Breadth; also if the length of two sides of a Parallelogram be given.

2. Hence to procced to Measures of Capacity, which have three Dimensions.

3. Lastly, to consider Weight, which supposes a solid Body, but superadds the notion of Gravitation in a Ballance wherein two heavy Bodies are compared.

As to a standard of Length, I considered, that although the Ancients often speak of the breadth of Barly-Corns to determine it by, and might probably use them at first to determine a Digit by six of them, as the first perfect Number; and then by Nature's four Fingers on a Hand, come to determine a hands-breadth, and by six of these, a Cubit: yet they must necessarily find, in the first Age, as now, variety, or inconstancy in these Productions of Nature, and therefore must soon see a necessity of setling a Standard-digit, Hand-breadth, and Cubit, either by mutual Agreement, or rather by the Authority of the Father of the Family, the most natural Governour.

Accordingly we find a Cubit mentioned in the building of Noah's Ark, by which all its Dimensions are determined, and a great number of equal Cubits must be put into the hands of the multitude of Workmen, which must be employed in building so great a floating Vessel or Ship; and their Cubits must be made to agree to some Standard, or common Measure, else the parts of it would be unfit to join to each other, and could not be made to serve the common End of them all, the preservation of Noah's Family, and the other living Creatures therein to be included.

This Agreement of the Oriental Measures in their Digits, and consequently in their Palms, and Cubits of the same number of Palms, is expresly delivered by Abulfeda, in words cited by Greaves, in the Preface to Abulfeda's Description of Chorasmia, which he hath set out: where although he acknowledgeth, that Cubits of eight Palms were used by the Ancients, and of six by later Writers; yet he affirms, that in their Digits they all agreed, and their Miles and Parasangs determined by them, were just the same, although expressed in a less number of Cubits, when they used a Cubit of eight Palms, and in a bigger number of Cubits, when they used that of six Palms.

On these Grounds I judged, that if we could recover one old Eastern Standard Cubit, of a known number of Hands-breadths, we should be able to determine all their Measures of length by that Standard. Such I conceive and think I have prov'd the Egyptian Derah, or Cubit, still kept at Cairo, to be, whose length is evidently six Palms. And this Mr. John Greaves, Astronomy-Professor at Oxford, in his Book of the Roman Foot, hath given us accurately adjusted, to the 1000 part of our English Standard-Foot. What use this very Learned Man intended to make of this Egyptian Cubit, I find not, but heartily wish that he had liv'd to finish the Work he intended, about the Measures and Weights of the Ancients. The Jewish Cubit he hath no where stated that I know of; only in his Epistle Dedicatory to Mr. Selden, he intimates it to be investigable by help of the Roman Foot: how he thence could have deduced it, I know not. But since his Death hath deprived us of that great help, which we might have expected from his great Reading, Travels, Diligence, and Judgment; I have thought fit to single out this Cubit, from those many Foreign Measures which he hath with equal care adjusted to our Standards, and to try, by comparing it with the best Notices of the Jewish Cubit, which my Reading hath suggested, whether this may not prove of the same length with the Cubit of the Sanctuary.

In the second place I have endeavour'd to state the Epha, and other Jewish Measures of Capacity; deducing it from,

1. A fixt proportion to the Cube of the Cubit.

2. From the proportion of a known part thereof to the Standard Congius of Vespasian, still at Rome: Besides other useful Methods from the Capacity of Eggs, which the Rabbins much insist on; and from the Weight and known Number of solid Inches of Water, that would fill either it, or its known aliquot parts.

Only I think fit here to advertise the Reader, that he is not to be offended, if he find some difference in the issue of the several Methods of investigating the Epha: because in all, I pretend not to Mathematical preciseness in determining it; but in some have stated it as thereabouts. Yet observe that the finding it by the soild Inches of 1000 Ounces of Water, which is the least, doth not differ a Pint from the biggest Content, deduced Mathematically from the Cubits Cube. And this small difference might arise, either from the neglect of Workmen, makers of Measures, who in making an Epha by Cubit-Measure, consider'd not the Centesimal parts of an Inch in the Cubit, as my Account doth: or else I may affirm that the Rain-water of those hotter Countries is lighter than our Fountain-water is; and therefore a thousand Ounces of such Water would fill up more solid Inches of room, than so many Ounces of our Water doth: and by either of these ways, the difference of the Accounts may be fully reconciled, or by the concurrence of them both.

Lastly; I descend to consider Shekel, and both to state its Weight exactly, and thence to deduce other Weights, and their Value in our present Coin. To which I shall say nothing here, having produc'd, I think abundant evidence in that Chapter, which by help of the harmony in the last Chapter will prove all the other.

By help of this method, I have endeavoured to make this Doctrine, hitherto very intricate and uncertain, more easy, exact, and uniform than I found it; constantly reducing all our Measures of Length and Capacity to Inch-Measure, with its Decimals, as more commonly understood than Foot-Measure: reducing also Weights rather to our Averdupois, with its Decimals, than to the Troy Ounce; because I have prov'd the Ounce Averdupois, to be exactly equal to the old Roman Ounce, and to be just equal to two Jewish Shekels, the conjunction of two Shekels, I believe, is the true original of it.

By this means, the several parts of this Enquiry, will help to illustarate and prove the truth of the other; the Measures of length will clear those of Capacity: and both of them may be proved or restored by help of the Weights. Only its requisite that the Student hereof should be acquainted with Decimal Arithmetic, and a little Geometry; otherwise the necessary Reductions, and some reasonings here made use of, will not be fully understood: However such Mathematical Reasons may safely be supposed true, because they have been examined and found so, by the most competent Judges in these cases.

CHAP. II. Of the Ammah, or Jewish Cubit, with the Measures thence determined.

MY designed Method obliges me in this Chapter to do three things:

1. To shew, that the present Egyptian Cubit, is their old one, continued to this day.

2. That the Jews Cubit, or Ammah, was of the same length with the old one of Egypt.

3. To deduce the length of other Jewish long Measures from hence.

1. This being now in possession, is favoured by presumption that it was so always, or in Moses his time; unless the contrary be shew'd, and the time of the change can be sufficiently proved. But of such change, or introduction of a new Cubit into Egypt, I cannot find the least intimation in History: on the contrary, we find it asserted by the Arabians, Patricides, and Elmacinus, and the Nubian Geographer, whose words may be seen in Hottinger's Smegma Orientale, and other Proofs in Kircher, that the Nilometrion, or Column divided into Egyptian Cubits, to measure the increase of the overflowings of Nile, are as old as the time of Joseph's Regency there; yea, and that he first made them. Now because the same height of its increase, viz. about 16 Cubits, is agreed in all Ages (Herodotus, and the latest Writers consent herein) to have been necessary to the fruitfulness of Egypt; it follows, that this Cubit must all along be the same, sixteen lesser Cubits would be insufficient, bigger would be prejudicial. Here we have a natural necessity to keep to the same measure from the time of its first Constitution; and this natural Reason is a thing of so great consequence to the welfare of a whole Kingdom, that none can be thought of sufficient to move any Governour to alter it; nor can the inferiour People have any cause, or any ability to make such alteration; the Publick Standards being so religiously kept, first in the Temple of Serapis (besides on the Nilometrion) and afterwards in the Christian Churches.

Hereunto we may add that which Proclus hath suggested concerning the Necessity and Antiquity of Geometry among the Egyptians, that Nile, by its Annual overflow, used to cover with Mud the common Boundaries of Mens Land, viz. Stones, and Trenches, or Ditches; whence it became necessary to them, to determine, preserve, and recover each Man's proper quantity thereof, by exact measure of its Area or Surface, which must be found, by knowing the length of the Sides, and of the Perpendiculars of Triangles; or of Rectangular Parallellograms, into which any Plot of Ground may easily be cast, to which purpose they must necessarily study the first Elements of Geometry. But I must add, that they must also necessarily fix, and Reason would advise them to be constant to some Standard-measure of length; by the Repetition and Parts whereof, they might determine the lengths of the sides of those Figures that contained their land. And we know also that their Cubit was their primary Measure: By this they setled the length of their 〈 in non-Latin alphabet 〉 , which Herodotus mentions as used in Survey, because consisting of a known number of Cubits, it saved the repeating of a Cubit so often, and was easily resolved into the number of which it did consist. Wherefore to make any change in their Cubit would have been very unadviseable, and apt to endanger loss in all sorts of Mens Estates, which had been setled by another Cubit before And such change could never be necessary, because the first setled Cubit, and its Parts, would certainly attain all the Ends of exact measuring, as well as any other Cubit that could be introduced, and might justly challenge to be preferred before any later, by its being setled and in possession already.

The Strength of this Reason may be understood more clearly by help of an Example, which I remember in Herodotus his Euterpe. There he tells us, that in Egypt their setled Militia consisted of these two sorts of Souldiers, who were esteemed above all Tradesmen, the Hermotybie, and the Calasiries. The full number of the latter of these was 250000 Men, who in courses were their Kings Guards, and every one of them had to maintain him and his Family, Land (free from Taxes) whose Area, or Superficial Content, was 12 Arourae, each Aroura being 100 Cubits on every side; which imports that it was the Square of an 100 Cubits. Wherefore to know how much Land this was in our Measure, I took the Cairo Cubit an hundred times, which is 182.4 in our foot-measure, as may be inferred from Mr. Greaves his Table: and by squaring this Number, I find an Aroura to be 33269.76 Square Feet English; which is considerably less than one English Acre, for that contains 43560 Square Feet. Hence it will follow that 12 Arourae will amount to 399237.12 Square Feet. And this divided by the Feet of an English Acre, will quote 9.165: which demonstrates that the Land of each Calasyry amounted to 9 English Acres, and .165 Millessimals of an Acre, or 1 tenth part of an Acre, 6 Cents, &c. above the 9 intire Acres: And it's clear that so much good Land lying where he places it, might maintain any of them with his Family very well. But if this Cubit were changed, whereby so many thousand Estates were set out, it must needs make a great change in all these Estates, consisting of so much Land set out by this first number of Cubits; which are now supposed to be all altered, and great disorder must be expected among these Men in whom the strength of the Kingdom chiefly lay. For if a longer Cubit were taken, those of them that were first served, would have more Land in each Aroura; but then there would be none left for those that should come to be served last; or else they must trespass upon the Land that did not belong to the Militia, which would beget Discontent and Sedition: if they took a less Cubit, this would lessen all the Souldiers Estates, more than any Man unskill'd in Geometry can expect, and would beget a Mutiny, for want of a sufficient Maintenance for the Souldiers and their Families, as may appear by this Instance: Suppose that instead of the Cairo-Cubit the Arourae of the Calasyries should be set out by the Roman-Cubit, which is not quite 4 Inches shorter, amounting, in our English Foot-measure, to 1.45, as may be inferred from Mr. Greaves his Table. An hundred such Cubits are 145 Feet, and the Square thereof making an Aroura, would be 21025 square Feet, and 12 such Arourae would be 252300 square Feet, which amount to little above 5 Acres, and three quarters, or Roods. Whereby its evident that much above a third part of every Souldier's Estate would be taken away; whence nothing less than great Distress in all their Families, and Rebellion against their Governors must be expected.

Concerning the Antiquity of these Arourae, I cannot find when they were introduced into Egypt; For though Herodotus do not mention them till he speaks of Apries King of Egypt, whom Chronologers agree to be that Pharaoh who is called Hophra in our Bibles; yet he supposes them setled on the Military Men before his Time, and confines them to twelve of those Nomi, which are Shires or Praefectures in Egypt, of which Sesostris, the most Martial King of Egypt, was the Author or Founder; which makes me conjecture that he setled these Arourae on the Souldiers, as well as that Division of the whole Land into 36 Nomi. If this be admitted, they were much elder than Moses his Time, according to the first Book of Eusebius his Canon Chronicus in Graec. where he from Africanus, and he out of Manetho the Egyptian Priest, places Sesostris in the twelfth Dynasti, and afterwards places Moses in the eighteenth. Yet they will be of Antiquity sufficient to my Concern, if Sesostris setled them about Moses's Time; to which the Learned Bishop Vsher makes Sesostris contemporary. But however this be stated, when I compare 100 Cubits, the side of an Egyptian Arourae, with 1000 Cubits, the side of the Side of the Levites Glebe-land in their Suburbs, and observe the decuple proportion exactly kept between them, I cannot but think both these Measures were used in the same Age; and that the way of setting out Land in the Jewish and Egyptian Countries, was near of Kin to each other, which serves my main End; although it be more than I was obliged to prove in this Paragraph, where I undertake only to evince that the Cubit in Egypt could not easily be altered, without making great disturbance, or making new Measures to all their Estates hereby determined, which I suppose I have prov'd.

Besides, if it had been altered, it's reasonable to presume it must be by some of the great Empires who conquer'd Egypt, who would have introduced their own Cubit: but that was not done, for the Babylonian Cubit of five Palms is shorter, that of six Palms the same with this (as we shall hereafter shew) and so needed make no alteration. The Greek and Roman Cubits are known to be shorter also than this: and the Turks, under whom they now are, have not introduced their Pike, corrupted of 〈 in non-Latin alphabet 〉 or Cubit; for whereas there are two Standard-Pikes at Constantinople, they are both much longer than this now at Cairo, as may be seen in Mr. Greaves Table of Measures, compared with the Roman & English Foot.

I shall add, as over-weight, to conclude this first Assertion, a probable Argument founded upon this probable Principle; that the Ancient Architects, being left to their liberty of designing the outmost Lines of a stately Building, would chuse to determine them by some round even Number of the most known Measure whereby they wrought. So God himself design'd the Ark's Dimensions in such numbers of Cubits; its length 300, its breadth 50, its height 20; all round even numbers: the like even numbers we find chosen in the measures of the Temple, 2 Chron. 3.3 length 60, breadth 20 Cubits; and the Oracle a perfect Cube of 20 Cubits in length, breadth, and height, 1 Kings 6.20. So the Learned Greaves found the Marble Stones of the Pavement of the most accurately built Pantheon at Rome, the larger of them precisely three Roman Feet, the less of them just half so much: which shews they took care to determine them precisely by their most known Measure, the Foot, or its most obvious part, the half Foot; and though the Number be not even, yet constant respect is had to even Feet, or equal division into Halves. Such respect therefore I hoped to find the old Egyptians to have had to their Measure the Cubit, in building the greatest Pyramid, and in determining the outward Measures of the Tomb contained in it.

Wherefore, remembring that Mr. Greaves had given us exactly in our English Foot-Measure, the sides of the Base of the greatest Pyramid; and the length of the Tombstone contained in it, both which fall into odd Numbers and Fractions of our Measure, by which they were not designed; I resolved to try the Reduction of this Foot-measure (which he had taken) into Cairo-Cubits, and I found them both to fall into round very convenient Numbers of Cairo-Cubits, making very reasonable allowance for such small error, as may justly, or rather necessarily be supposed to have fallen out, either in the first measuring of the Pyramid's Base, or in the late measuring which Mr. Greaves performed, and I least suspect.

Particularly, First, the sides of the square Base of the greatest Pyramid are delivered, p. 68, of his Pyramidographia, to be 693 English Feet. For reduction these must be divided by 1.824, which is his length of the Cairo-Cubit in our foot-measure, the quote is, 379.934, which is so very little short of 380 Cairo-Cubits, that I think it reasonable to believe, that the old Architects designed just this even number of Egyptian Cubits. For if we suppose Mr. Greaves to have missed but .12 of a Foot, which is not one Inch and an half in taking this long Measure of near 700 Feet, then the side must be put 693.12: this Number divided by 1.824, will give precisely, 380.

Or rather, if we suppose the old Architects Cubit to have been but one thousanth part of a Foot shorter than the present Standard (and such error is scarce perceptible by Mens Eyes and there is greater difference in allowed Measures try'd by the Standard, and ordinarily used) its demonstrable that such a Cubit being repeated 380 times, would make the side of the Base shorter than now it is found; for 380 multiplied into 1.823, produceth but 692.74, which is shorter than Mr. Greaves hath found it. Wherefore since such small difference from Mathematical Exactness of Computation must necessarily fall out, in designing such vast Foundations, either from imperceptible difference in the Measure applied, or from inequality of Ground, or oversight of Workmen: I conclude, that the Measure at first intended, was just 380 Egyptian Cubits. And I incline to it the rather, because the Square of this Number, which is the Area of the Pyramid's Base, is as remarkable a Square as can be pitch'd upon in the whole Table of Powers of Number, viz. 144400, and might therefore more easily please the mind of the Designer.

2. In like manner I remembred, that Greaves, p. 96, 97, gives the length of the Exteriour Surface of the Tomb, contained in the midst of the greatest Pyramid, to be in our Foot-measure 7.296. This reduced into Cairo-Cubits, by dividing by 1.824, gives just four such Cubits: and if there be found a difference in the Millesimal Parts of the Foot-measure, (which I cannot now correct, having not the Book by me, but my own Notes taken out of it) I am sure it is less than a Barly-corns breadth.

Wherefore that Tomb, or Stone-Coffins length, may reasonably be judged to have been designed just four of their ancient Cubits. And this designment could not agree so exactly with the same number of their present Cubits, unless the old Measure had been continued unto this day. Thus this Tomb will preserve to us the old Egyptian Cubit, four times repeated, as the Monument of Cossutius at Rome preserves the old Roman Foot: but with more significancy concerning the usual proportion observed of old in humane Bodies; that in most comely shaped Bodies, the length, from the Elbow to the Fingers end (called a Cubit) being four times repeated, gives the Stature or Tallness of a Man. And the differnce between the length of the hollow part of this Coffin, fitted to his Body that should lie therein; and the length of its exteriour Surface might instruct the beholders how much shorter he was than those elder and taller Men, from whose Arms, it's credible that the Egyptian Cubit was taken at the first; this difference was very near an English Foot.

Upon review of both these Instances, I cannot believe that the old Egyptian Builders of this Pyramid and Tomb, could make them by chance to agree with such well-chosen even Numbers of the Cairo-Cubit, if the same Measure had not then been in use, and had not guided them in their Work; it being scarce possible that they should design and work by some other Measure, and pitch upon other fitting Numbers of such Measure, and yet that the Work remaining should so justly agree with both other well-chosen Numbers and Measures, and with these also.

For proof of the second Proposition, viz. That the Jews Cubit was of the length or measure with the old (or new) Egyptian, I offer some general Evidence from Historical Observation of these and older Times, useful to this and other Measures.

2dly, Particular Evidence.

1. The Mosaical History assures us, that the Jews Progenitors went into Egypt, a then flourishing Kingdom, in the condition of a Family of about 70 Men, and were there Subjects at the best, who must use in all Commerce, the legal Measures of the Kingdom in which they dwell, and not long after were made Bondmen, who cannot be supposed to be allowed to make Laws to keep distinct Measures and Weights from the Nation which they serve. This little and low Estate they were in about 200 Years before their deliverance, and therefore must needs know the Egyptians Measures, but cannot be presumed (and proof there is none) to have any distinct peculiar to themselves.

Wherefore Moses often mentioning in his Laws, Weights and Measures, must needs mean, and by the Israelites be understood to speak of such as they know before in Egypt: for he never constitutes in his Law a new Cbit or Epha; and therefore presumes them to know what Measures those words signify, by former use of them. Now it's evident that they and their Fore-fathers for above 200 Years must needs use the Measures of that Kingdom in which they were Subjects, and in whose Markets they must buy and sell for so long a time.

And certainly it was neither unlawful nor dishonourable, in any comparison with Slavery, to use the publick Measures of a Kingdom, famous for greatest skill in the Art thereof: on the contrary, Moses is celebrated for being skilful in all Egyptian Learning, of which Geometry and Arithmetick, both used in measuring, are the best parts.

Nor were the Jews so shy of imitating Egyptians, but that they did many of them receive a strong tincture of their Idolatry, their greatest degeneracy; and therefore would more easily comply with them in so lawful a practice as the use of their Measures was.

Besides, to take away all stumbling at this, I consider that it's highly probable that the Egyptians received their Measures from their first King's (Mizraim) Authority, and he received them from his Ancestors, Ham and Noah: and so, I believe, did both Abraham's Family receive the same Measure from Noah, by the hands of Sem; and the Canaanites, with whom they dwelt before they came into Egypt, by the hands of Ham.

That the Philistines also in Canaan, before and after Moses his Time, used the same Cubit with the Egyptians, may be probably argued, partly from their descent from Mizraim, Gen. 10.6, 14. Partly from Herodotus in Euterpe his Affirmation, that the Cubit in Samos (which Bochartus hath proved peopled from Palestine, i.e. the old Philistines) was the same with that in Egypt. For it's certain, that Mens Children, and the Colonies they send abroad, use to retain the Measures of their Ancestors.

Thus although the Jews Cubit be the same with that of Egypt; yet the Israelites might use it before as well as after their descent thither, both receiving it from Noah and his Sons.

To which purpose I observe;

1. That there is no evidence that different Measures or Weights were yet introduced into those parts of the World.

2. It's evident by the Bishop of Armagh's Annals, that the Kingdom of Egypt was founded in the Year of the World 1816, which was 190 Years before the Death of Noah.

Now, Civil Government cannot be supposed to be without determinate Measures and Weights: nor is there any reason to believe, that Ham or Mizraim, in the life-time of Noah, could be unacquainted with those which he used, or could see any cause to alter them in his Life-time. They may justly be supposed to have had occassion in that time of 190 Years, to have frequent commerce with him, and his Descendents, dwelling in other Lands: and such Commerce would be facilitated by keeping the same Measures and Weights, but would be made more troublesome by changing them.

3. It appears by the same Chronology, that from the death of Noah, to Joseph's Promotion and Authority in Egypt, there were but 283 Years, in which interval no change of Measures, from what Noah's Family used, is read of. And that his Regency continued 80 Years; so that from his Death to their departure out of Egypt, were but 144 Years, to Moses his Birth but 64 Years. And several Arabian Writers affirm, that Joseph, during his Regency there, set up the Nilometrion, or Column, for measuring the Increases of Nile; which Column is now divided by this Egyptian Cubit, and must reasonably be judged from the first to have been divided by the same; because, in all Ages the same number of Cubits, in the overflow, have been esteemed necessary for the judging of Plenty or Scarcity like to follow in that Country. And there is reason to believe, that the Column when divided by him into Cubits, was divided according to a Cubit that had been used and known before his Time, above 283 Years, constancy in these things being usual in all setled Dominions, is to be presumed rather than change, of which there can no proof be offered. And there are many Instances of Measures being preserv'd unaltered for a longer time than that, as we shall hereafter shew.

Now I only suggest, that the Numeration by Decads, hath been kept among all Nations, that I know of, from the eldest times of History; and yet it's as alterable by humane Authority, or Agreement, as the Measure by Cubits and Epha's &c. or as the Cize of such Measures. Now that these Measures and Weights were of elder use than Jacob's descent into Egypt, may be argued;

1. From the Measure whereby Noah's Ark was designed, viz. round even Numbers of Cubits, and such Cubits as were used and known in Moses his Time, else it would have been in vain to have described its Measures by a word whose sense was unknown. And if Noah's Cubit had been a different Measure from the Mosaical Cubit, Moses must have reduced that into the then known Measure, before he wrote the History, which we have reason to believe he did not; because it cannot be expected that such different Measure would, upon reduction, have fallen into such even round Numbers as Moses sets down; its length just 300 Cubits, breadth 50, height 20. The same reason holds in 16 Cubits height of the Flood above the Hills. So also we read of Sarah's preparing three Seahs of Meale, which are an Epha (the chief Measure of Capacity, and the sixth part of the Cube of a Cubit, as hereafter I shall shew) long before the Egyptian Bondage.

We have also Shekels, the Original Weight mentioned in Abraham's Time, both in Abimelecb's Gift to Sarah, as the Septuagint and Targum Onkelos express it, Gen. 20.16: and in his purchase from Ephron the Hittite, in the Hebrew Bible, Gen. 23.15, 16. And just before Jacob's going into Egypt, his Mony out of Canaan passing by its Weight (which therefore must be agreed on) in Egypt, Gen. 43.21. And there being no Mark to distinguish these Weights and Measures before the descent into Egypt, from those of the same name mentioned by the same Writer after it; it is to be presumed, they signify the same quantities exactly, else the Word must be equivocal, which ought not to be presumed without full proof.

2. For special evidence of the equality of the Jewish & Egyptian Cubit, it wil be requisite to reduce this Cubit to our Inch-measure, and Decimals thereof. Whereas Mr. Greaves hath given us it from Cairo-Standard, in English Foot-measure, thus, 1.824, that is, 1 Foot, 8 Tenths of a Foot, 2 Centesimals, and 4 Millesimals of the same Foot; most Englishmen will more clearly apprehend its length, when reduced thus, 21.888, that is 21 Inches, 8 Tenths of an Inch, and as many hundreth and thousanth parts of an Inch.

A Geometric Method to exhibit to the Eye, those small parts of an Inch, as in the Scheme hereunto annexed.

The whole Line is an English Foot divided into 12 Inches; each Inch also is divided into Parts called Decimals. Only I have annexed to this Foot, a very short Line, that's but the twentieth part of an Inch, or, 05, five Centesimals; because our Foot, with this small addition, is (proxime) the side of a Cube, containing the true Epha, or Bath, as I have endeavoured to demonstrate in its proper place.

The first ten Inches thereof, numbred from the right-hand towards the left, are contrived so as to be the Base of a Right-angled Triangle, whose Cathetus is but one tenth part of an Inch high, and its Hypotenuse is drawn sloping from the top of the Cathetus to the beginning of the Base. The use of this Triangle is this; Parallel Lines to the Cathetus, taken between this Base and this Hypotenuse, with Compasses, or observed by our Eyes, are true Centesimal or Millesimal Parts of our Inch, often mentioned in this Treatise: they are Centesimals, when taken from the just Inches of the Base; Millesimals, when from the Decimals of an Inch. So a Perpendicular from 4 in the Base up to the Hypotenuse, is just 4 Centesimals: and if it be taken from 8 tenths of an Inch, further towards the left hand, the Perpendicular will be 4 Centesimals, and 8 Millesimal Parts of an Inch; which being added to 3 Inches, and 6 Tenths, already actually divided on the Line will give us a precise Jewish Palm So .912 the Digit, and (Inches) 10.944 is the Jewish Span, or half a Cubit; and therefore being doubled, gives the whole Cubit. Wherefore these Lengths are marked in a distinct Line near the Base of our Triangle, that the reductions to Inch-measure made in this Discourse, may be more fully understood by beginners in this Skill.

Arg. 1. From the Number and determinate measure of 6 such Palms agreed generally by Christians, Jews Persian and Arabian Mahumedans to constitute the Jewish Cubit: The Sum or Result of which, agrees exactly with the Egyptian Cubit now specified. Among Christians, I will only mention Jerom on Ezekiel, and elsewhere generally. The Jews may be seen cited in Arias Montanus his Tubal Cain; in Waser, and Hottinger's Preface to his Book de Cippis. Persians and Arabians own this in generaller terms concerning the Eastern Cubits, elder and later, as Greaves hath produced them in his Tract of the Roman Foot, and his Preface to the Description of Chorasmia, by Abulfeda.

I avoid the dispute about different Cubits; it seems to me all founded in the more indefinite signification of Ammah; which it's certain from the Arabic, signifies often generally any Measure, whereby the Dimensions of Bodies are adjusted. Now because this may be done by any known length divided into known parts, or repeated as need requires; it's no wonder if it were done sometimes by a Rule divided into five handbreadths, sometimes by one of six, other times by one of eight hands breadth, as convenience might prompt. But the legal setled or sacred Standard, most properly or peculiarly called Ammah, or Cubitus Verissimus, as the Vulgar Latin translates it, in Ezek. 43.13. this all agree to be of six Palms.

This proper Standard-Cubit only I took as the rule of other Measures; and I believe the Scripture always means this, when it useth Ammah without any mark of distinction or limitation in the Context: for words of different significations being set alone, are to be understood in their most famous or noted sense; else there will be so much place for equivocation, that the use of all Speech and Writings, even of the Bible, will be destroy'd. And the Scripture marking out a distinction in a few places, shews it was carefully written; and that that distinction is not to be understood, where not express'd. Non est distinguendum, ubi lex non distinguit. Exceptio sirmat regulam i non exceptis.

Particularly; I observe non intimating a difference of Cubits, but one in Moses his Books, Deut. 3.11 where speaking of the Dimensions of the Bed of Og, a Foreigner from Israel, who therefore had not respect to the Jewish Standard, he saith, his Bed was measured by the Cubit of a Man, i. e. an ordinary Man, not like him; and a more precise Measure in this case was not at all needful. The other two places that intimate some difference of Cubits, are in Ezek. 40 5. & 43.13. Now he writing while he was Captive in Babylonia, must be thought to have observed that Measure differing from the Jewish Standard, was there often used, even by the Jews also, who must use the Measures allowed in the Kingdom where they live; and therefore being to give them the Measures of the future Temple, he was obliged to intimate that the Cubits whereby they were expressed, were not such as in this Foreign Kingdom they oft used, but longer by one hands breadth.

This being premised, I pursue my Argument, by shewing, that the Eastern People determined their Digit, and consequently this handbreadth, by the breadth of six Barly-Corns making a Digit, 24 a handbreadth, as appears, not only by the Jews, but by the Nubian-Geography, Ali Kushgi, Abulfeda, &c. taking ordinary Barly; yet the better and plumper, rather than the worse: Optimum in suo genere mensura reliquorum. Now six such Grains (any Man's Eyes may satisfy him) will make above 9 Tenths of an Inch English; and although there be some inconstancy in different Grains, it may rationally be fix'd in order to a setling a Standard, at .912 of an Inch, as a middle rate, which is sometimes exceeded by Nature, but oftner she falleth short of it; that is, the Eastern Digit may be exactly stated at 9 Tenths of our Inch, 1 Centesimal, 2 Millesimal parts thereof.

Wherefore since there be 4 Digits in a Palm, it shall be by Multiplication of .912 into 4, 3.648; that is, 3 Inches, 6 Tenths, &c. And the Digit .912, multiplied by 24, produceth 21.888, which is just the Cairo-Cubit, as was to be demonstrated.

Here observe, that this Hands-breadth, and Digit, agree well enough with middle-siz'd Men among us; and these may well be kept constant in this Sandard, as so agreeable, both to the nature of the Vegetable Barly, and the animated useful part of Man, which were before Standards, and these derived from them: whereas in Measures more lately constituted, as the Greek and Roman Cubit and Foot, it's manifest that they make their different Palms, and Fingers-breadth, by first fixing the Cubit or Foot, then dividing the Foot into 12 parts, and calling them, though different in the several Notions, by the Names of Fingers and Palms, to which they are somewhat near, but with great uncertainty.

My first Argument bore upon Natures usual bigness of Barly, compared with the agreed number of Fingers-breadths and Palms in the Jews Cubit, adjusted with the Egyptian: My Second shall be from Divine Authority, of Ezek. 43.13. parallel to 40.5. describing the Cubit the Altar should be built by, to be a Cubit and a Hands-breadth. The most natural Exposition of which place, I conceive to be this, that they should determine the Altar's Measure by a Cubit, which should contain one Hands-breadth more, than that Cubit which they now ordinarily saw and used in the Babylonians Country, where now they were Captives.

Hence I infer two things useful to my purpose.

1. That the Hands-breadth was a Measure fully known and agreed of in Babyloniae, the same that in Judaea: For if they had differed in this, as they did in the usual Cubit, it had been in vain for the Prophet to describe the Sacred Cubit by an additional Hands-breadth, whose true quantity was as unknown to them, as the true quantity of the Sacred Cubit is intimated to be: he ought first to have stated a Sacred or true Jewish Hands-breadth; but he not doing so, and yet purposing to lead them to an exact Jewish Cubit, by these words implies the Hands-breadth used in Babylon and Judaea to be the same. Other Hands-breadths, as the Roman and Greek, differ considerably, as their Feet do.

2. Because it's agreed that the Jewish Cubit was just six Hands-breadths, and affirmed here to be one more than the Babylonian; it follows that the Babylonian now used, was but of five Hands-breadths in length: wherefore in our Inch-measure, if we substract the Hands-breadth 3.648, from 21.888 the Cubit, the Remainder is the Babylonian Cubit 18.240, which is not a quarter of an Inch longer than ours. And the addition of this Palm to 18.24, makes the Egyptian Cubit as before: Or rather thus, 6 multiplied into the Hands-breadth 3.648, produceth 21.888.

I am confirmed in belief of such a Babylonian Cubit often used, as differed in number of Hands-breadths, but agreed in the quantity of every single one, by these things;

1. By a Testimony out of the Misne Chilaim, cap. 17. cited by Arias Montanus; that there were two Standard-Cubits kept in Susan, which he referrs to, one of five Palms, the other of six. And Dr. Castle in his Lexicon in Ammah, proves from Jophe Toar, that there were even in the Sanctuary, Cubits (or Measures) of 5, 6, and 10 Palms; which might all be of convenient use, for the measure of little and greater Lengths, if they agreed in the quantity of the Palms whereof they were made; because all Sums of Length measured by them, might easily be divided by 6, and so reduced to the setled Standard of six Hands-breadths; but otherwise such diversity of Measures must breed infinite confusion and uncertainty.

So we can find the number of our Yards in any length, as a Mile, although we measure it either with a two-foot Rule, that is shorter, or with a Pole of 16 Foot and an half, that's so much longer; but still the Standard-foot must be supposed in both of them to be fixed; only we find it convenient, both for dispatch and truth, in measuring greater Lengths, to use such longer Measures, as have in them the shorter, often exactly repeated.

2. By a Testimony of Abulfedas, who in the Preface to his Description of Chorasmia, informs us, that the Ancients used another Cubit, consisting of 32 Digits (that is, eight Palms) besides that of 24 Digits, or 6 Palms: yet this made no real difference in their Measures, because they all agreed in the Quantity of the Digits, and in the Sum of them, and consequently in the Quantity and Sum of the Palms.

3. By a passage in Herodotus, (who flourish'd not much above 100 Years after Ezekiel) in his Clio, describing the height of the Wall of Babylon to be 200 Cubits, adds for greater exactness, that they were Royal Cubits, which are three Fingers-breath longer than the 〈 in non-Latin alphabet 〉 , moderatesiz'd Cubit.

Hereby he seems to intimate these two things to my purpose.

1. That the Babylonians had, and might most obviously have been conceived by his Reader, to have used a middle-sized Cubit, meaning, one like the Greek Cubit; for to such Readers use he wrote: but he informs them, that in determining the Wall's Height, they used a longer, called the Royal Cubit.

2. He informs us, that that Royal Cubit, was 3 Fingers-breadth longer than the other. Here by Herodotus his Fingers-breadth, I think we must understand, Greek Inches, which they called 〈 in non-Latin alphabet 〉 , because he wrote for the use of the Greeks, who must not be supposed generally to understand the Babylonian Fingers-breadth.

This sense of Herodotus being admitted, we have here intimated all that I designed in this Argument to prove; viz. That the Babylonians had two Cubits; one of a cize near agreeing with the Greeks, which differs very little from our English Cubit; and which being shorter, might be oftner used: another, a Hands-breadth longer: for three Greek Inches are somewhat more than three of ours, and the Eastern Hands-breadth we have shewed to be but three of our Inches with a Fraction annex'd, which was too nice a Matter for the Historian to take notice of.

And agreeably hereto I find, that Almamon the Learned Calif of Babylon, about 900 Years ago, did make use of such a Royal Cubit, consisting of six Palms, in the measuring of a Degree of a great Circle of the Earth on the Plain Sinaar.

The Issue of these Observations, in relation to the Text of Ezekiel, is this; that whereas there was a less Cubit of five Palms, often used in Babylonia, the Prophet informs them, that they should not determine the Altar's Measure by his numbers of Cubits in that short one; but in the larger Cubit, called the Great Cubit, Ezek. 41.8. which had a Palm added thereunto; and was the fitter, as agreeing with both the ancient Measure of the Sacred Buildings; and also with the Royal Standard of the Prince under whom now they were. Which Royal Cubit, I suppose to have been kept there from the Ages nearest to Noah; as the Egyptian, with which it agrees, we have suggested to have been setled by Mizraim, and derived from Noah.

In passing through this Argument, we have observed a near agreement between the Babylonian lesser Cubit of five Palms, and the Greek Cubit, which Herodotus supposeth known by his Readers. I will now express it precisely, that of Babylon in our Inch-measure, I said, was 18.24; that of the old Greeks was, 18.13; the difference is not a Barly-corns breadth. And our Cubit is no more less than the Greeks.

This makes me conjecture, that the first Planters of Greece coming from Asia, brought thence that Measure: a little neglect, in process of time, might easily make those small Alterations. Agreeably hereunto I find in these Western and Northern Parts, very near approaches to the Eastern Cubit of six Palms: for such is the Ell at Frankford on the Main, at Florence, and at Dantzick; and such is the Standard Foot at Riga; as may be seen in the Table of Foreign Measures, given us by Sir Samuel Moreland.

Third Proof taken from the Measure of the outward Wall of the Temple, which is given by Josephus and the Talmudists, in very different Measure; whereof Josephus his Measure seems to be the Jewish Stadium, or Furlong, composed of 400 Jewish Cubits; and the Talmudist's Measure is 500 Roman Cubits; which they may reasonably be presumed to measure by, because when they wrote, the Jewish Polity had been dissolved some Centuries of Years; but the Roman Monarchy, and consequently the knowledg of their Measures, flourished. By comparing these, Jacobus Capellus hath stated the Jewish Cubit to be to the Roman, as five is to four; which is the only way to reconcile Josephus with the Talmudists, in a Matter wherein they may both be presumed to have been good Witnesses, sufficiently skilful, careful and faithful. For proof of this Proposition of Jewish and Roman Cubits, Jacobus Capell. de Mens. &c. may be consulted. An Epitome of his Argument is delivered by his Kinsman Ludovicus Capellus, in his Discourses about the Temple, printed in our Polyglot. Pag. 23. Col. 1. about the middle.

That which I have to supperadd to him, is;

1. To reduce the Roman, and thence his Jewish Cubit, to our English Inch-measure.

2. To shew that his Jewish Cubit, so found, comes within a Barly-corns breadth of the Egyptian Standard; which yet I suppose he knew nothing of, but which is my main Concern to prove. These I shall soon dispatch together.

For Reduction, observe, that the Roman Foot, on the Monument of Cossutius, now by most thought the truest, in English Inches and Decimals thereof, is 11.604; to which if we add half thereof, we have the Roman Cubit in our Inches, 17.406. Then by Capellus his Proportion, as 4 is to 5, so is the Roman Cubit 17.406, to the Jewish 21.757. Thus his Argument, from the measure of the Temple's outward Wall, finds such a Jewish Cubit; as wants little above one tenth part of an Inch of the Cairo-Cubit. And it's no wonder, if in such a length as a Furlong, such a little quantity be mist (from the Cubit) which is less than a Barly-corns breadth: therefore I may even hence conclude, that these Cubits agreed.

Nevertheless I will suggest, that there is another Roman Foot a little different from the forementioned, that on the Monument of Statilius, which in our Inches is 11.664: if this be rather chosen, (as it hath some great Approvers) the Roman Cubit will be 17.496; and by the former proportion, the Jewish will be 21.87; which is nearer our aim, the Difference being only one Centesimal part of an Inch But the former Approach satisfies me.

The fourth Argument, shall be from the consent of some Learned of the East, if not to the Word, or particular Standard that I point at, yet to a Measure agreeing therewith, which is the thing I seek. Here I shall first mention Abulfeda, whom Kircher in his Oedipus cites, expresly affirming, that the Jew's legal Cubit, was equal to the Egyptian Cubit of 24 Digits, which he calls their less Cubit, in comparison with a longer Measure sometime used by the Egyptians, consisting of 32 Digits, or eight Palms. Now Abulfeda being King of Hamath, a City and Territory very near Judea, and not far from Egypt, and exceeding curious and diligent in the Doctrine of Measures in the East, I confide very much in his Testimony, agreeing with such Reason as I have before produced. But Kircher appears not to have known the Egyptian Standard, and therefore could not improve this Testimony of Abulfeda, to the determining of Scripture-Measures; and Abulfeda being a Mahumedan Prince, although not unacquainted with the Bible, yet took no care to explain the peculiar Measures thereof, which is my Business.

Another Testimony I shall offer from a Learned Jew, Rabbi Gedaliah, who deduceth his Assertions from the Doctrine of Maimonides, who so throughly understood the Talmudists, that his Judgment may well represent the sense of all the Jews. But I take it rather from Gedaliah than the rest; because he, under the conduct of Maimonides, and other Jews, hath adjusted their Notion of their Cubit to a known Standard among us, viz. to the Standard of the Cubit or Ell of Bononia, where he resided. This Testimony of his may be seen cited at large, and translated by Hottinger, in the Preface to his Tract, de Cippis Hebraicis: And the Bononian Ell is given us reduced to English Inch-measure, by my Honoured Friend Sir Samuel Moreland, and by Sir Jonas More, to be 25.76 Inches and Decimals.

Now, Gedaliah affirms two things in his Adjustment:

1. That 14 Jewish Digits are equal to half the Bononian Cubit: Whence I infer, that 28 such Digits are equal to the whole Bononian Cubit; and consequently that the Bononian Cubit, 25.76, being divided by 28, the Quote will be a Jewish Digit. This Quote is in Decimals of our Inch .92, a little bigger than the Jewish Digit by me formerly assigned, viz., 912; and therefore 24 such Digits will give a Jewish Cubit somewhat longer than mine, viz. his will be 22.08, which exceeds mine a little above the breadth of a Barly-corn, viz. 2 Tenths of an Inch.

But then in the second place he affirms, that the Jewish Cubit is equal to ⅞ of the Bononian, wanting one Digit.

To examine this, and to compare it with his former Assertion, I found it necessary to divide the Bononian by 8:8) 25.76 (3.22; and this Quote so found, must be multiplied by 7, the Product is 22.54. Hence substract 1 Digit (by his Account) .92; the Remainder is affirmed by him to be the Jews Cubit 21.62. Now, this is less than his former Account by .46, very near half an Inch; and is also less than the Cubit I assign 21.88, by above a quarter of an Inch, viz. by .26.

Thus it's plain that my Length assigned to their Cubit, lies between his two Mistakes, which contradict each other; Nevertheless, I think he hath done us very good Service by the approaches to Truth, which are in both his Mistakes: and I see reason to believe, that in both these Attempts to express the Jewish by proportion to the Bononion-Cubit, he slipt only, through want of skill or accuracy in the Doctrine of Fractions, which if he had understood, he might have made his Accounts to agree better. However, the worst of his Accounts differs but a quarter of an Inch from me, and his other is nearer agreement; so that he differs more from himself than from me, or is nearer agreement with me than with himself. And by his so near approach to me on each side, he confirms me in my Opinion, that I have assigned a Standard sufficiently agreeing with the Doctrine of the Jews concerning their own Nation's ancient Cubit, which is all I undertook in this Argument.

After I had finish'd this Discourse, it was suggested to me, by a Learned Friend, that Rabbi Gedaliah's words, wherein he affirms the Jewish Cubit equal to ⅞ of the Bononian Cubit, wanting one Digit, are capable of another sense than that wherein I took them, viz. he may mean, That a Digit—.92 Decimals of our Inch, being taken out of the Bononian Cubit —25.76: the Remainder, which is 24.84, must be considered, and ⅞ of that will be the Jewish Cubit. Wherefore divide 24.84 by 8, it quotes 3.105: multiply this Quote by 7, the Product will be 21.735 for the Jewish Cubit, which differs from mine not much above 1 Tenth of an Inch; and therefore still the more confirms mine Assertion, and brings him nearer to agreement with himself, which makes his Testimony the more valuable.

My last Argument for this Cubit, should be taken from its greater fitness to all the uses, to which a Cubit-measure is assigned in the Scripture. As to give more convenient grandeur to the Tabernacle, to the Temple, and to those other sacred Things that belonged to God's Service in them both. But all these things will require larger Discourse than can be allowed in this Work. Wherefore I shall only instance in two things.

1. In the Height of the Table of Shew-bread, because the account of that will be very short, and yet seems clearly to favour this Measure which I have proposed. Moses expresseth its Height to be one Cubit and an half, Exod. 25.23. This, in my Account, ariseth to above 32 Inches and three quarters, viz. in Decimals 32.83, which is a convenient height for a Table. But if we take a shorter Cubit, suppose the old Roman Cubit, its height will be, in English Measure, but two Foot and two Inches above the Floor, which seems very inconvenient for a Table.

2. In the Capacity of Noah's Ark, of which because the most Learned Dr. Wilkins hath written very particularly, I will only add this general Remark; That if instead of a Cubit of 18 Inches, our Cubit which is 21.888 be admitted, the Capacity of the Ark, built according to Moses his Numbers of Cubits, will be very near twice as great, which will make it much more convenient for all the Ends to which it was designed. For such an Ark made by this longer Cubit, will be to its like made by a shorter Cubit, as the Cubes of these different Cubits are to each other; but the Cube of my Cubit is very near double to the Cube of 18 Inches, therefore so will the Capacity be: The Major all Geometricians know to be true, and the Minor any Arithmetician may find; therefore the Conclusion is true.

Our third Proposal, was hence to determine other Scripture and Eastern Measures of Length: Now this is easy, because it's agreed of lesser.

    Inches. 1. That the Span, or Zereth, was half a Cubit 10.944   A Palm, or Hands-breadth ⅙ 3.648   A Digit, Fingers-breadth 1/24 ,912

So also, 2. of their biger Measures, 〈 in non-Latin alphabet 〉 , a Fathom, 4 Cubits, Ezekiel's Reed 6; Canna, or a Pole, was 8 such Cubits, in English Feet 14.592.

Schenus, or their Line or Chain, 80 Cubits— 145.92 Iter Sabbaticum, Sabbaths Journey, 2000 Cubits 3648 Their Mile, its name from Romans 4000 Cubits, Mil. Eng. 7296—.3816 Their Parasang 12000 Cub. 21888—4.1454 The 30th part thereof is a Stadium, as Herod. and Hesychius witness — 400 Cubits. Their days Journey not always equal, but at a middle rate, set by Abulfeda, is 8 Parasangs Cubits 96000-33.1632.

It will not be necessary for me to give the Proofs of the Proportion of these Measures to the Cubit, or to each other: this is generally agre'd on, and the common Writers on this Subject have produced them: Wherefore I have thought my self only obliged to reduce them to our Standard-measure, supposing the Cubit to have been already rightly stated. And the like Method I have used about the Measures of Capacity, deduced from known Proportions to the Epha, and the other Weights deduced from Shekel.

I shall only add this Observation, That because so many Measures were determined by relation to the Cubit, the Egyptians and Jews were obliged to be constant in the Standard thereof, else the proportion to all their other Measures would be altered, and the ancient Measures of all their Lands, and best Buildings, would be greatly disturbed: as we might shew by instancing in the Levites Suburbs, set out by 1000 Cubits on each side of their Cities, and the Egyptian 〈 in non-Latin alphabet 〉 , mentioned by Herodotus, which were determined by 100 Cubits on every side.

CHAP. III Of the Epha, and other Measures of Capacity thereby determined.

MY next endeavour shall be, to find the true Capacity or Content of the Jewish Epha; which I think will be most exactly express'd, both by the number of solid Inches (English) of Water, which is contained, and by the number of Gallons and Pints, or known parts thereof, taken in Measures agreeing with our Standards. But both these must be found by help of the ancient Roman Standards yet remaining, to which both the Greek and Jewish Measures have been reduced by the Ancients.

For the clearing of my way of expressing the Capacity of this Measure, I must premise two things.

I.That the most exact and Geometrical way of expressing the Capacity of any Vessel, or Measure, is by expressing, in known terms, the solidity of a Body which will precisely fill it; the fittest will be Water, such as drops from the Clouds, which we suppose not to differ so considerably in the several Regions of the World, as Spring-waters do. Now, the Solidity of all Bodies is best express'd by help of a Cube, whose equal sides and height we know by a Standard-Measure of length; such is a cubic or solid Inch, whose side is the twelfth part of a Foot, and a Foot the third part of the Iron Yard, kept at Guild-hall for the Standard of England.

And it appears, that this way of determining Measures of Capacity, is not only most Geometrical, but also exceeding Ancient; because the Egyptians made their Ardob to be the Cube of their known Standard, the Cubit; and the old Romans made their Quadrantal, the Cube of their Standard, the Foot, as both Festus, and the ancient Verses of Rhemnius Fannius witness; which I need not transcribe, being obvious in divers Writers; my design being only to shew, that the Ancients aimed at this Correspendence between Measures of Length, and those of Capacity.

And indeed, a Cube is the only regular Solid which I have observed to be described in the Scripture, by all its Dimensions of Length, Breadth, and Heighth; and there such cubical Dimensions are assigned (what ever is the Mystery of it) to the most Sacred Type, the Holy of Holies, 1 Kings 6.20 and to the most holy Antitype, the New Jerusalem, Rev. 21.16.

Perhaps (because the simplest Soild hath all possible Dimensions in it) it may intimate;

1. The solid or compleat felicity of the Heavenly State, respecting the Length, Breadth, and Height of Divine Love, Eph. 3.18. which is the Fountain thereof.

2. The perfect rest and constancy thereof, because the Hedra, or Resting-Bases of the Cube, are six, which Euclid hath shewed to be a perfect Number: and they are all Squares, whence the Cube is less subject to be shaken, than the other regular Bodies. Something to this purpose is intimated in the old Maxim, 〈 in non-Latin alphabet 〉 .

II. I premise, that amongst us English, it is agreed, that our Wine-Gallon, now most frequently used, contains precisely 231 Solid or Cubical Inches of our Standard-Measure; and our Corn-Gallon, which is the Statute-measure of Capcity in England, contains 272 such Inches: for although Mr. Oughtred affirm it to contain ¼ of a solid Inch more (which is very little difference) divers others since, upon exact tryal, see no cause to add that Fraction to its Capacity.

For these Reasons, and to shew the dependance of the Epha on the Cubit already stated, I shall express my opinion concerning the Content of Epha, &c. in a number of our solid Inches, and in Decimal Fractions thereof, rather than any other sort of Fractions, which are more troublesome or difficult to be understood and reduced.

I conceive that Epha was about 1747 solid Inches of English Measure, not much distant from the English Foot Solid, which is 1728; and is near the Inches Solid of 1000 Ounces of Water. Or in Wine Measure it was 7 Gallons, 2 Quarts, and about half a Pint. In Corn Measure, 6 Gallons 3 Pints, and 3 Solid Inches.

This Capacity of Epha, or at least For approach thereunto, I shall endeavour to prove by four Arguments.

1. From its proportion to the Cube of the Cubit of Israel, formerly stated. 2. From its proportion to the Corus, or Chomer. 3. From its proportion to the Seah. 4. From the agreement of this Capacity with the content or solidity of 432 Eggs, whereby the Rabbins ordinarily determine it.

But I confide more in the two former Arguments, because taken from bigger Measures, than in the two latter, which arise from less. And therefore have altogether omitted the investigation from Number and Weight of Grains of Wheat, which I find elsewhere used: because every little Errour (which is unavoidable in small Measures) grows greater in the progress by multiplication; whereas little Errours in bigger Measures, when we pass from them to lesser by division, grow still less than the former, which tends to exactness.

Arg. 1. Epha is the sixth part of the Cube of the Egyptian Cubit, which Cube is called an Ardub: but the sixth part of that Cube, or an Ardub, is 1747.7 solid Inches: therefore so is Epha. The proof of the Major is from the express affirmation of the Arabian Accountants and Mathematicians, Alsephadi and Ebn. Chalecan, printed in Dr. Wallis his Arithmetic; cap. 31, and received from Dr. Pocock. Only there the Epha is by an usual commutation of the quiescent Letters, and of the Labial p into b, called Oeba, or as Dr. Wallis expresseth it, Waibah. But Salmasius, and Dr. Castle, and all the Learned in the Eastern Languages, that I have met with, acknowledg that Arabic Word to express the same Measure, that the Jews call Epha. And the matter seems clear, by comparing the Hebrew Exod. 16.36. with the Arabic Translation, in which Waibah is put to express the Hebrew Epha.

Add hereunto, that it may be deduced from what Golius affirms, treating of Corus as a Bablylonish Measure; that at Babylon also the Ardub was equal to six Ephas: for he asserts 40 Ardubs, equal to 720 Seahs, which are known equal to 240 Ephas. Wherefore divide the number of Ephas by the number of Ardubs, the Quote wil be 6; which shews that one Ardub i equal to six Ephas.

Thus this Proportion appears acknowledged wide in the East; although I do acknowledg that severa Ardubs of different Capacity from this are mentioned by Kircher, as used among the Egyptians; and othe 〈 in non-Latin alphabet 〉 , stated by the Greeks. Ye this sense of the word being as full attested, and this being determine by a sure Standard, I shall consider only in this sense, having no use of it other various significations.

Thus the Major is proved by Authorities; the Minor is demonstrab •• thus. The Egyptian Cubit reduced to English Inches, hath been proved to be 21.888. This number multiplied by it self, produceth its Square; that multiplied by the Side, or first Number, produceth the Cube, which is the Content of the Ardub in solid Inches.

Lastly; This being divided by 6, the number of Ephas in Ardub, the Quote is 1747.7. The Arithmetical Operations need not be set down at large in this Paper, but may be tried by any Arithmetician at his leisure.

But because it is not easily credible that the Ancients, in making their Ardub, did consider the thousandth, or the hundredth part of an Inch (which yet I have expressed by Reduction from Greaves his Measure of the Egyptian Standard, that I might not willingly depart from his exactness) and because the Abatement of the Centesimals of an Inch, in the side of the Cube, will err less from preciseness, than the addition of a like quantity, and will reduce the Epha to a Measure so well known among us; I have express'd it also by an English Foot Solid; which will be found to come from the sixth part of the Cube of 21.8; for the Cube thereof is, 10360.232: and that divided by s •• Quotes 1726.7, differing less than two solid Inches from the Foot solid 1728.

From this approach to Agreement we may not only help our Memory but also probably conjecture, that a our Foot is two thirds of our Cubit so the Eastern People had a Measure which we may call their Foot, which also was two thirds of a Cubit, sometimes used among them, viz. a Cubi of five Palms: Which differed no much from our Cubit, as I formerly shewed. And the Cube of that Foo of theirs, was probably the Origina of this ancient Measure, the Eph which a little exceeds our Foot Solid as also such their Foot and Cubit, i length, a little exceeded ours.

However it's certain, that the excess of the Cubic-Root of an Eph above our English Foot, is not quit five Centesimals of an Inch, or no the twentieth part of an Inch.

I have also observed, that the Epha, or Bath, contains just 1000 Ounces Averdupoise, or 2000 Shekels weight of pure Rain-water; which being lighter than our Fountain-water, and of a more constant equality in its Weight than Spring-waters are (which differ a little in weight from each other) takes up a little more room than so many Ounces of our Water will do: so that though we reckon 1726 Cubic-Inches to 1000 Ounces of our Fountain-water, we may well allow about 1747 such Inches to 1000 Ounces of their lighter Rain-water.

And it's evident that the Ancients determined their Vessels of Capacity by weight of Water. So the Roman Congius held just 10 pounds of Water, and that of Rain, as Dioscorides hath noted: their Amphora 80 such Pounds, their Sextary 20 Ounces. And it's certain, that the reckoning of Weights by round Numbers of Shekels, or their double, which are Ounces, is most ancient. And universally, that most ancient expression of Job 28.25. He weigheth the Waters by Measure, intimates, that their ancient Measures of Water were of a known weight, else it were impossible to weigh them by measure, or thereby to estimate and adjust their Weight. But this will be clear when we handle Shekel.

Here I thought fit to remark, that the concurrence of the Measure of this Solid Foot, and of the Weight of 1000 Ounces of Water, might recommend this Measure called Epha, or Bath to the first Founders or Authors thereof: and this happy concurrence is the true cause, that all their Measures and Weights may be investigated and prov'd, both à priore, by beginning with the simplest Measure of Length, and thence proceeding till we end in the Weights; and à posteriore, or peregressum, by beginning with the weight of a Shekel, and passing through all the Measures of Capacity, until we come to the Cubit, their Root; as I shall shew in their Harmony at the end of this Discourse.

The Reduction of this Measure to our usual Measure by Gallons, &c. i thus performed: divide 1747.7 by 231, the Inches Solid in a Wine-Gallon the Quote will be 7.566: which signifies seven Gallons; half a Gallon, or two Quarts, and about half a Pint. The like Method may be used for the Corn-Gallon. This may suffice for the first Argment, which may pretend to accuracy, because its Major is the affirmation of Mathematicians, referring the Ardub, and its sixth part, the Epha, to a known Standard, the Egyptian Cubit; and the Minor is certain by true Calculation. Those that follow pretend not so high, yet are of good moment, because they make some approach of agreement herewith; and many Witnesses agreeing in the Main, do corroborate each others Testimony.

Arg. 2. Is taken from the Chomer or Corus, which all agree to be the same, and to contain 10 Ephas, and is made the Rule of Epha, by Ezekiel 45.11. regulating prudently the less by the greater. Now Josephus, lib. 15. cap. 11. saith expresly, That 〈 in non-Latin alphabet 〉 : Wherefore he hereby intimates, that Epha, the tenth part of Corus, was equal to the Medimnus Atticus. The Content hereof we must first find in Roman Measure, to which the ancient Greeks and Romans have reduced it; and then we must reduce the Roman Measure, by help of Vespasian's Standard Congius, still remaining at Rome, to our English Standards: and so we shall see how far Josephus his Estimate of the Epha, agrees with, or differs from that which I have proposed.

But I must premise, even to the first Reduction, that two things are agreed among the ancient Greek Writers:

1. That Medimnus Atticus was equal to 48 Chaenices. So say Pollux, Aarpocration, Galen, &c.

2. That one Chaenix was equal to three Cotylae. So Pollux in two places, in words at length, not subject to so much corruption, through mistake, as Characters are; and Cleopatra, and others.

Hence the first Reduction to Roman Measures is thus made; every Cotyla is equal to half the Roman Sextarius, and consequently 12 Cotylae to the Roman Congius. So Galen, and the Author of the Hippiatric Weights and Measures, Dioscorides, and others, to be seen in the Treatises set at the beginning of Stephanus his Appendix to his Thesaurus. Herewith agrees what the same Authors and Cleopatra affirm, that 4 Chaenices are equal to the Congius, or to 12 Cotylae. Hence it follows, Medimnus Atticus being equal to 48 Chaenices, must be equal to 12 Congii Romani; for 48 divided by 4, which is the number of Chaenices in a Congius, quotes 12.

For the second Reduction, whereby the Roman Congius, and the Greek Medimnus, Chaenix, and Cotyla, may be brought into solid Inches of English Measure, and so compared with our Measures of Capacity, I offer this Expedient. It is agreed, and the Inscription on the Congius of Vespasian, witnesseth it, that Measure contained just 10 Roman Pounds of Water, or Wine. Each Roman Pound was 12 Roman Ounces; each Roman Ounce hath been found, by Greaves and others, to answer exactly to 438 Grains of our Troy Weight: Wherefore it wants 42 Grains of our Troy Ounce. And just so many Grains as Dr. Chamberlain in the State of England affirms, doth our Averdupoise Ounce fall short of the Troy Ounce, which is 480 Grains. Hence I conclude, that our Averdupoise Ounce, is the same Weight with the old Roman Ounce, which hath continued to be used, both in Rome, and here in England to this day, from the eldest Times. And we must consider, that the name Averdupoise, which signifies Weighty, was not at first given to this Ounce, but to the Pound, consisting of sixteen of eighteen such Ounces; which therefore was much more weighty than the usual Roman Pound, which had but twelve such Ounces: which Pound is not used among us, although the Ounce, as part of a weightier Pound, be still retain'd.

Sir Jonas More hath calculated a Table (founded in Experiments, concerning the Weight of any known Number of solid Inches of Water, made by Dr. Wibberd and others, whereby we may turn any given Ounces Averdupoise of Water, into solid Measure, expressed in Inches and Decimals thereof; which because it is short and useful for my purpose, I will transcribe.

Ounces. Inches Solid and Decimals. 1 1.72556 2 3.45112 3 5.17668 4 6.90224 5 8.62780 6 10.35336 7 12.07892 8 13.80448 9 15.53004

For an Example to shew the use of this Table; Let us take the 10 Pounds of Water that fill the Roman Congius; and because each Pound is 12 Ounces Averdupoise, call them 120 Ounces; the highest Figure signifies 100 Ounces. Wherefore take out of the Table the Number answering 1; and because of the two Cyphers which make it an hundred, remove the Separatrix two places further; thus writing 172.556. So also for the 20, remove the Separatrix one place thus, 〈 math 〉 This Sum gives the solid Inches of Water that fill the Capacity of Congius Romanus; and shew it to be less than our Wine-Gallon of 231 Inches, by almost 24 solid Inches. So Cotyla containing 10 Ounces of Water, is found in solid Inches, 17.25; and Chaenix containing 30 Ounces, must be in solid Inches 51.76. So, lastly, to determine the Medimnus by the solid Inches of Water that it contains, multiply the Content of Congius by 12, the Product is Medimnus, 〈 math 〉

The Medimnus thus found, when compared with our proposed Epha, proves bigger than it by 737 Inches, or above three Gallons Wine-measure. This shews that although I have exceeded the common estimate of Epha, which makes it the Cube of the Roman Foot, on very weak grounds, yet I have not gone so far as Josephus.

Nor can I recede from the Reason I have alledged for Josephus his affirmation, but shall answer his Authority, by saying;

1. That I conceive he did not intend to assert a precise Mathematical Equality between Epha and Medimnus; but to express the content of a Jewish Measure, as an Historian, somewhat near the truth, by comparing it to this most famous approaching Measure, known among the Greeks, in whose language he wrote.

2. That an Epha heaped up, will answer very well to a Medimnus not heaped: this seems a sufficient conciliation, that he respected an Epha cumulated; my number respects only an Epha strickled (as the Country-men speak) which is most certain and constant; because the Breadth or narrowness of the Measure, will alter the heaping very much.

To this head I shall adjoin another approach to Epha, by help of the Greek Chaenix, which is founded on a probable emendation of Hesychius, which I crave leave to propose, because the place is certainly corrupted, and I have not met with any attempt to mend it. Thus it is now printed; 〈 in non-Latin alphabet 〉 . That it is an Egyptian Measure, is truly and judiciously affirmed; but that it contained but four Chaenices, is far from credible, for that would make it all one with the 〈 in non-Latin alphabet 〉 , or Congius, which it far exceeded by the acknowledgment of all.

Therefore I have thought it probable, that Hosychius did write it, either in Characters thus, ΔΔΔΙΙΙΙ 〈 in non-Latin alphabet 〉 , as Herodian informs us the Greeks anciently wrote 34, putting three 〈 in non-Latin alphabet 〉 's for 30, because each Δ stood for 〈 in non-Latin alphabet 〉 , or Ten, being the first Letter of that word, and each Ι for single Units. And some Transcribers afterward being ignorant hereof, did take Δ to signify 4, as in later Times it doth, and the Ι's the same; and to avoid Tautology, wrote 〈 in non-Latin alphabet 〉 . Certain it is, that there should be, and probably was, either a Word or Character signifying 30 (either ΔΔΔ or λ) placed before 〈 in non-Latin alphabet 〉 , to make it fit to signify the number of 〈 in non-Latin alphabet 〉 in an Epha; which word, or Character, is now lost. And that no Number is so fit (as thirty) to be added, will appear by the coincidence of 34 Chaenices with the former Calculation from the Cubit. Thus Chaenix— 51.7 multiplied into 34, produceth 1757.8, and this differs from my assertion but the third part of a Pint, which is as little as can be expected in so big a Measure.

However, I trust not this Emendation alone; but if a better can be offered, shall thankfully admit it: Wherefore I will offer another approach to the finding a Corus, and Epha, by help of a Roman Measure taken out of an ancient Anonymus Latin Author, cited by Salmasius, in his Epistle to Walaeus, called by him, Auctor vetus adjectus Scriptoribus Rei Agrimensoriae. He affirmeth, that dou Cori Culloum reddunt. Hence I would draw an Argument (which it appears not that the Authors from whom I take this Testimony, did think of) to determine an approach to the Capacity of Epha.

For if the Roman Culaeus (as it's oftner written with single l) be equal or near to two Cori, it must be so to 20 Ephas. Now the Capacity of Culaeus is intimated, both by Pliny, lib. 14. cap. 4. and by Columella, lib. 3. cap. 3. to be twenty Amphoreae, or Quadrantals, each of which is known from Sextus Pompeius his Plebiscitum Siliorum, to contain 80 Roman Pounds of Water, or 8 Congil. So by this Argument the Roman Amphora, and Jewish Epha, will be made equal, or near each other; for Mathematical Exactness is not to be hoped for in such Authors.

The Roman Amphora did contain 1656 solid Inches, and near half an Inch more; as appears by multiplying the Content of Congius 207.06 by 8. And this is indeed bigger than the Cube of the Roman Foot on Cossutius his Monument, by above three Pints of our Wine-measure, as Greaves attests he experimented, pag. 35. of his Learned Treatise on the Roman Foot. But still this 1656, is less than our Number 1747, deduced from the Egyptian Standard; and more below the Content of Medimnus 2484, which Josephus thought near enough. Wherefore since our number falleth above the Amphora, which this Author must make equal to Epha, and below the Medimnus, which Josephus points at, as equal thereto; I hope, that being in a mean, and keeping to a publick Standard, I may have determined more exactly than either of them. And both their Testimonies will agree to assert, that I am not very far from the Truth, each of them coming nearer to me, than they come to each other. This is the sum of my second Argument.

My third Argument shall be, an attempt to prove my determination of Epha to be true, from Evidence, that the best Determinations which the Ancients have given us of the Capacity of Seah, comes near to the third part of the measuring Number which I have assigned; this being agreed by all, that Seah was the third of Epha.

And here I shall first consider, what Suida affirms, referring to a Number of Roman Sextarii, which we know by the Standard yet remaining: and then supply what is confestly deficient in him, by the elder Testimonies of Josephus, Epiphanius, and Hierom.

Suidas, in 〈 in non-Latin alphabet 〉 , which is the Hebrew Seah, altered after the Greek fashion, affirms it to be the Roman Modius, filled so as to run over its brinks; and that it holds in Liquids 15 Sextaries, or 25 Pounds. The weight in Water annex'd, secures us he speaks of the Roman, not the Attick Sextary. Now fifteen Roman Sextaries are equal to two Congii and an half; which in solid Inch-Measure of Water, 517.66, being 300 Ounces in Weight. But this is less than the third part of our Epha, that being 582: So there wants above a Quart of our Wine-Measure. And Suidas implicitly confesseth his Measure too little, by saying it must be 〈 in non-Latin alphabet 〉 , heaped up so as to run over. This Heap might easily supply the Quart wanting in the Account in Water, which will not be heaped, and which indeed is less than commonly is allowed to the Modius, it being usually reckoned sixteen Sextaries, and that would bring the Capacity of Seah to agree with mine within a Pint.

However, to inform us that the Modius was less than Seah, Epiphanius tells us, that it was equal to Modius, and ¼. And Josephus, lib. 9. c. 2. and Hierom, on Matth. 13.33. say, it was an Italian Modius and an half. I know that the Modius is a disputed Measure; therefore to avoid that dispute, I counted by Sextaries, which being ⅙ of Congius, are indisputable. And if the least Capacity of Modius be taken, yet 1 and an half will somewhat exceed the Capacity I have assigned. Therefore the Seah which my Number requires, falls between a confest Defect in Suidas, and an Excess in Hierom and Josephus, yet not far from either of them, and therefore is probable, being nearer to both Extreams in those Authors, than they are to each other.

My fourth Argument is from the agreement of this number of solid Inches, with the content of 432 Hens Eggs, whereby the Jewish Doctors frequently determine the Capacity of Epha; as may be seen in Buxtorf's Lexicon, in 〈 in non-Latin alphabet 〉 in Arias Montanus, Tubal-Cain, &c. Now if we divide my Number 1747, by 432, it will quote 4.04: which shews, that little above four solid Inches must be in an Egg, that 432 of them may make this quantity. And Experience attests, that the larger sort of Hen Eggs, which yet are common, will contain four solid Inches of Water, or two Ounces and a third: and Measures when taken from Nature, are rather taken from the bigger Instances, than the less, as the Greek Foot from Hercules his Foot, and the Cubit from the Elbow to the Fingers end of a tall Man.

This experimental way I chuse as more easy, than the Geometrical reduction of an Egg to a Sphaeroid, or two Conoides, which few would understand. I might also shew, that as some, both Jews and Christians, have assigned less Capacity to the measuring-Egg than I; so others, particularly Capellus, have given more: And that this Capacity may therefore be called a Mean Capacity, although it come near to the largest sort of Hen Eggs; but it is sufficient to have pointed at these things.

The Fruits of this long, because difficult investigation of the Epha, will be gathered in the easy determination of the other Measures of Capacity, whose Proportions thereunto are generally agreed on. For besides a Bath, which is equal to it, it will follow, that

  Sol. Inches. Wine Gal. P. Inch. Corus, or Chomer, viz. 10 Epha's 17477 75 5 7 Seah the third of Epha 582.5 2 4 3 Hin the sixth 291.25 1 2 15 Homer the tenth 174.77 0 6 05 Cab the eighteenth 97.08 0 3 10 Log the seventy-second 24.27 0 0 24.2

In this Reduction to our Measures, I have used the Wine-Gallon, because more generally known and used among us, notwithstanding the Corn-Gallon is the Statute-Measure. And because the Epha and Homer after this Reduction fall out to answer very near known Meafures; Homer to three Quarts; Epha seven Gallons, a Pottle and half a Pint. Also in the Corus I have express'd the last seven solid Inches, although in Epha, its tenth part. I often omit the seven Tenths of a solid Inch as inconsiderable, because it grows considerable when it's multiplied by Ten.

To remove the Objection which lies open against these Measures, that thereby an Homer becomes too great a quantity of Manna, to be allow'd, as it was by God to every Man, for his sustenance in the Wilderness; let these things be considered.

1. That Divine Bounty is concerned to proportion to each Man, now travelling, so much, that he may rather leave somewhat, than lack.

2. That Manna being like Coriander-seed, of a globular figure, when it was in the Homer, must necessarily leave many empty Spaces, between every three or four Sphaeres, which had no Food in them; and these Vacuities added together, may reasonably be estimated about a third part of the Vessel's Capacity. For the solidity of a Cube, many of which will fill up a space without any empty Interstices, is almost as big again, as a Sphere, whose Diameter is equal to the Cube's side: the Geometricians say, as 1 to .523 ∷

3. It being light food, must needs be inwardly porous, and of a spongy contexture of Parts.

4. It would probably waste somewhat in dressing by the Fire, as it melted and wasted when the Sun grew hot. By these Reasons the three Quarts at first measuring will be reduced to to about three Pints of an oily liquid substance, which will not be too much for a Traveller, that needs eat thrice a day.

The Homer being thus freed from an obvious Objection, before I leave it, I think fit not only so observe the Antiquity of the Numeration by Tens in these Measures, Corus holding 10 Ephas, Epha 10 Homers: but also to add, that I have observed, that the Athenian Measure, Cotyla, (which, as I have intimated, held 10 Ounces of Water, and so was half a Roman Sextarius) must needs therefore be the tenth part of an Homer, as I before shewed it to be the twelfth part of the Roman Congius. And we shall less wonder that Athens carried on this Subdecuple Proportion in one of their Measures; if we consider that Athens was a Colony both from Sais in Egypt, and from the Phaenicians, as the best Antiquaries and Geographers agree.

By help of this Observation, we may note, that this Cotyla is a common Measure, to most (if not all) the Measures of Capacity, used among the Jews, with other Eastern People, and these Western famous Nations, the Greeks and Romans: and so may serve to shew the Harmony between them, and their Reduction to such an ancient Standard as the Congius of Vespasian, which is yet kept at Rome; and may suggest a probability that the common Original of them (as also the rise of Mankind, and of the most necessary Learning) was from the East. Ten Cotylas make an Homer, hence the Jewish Measures may all be determined: two of them made a Sextary; hence the Congius, and other Roman Measures, three of them made a Chaenix; hence the Medimnus, and other Greek Measures. The word also is received at Rome, as well as at Athens; and I find, by Dr. Castle's Lexicon, that it's used by the Syriac and Arabic Writers of the East, although not found in the Hebrew Bible, wherein I meet not with any less measure than the Log. However, because its Root, and other words akin to it, are found in the Hebrew, and other Eastern Languages, but no Root nor Kindred in the Western: I rather believe that its Original was in the East, and the Greeks received it thence, than that the Eastern Nations received it from the Greeks.

By this Analogy between Eastern and Greek Measures, I am induced here to mention the Metretes, which St. John mentions, chap. 2.6. which we translate a Firkin, which is eight or nine Gallons Ale-measure: at which rate the Water which Christ made Wine, will rise to about 100 Gallons; which may well seem too much for our Saviour, the great Teacher and Pattern of Temperance, miraculously to provide for the Guests at a Wedding, after they had well drank before.

To remove this Difficulty, our Criticks have said many things, which I need not repeat. But I will add one Notion about this Metretes, which I have not found amongst our Commentators, which if it be admitted, will altogether prevent the Objection. I find in Cleopatra's Discourse about Weights and Measures, which with others of that Subject, is in the Appendix to Steven's Thesaurus, that Metretes, among the Syrians, consists of six Sextaries. Now it's known that the Greeks and Romans too, did often so extend the Name of Syrians, as to comprehend the Jews, especially those of Galilee, that just toucht Syria, strictly called.

Wherefore I conceive St. John, speaking of this Miracle done in Galilee on the Syrian Coast, calls that 〈 in non-Latin alphabet 〉 , which the Syrians called so, and that is the Roman Congius, consisting of six Sextaries. Now I have shewed already, that this is near a Pint less than our Wine Gallon. And so the Miracle will produce about ten Gallons and an half of our English Measure; which if the Guests were of any considerable number, might easily be drank without danger of Intemperance, especially since Marriage-Entertainments did use to last for many days, Judges 14.12.

I shall conclude this Discourse with the consideration of Solomon's Brazen Sea, that capacious Vessel for Water required in the Temple-Service. Its Height is five Cubits; its Diameter, called Breadth, ten; its Figure affirmed to be round: but it's not determined in the Scripture, whether this round Figure were an Hemisphere or a Cylinder, equally wide at the bottom and the top, or a decurted Cone that was wider at the bottom than the top, where its wideness is expressed; or whether some other irregular Figure of a protuberant Belly. Yet it's ordinarily represented to us in Cuts as an Hemisphere.

But the main Difficulty ariseth from the Capacity of it, which in 1 Kings 7.26. is expressed 2000 Baths; and yet in 2 Chron. 4.5. it is affirmed to hold 3000 Baths. The Hebrew Copies, and the ancientest Translations, constantly delivering this different Account; it's not prudent to affirm either place to have been corrupted by Error of Transcribers.

Therefore I think Grotius hath well suggested, that in the first place ordinarily, when it was not filled up, it had 2000 Baths of Water in it; but, secondly, upon extardinary Occasions, when more was requisite, as at the great Festivals, it could, and did hold that greater number of Baths. This answer gives a good general Reason of a different Content ascribed to this Vessel.

But when we come to express the Cubits of its Dimensions in determinate Numbers of Inches, and after Multiplications suited to the Figure, divide the Product by the solid Inches of the Bath, or Epha, we shall find Difficulties to arise, which this Answer will not remove.

For instance; Let us suppose the Figure of this Sea to be Cylindrical, because I shall soon shew this to be more likely than that of an Hemisphere. The Diameter of the Base of this Cylinder being ten Cubits, must, according to our determination of the Cubit, be in Inch-measure 218.88; and its Height five Cubits, is in Inches 109.44. To find the Solidity or Content of this Cylinder, we must, first, find the Area of its Base, by this Analogy taught by Archimedes. As 14 is to 11; so is the Square of its Diameter, viz. 47908.4544, to the Area of its Base 37642.1357. Then we must multiply the Area by the Height; the Product of which Multiplication is the Cylinder's Content, viz. 4119579.44. Lastly, This divided by the solid Inches of Epha, 1747, will quote 2358.08; the number of Ephas contained in that Cylinder. Hence it appears, that it will contain above 2000 Ephas, or Baths, which is the Number expressed in the Kings; yet not 3000 as the Chronicles faith, but there want 642 Baths almost.

Hence we may learn, that since a Cylinder of these Dimensions is somewhat too little to hold the 3000 Baths; therefore an Hemisphere, which is commonly offered to us of such Height and Diameter, will be much more too little. For Archimedes assures us, that it is but two thirds of such a Cylinder, and therefore will hold but two thirds of its number of Ephas, viz. 1572, and so will want 428 Baths of the 2000, or lesser Number.

Wherefore we must conclude, that either our Cubits, and Ephas, one or both, are too big; or that this Figure is to be rejected as too little. But because we have given much proof of the truth of our Cubit and Epha, and no Proof is given of this Hemispherical Figure, let that rather be rejected: but because our Cylinder doth not only answer the less number of Baths, but gives us above a third part of the superadded thousand, which is in the Chronicles, I dare not reject it. For I acknowledge that it's possible, that the Author of the Chronicles adding 1000 to those in the Kings, might only by that round Number intimate, that it held many hundreds of Baths, upon extraordinary Occasions, above those 2000 which the Author of the Kings had expressed, as ordinarily contained in it.

And indeed it's certain, that he doth not in this matter of the Sea, speak according to Geometrical accurateness: for when he had said that 10 Cubits were its Breadth or Diameter; he adds, that 30 Cubits would compass it round: whereas Geometry assures us, that above 31 Cubits are requisite to make the Perimeter to a Diameter of 10. And yet it's ordinarily allow'd in Discourse, that pretends not to Mathematical Rigour, to say, that thrice the Diameter is the Circumference; so may this Sacred Historian say, in a round Number, that the Sea held 3000 Baths, when in strictness its Content was not quite so much, but yet considerably above 2000.

Those that are not satisfied herewith, may safely assert, that this Sea was either so much wider at the Bottom, or so much swelled in the Belly, that it would contain 642 Baths more than the Cylindric Figure will yield; because there is nothing contrary hereunto in the History. And it will be more reasonable to adjust the Figure which the History determines not, to the Capacity which it doth express, than to reject the Measures asserted by so much proof, because they do not perfectly agree with a Figure which is pitch'd upon only by conjecture.

Since I came to this resolution of the Difficulty now before us, I have been confirmed in my Opinion, by reading in Dr. Lightfoot's prospect of the Temple, Cap. 27. Sect. 3. that both the Talmudists, and the Rabbins, have acknowledged that 3000 Baths cannot be contained within the Dimensions of ten Cubits wideness, and five height assigned by Scripture, unless the Figure of this Molten Sea be affirmed to be wider than that of a Cylinder below the Brims. Thus far their Assertion agrees with my Accounts, and assures me, that their Notions, both of the Cubit's Length, and of the Ephas Capacity, were not greatly different from mine, because they own with me, that this number of Ephas is indeed somewhat too great for the Capacity of a Cylinder, the Diameter of whose Base is ten, and its Height five Cubits; but that what's wanting in this Figure, may be well supplied, by widening it towards the bottom, which I also have owned; We differ only in the manner of widening it sufficiently below the Brim. For the Talmudists assign this way, That it was made square at the bottom, each side ten Cubits, and rose in this Figure of a Parallellipedon (as the Geometricians call it) up three Cubits high, but the other two Cubits of its height were a Cylinder, whose Base had ten Cubits in its Diameter. But surely they did only conjecture that this Figure would enlarge it sufficiently, and never calculated its Capacity carefully. For upon a strict calculation of the Content of this their compounded Figure, I find that it will be too little by above 250 Baths. And yet the Cubit which I have assigned and calculated by, is longer than Dr. Lightfoot's Cubit, and therefore will make the Sea sufficient to hold more than his: and the Bath I have assigned, is less than his, and therefore more of them will be contained within the given Dimensions; and so both my Measures are fitted to remove the Difficulty; whereas by his Measures, bound to the Talmudist's Figure, it's made insuperable, and involves an impossibility. But adhering to my Measures, I find that a Parallellipedon, the side of whose Square at bottom is ten Cubits, and its Height full five Cubits, will contain 3001 Baths, and a little more: whence it's plain, that if two Cubits of its Height had been Cylindrical, it must needs hold less by a considerable quantity, the Angles being taken away, which held much. Yet because in this Parallellipedon we have above a Bath more than we need, we may take off a little of the Corners near the top, and there make it Cylindric, that so it may both answer the Scripture's Historical Dimensions of about thirty Cubits, compassing it round at the top, and in some Measure agree with the Talmudist's Tradition of a little Cylinder uppermost, though it must be much less in its Height than they affirm. For it's certain, by the Principles of Geometry and Arithmetick, that if 3000 Baths of the Measure which I have assigned, be comprehended in a Figure, compounded of Parallellipedon and Cylinder, whose Diameter is but ten Cubits, and their Height taken together but five.

That, first, the Parallellipedon must have its side in Inch-measure 218.88: The Square whereof we have shewn to be, 47908.4544; and the Height of it must be, in Inch-measure, 109.24, which is five Cubits wanting less than a quarter of an Inch. So the Content of this part of the Molten Sea, will be 5233519.558.

Then, secondly; the Cylinder's Base having its Diameter 218.88, the Area thereof will be 37642.1357, and its Height must be but .2, two Tenths of an Inch; so will the Content of that short Cylinder be, 7528.427: Wherefore the Contents of both parts of this Figure being added together, will be 5241047.985. This Sum being divided by the solid Inches of the Bath 1747, will give in the Quote 3000, with an inconsiderable Fraction overplus, which I allow'd, because I would not affect overmuch preciseness, neither would I take too little. By this Process I have both demonstrated the Defect of the Talmudists Figure, and also shew'd how it may be mended, so as to serve the End for which it was intended; Rectum enim est index sui & obliqui. And now I shall leave it to the Reader's choice, either to take the Figure with a protuberant Belly, which I before proposed, which seems more Ornamental, being like that of the Cisterns used in Noble-mens Dining-rooms; or to take the Talmudical Figure with this Emendation which I have offered. And I have thought fit to examine this Talmudical Notion the more diligently, both because the learned Dr. Lightfoot in the place fore-quoted doth (according to his usual modesty) desire it might be considered; and because it seemed to me proper to oppose this Doctrine of the Talmudists, concerning the Figure of this Molten Sea, to the Conjecture of Josephus, who intimates it to have been Hemispherical, (which Geometry demonstrates to be insufficient for the reception of so many Batlis; and it's certain he had never seen it, for it was broken and carried away at the Captivity, Jer. 52.17, &c.) and their Authority concerning things Sacred, weigh much more among the Jews, than any Opinion of his.

CHAP. IV. Of Shekel, and other Weights and Coins thence determined.

I Shall not distinguish between Shekel considered as a Weight, and the same as a Coin, having no concern to enquire about the Letters and Impress that it bears, but only to express its Weight, in Weight known among us, whence its Value in our Coin will easily be deduced. I conceive that it was just of the Weight of half an ounce Averdupoise, now and anciently used here in England; or it weiged 219 Grains used in our Troy-Weight, and so wanted 21 Grains of the half Ounce Troy.

This is proved;

1. By many Shekels still remaining that differ not sensibly from this Weight, which may reasonably be thought to have been tried by the Jewish Standards, when they were coined. Of these Villalpandus reckons up many; and Greaves two; one in the Library of King Charles the First, of Blessed Memory, weighed by Arch-bishop Vsher; and another in Mr. Selden's, weighed by himself, as he witnesseth, in his learned Treatise of the Roman Denarius, p. 76, &c.

I have also seen and weighed two Shekels with Samaritan inscriptions on them (which although I had not opportunity to weigh them to a Grain) yet I do testifie they weighed within a very few Grains, as is above expressed. Nor can I find any sufficient reason to reject these as counterfeit; and if any will believe them to be such, yet it must be acknowledged, that they are made so as to agree in Weight with the Testimonies of the Ancients, which is sufficient to our purpose, because their value in our Coin may certainly be deduced thence. For since it's known that now, by the Laws of our Mint, 62 pence are coined out of every Troy Ounce; it will follow that 2 s. 4 d. and a farthings worth of Silver, with 3 Centesimals of a Penny over, must be contained in 219 Grains, which is the Shekel's weight. By this Analogy; as 480 s. are to 62 d. so 219 s. are to d. 28.28 Decimals of a Penny, which make 1 Farthing, and near the 8th part of a Farthing.

My second Argument is taken from Testimony of Antiquity, thus: The Shekel was equal to the Roman half Ounce, but that was 219 Grains of our Troy Weight: therefore so was the Shekel. The Major is affirmed by Jerom on the 4th Chap. of Ezechiel, to contain four Drachms of the Latin Ounce. The Greek Author of Farrier-Weights saith, 〈 in non-Latin alphabet 〉 , -: which is the Mark for 〈 in non-Latin alphabet 〉 , or Semissis: where 〈 in non-Latin alphabet 〉 plainly signifies the Shekel, and is falsely rendred in Stephanus by Siciliquus, which is agreed to be but a quarter of an Ounce, whereas this is affirmed to be half, by the Author.

So also Stater, which is known to be the same with the Shekel, is twice affirmed by Cleopatra, to be four Drachms, which is half an Ounce.

To these may be added the clear Testimony of Moses Nehemanni Gerundensis, related in Arias Montanus; wherein he owns himself to have formerly doubted of this which was Solomon Jarchi's Judgment, but to have been convinced and satisfied by weighing a Shekel with Samaritan Inscription, which was just half an Ounce. Many more Testimonies of Rabbins might be added, but I think them not necessary.

Only I will add a Testimony of Anton Augustinus, concerning two fair Carthaginian Coins, weighd by him, which each of them answered to four Drachms, or rather little more. Now it's known the Carthaginians were a Tyrian-Colony, and that the Jewish Coins agreed in Weight with those of Tyre the Talmudists affirm. Hence the Major seems abundantly evident. The Minor is vouched by Greaves, who diligently compared and tried the Roman Standard Ounce, with the Ounce and Grains of our Standard. And Villalpandus, with others, have from the Weight of Water in the Congius yet remaining, proved, that the Ancient and Modern Roman Ounce, is exactly the same unaltered by Time.

From hence I collect, or conclude also, that our English Averdupoise Ounce also, being (as I before shewed) the same with the Roman Ounce, when they are both reduced to Grains of Troy-Weight, was probably introduced into our Kingdom by the Romans, when they gave Laws, and planted Colonies here, and hath thence continued unchanged to this day; which is not commonly observed, because we use the Averdupoise Weight only about heavier Commodities, not in weighing Silver and Gold, and therefore do not divide that Ounce into Grains, as we do the Troy-Ounce, which I suppose was introduced by the Normans, because it take its name from a French Town Troyes in Campaigne. I may add also, that it's probable hence, that both the Roman Ounce, and our Averdupoise Ounce, had their more remote Original from the Eastern Shekel doubled: and evidence may be given, that such Weights and Coins, consisting of two Shekels, were sometimes used in the East by the name of Selahs; but I must not digress farther.

A third Argument may be taken from the constant Tradition of the Jews, that their Shekel weighed 320 common Barly-Corns, in Schalsheleth: but these Corns ordinarily answer 219 Grains of our Weight; therefore, &c. Nevertheless it must be acknowledged, that there is no perfect constancy in this matter of Experiment, which I have made with success; yet variety of a few Grains will frequently fall out. But because Nature alters not much in the Weight of ordinary Barley, this may be accepted as a Proof, that we have assigned Shekels Weight, at least very near to exactness: but perfect accuracy is rather to be sought in the former Arguments, which bear upon the Jewish and Roman Standards, than on this which resolves it self into Nature's Constancy, to produce Grain near alike in different Times and Places; but yet doth reserve to her self a liberty of making some variety.

Such was the Shekel of the Sanctuary, or agreeable to the Standards of Weights and Measures there kept. Another Shekel half so heavy, is contended for by some Modern Jews and Christians: I confess I am not satisfied that there was any such Shekel. A piece of that Weight I acknowledg, but constantly it bears the Inscription of half a Shekel, called a Bekah, Exod. 38.26. However, it is sufficient that my care to determine the Sanctuary Shekel, doth fully determine also the Weight of its half, which must be 109 Grains and a half. They who are willing to see Arguments on both sides, may find them in Hottinger de Cippis, p. 110, &c. to whose Judgment I have nothing material to add. Also the near approach of the Roman Denarius, and of the Attic Drachma, to the fourth part of the Shekel, together with their difference from each other, and from the precise quarter of a Shekel, is well stated by Greaves, distinguishing the intrinsick Value rising from meer Weight, and the extrinsick rising from the Stamp, and Laws peculiar to several Kingdoms, in his Treatise fore-quoted, to which I therefore refer the Reader; my Business being only to give the true Weight and Value of Shekel in our English Coin, and not to compare it with those Foreign Coins for which it was sometimes exchanged by the Trapezites, who made considerable advantage by the Trade.

The Consequents of our thus stating the Shekel, are these.

1. Hereby all its Parts, and the lesser Weights or Coins, in known proportion to it, are determined: particularly hence it follows, that the Bekah, or half Shekel, is in Grains Troy 109.5. The quarter thereof, called Zuza by the Talmudists, is Gr. 54.75. Its twentieth part, which is called Gerah, Exod. 30.13. and is understood to be the same with Agurah, 1 Sam. 2.36. by Rab. Solomon and David, though we translate it indefinitely a piece of Silver, must be Gr. 10.95: which wanting but the twentieth part of a Grain of eleven Grains, may pass for just so many. And accordingly is well translated in the Septuagint, by the Greek 〈 in non-Latin alphabet 〉 : for there are Attic Oboli still remaining of this Weight mentioned by Greaves, which give another Argument to evince, that the Shekel's Weight hath been rightly stated by us, because its twentieth part, the Gerah, or 〈 in non-Latin alphabet 〉 , is found by the remaining Coins to be right.

And it's highly probable, that the Athenians being a Colony, partly from Egypt under Cecrops, partly from Phaenicia under Cadmus, brought this Egyptian and Phaenician little Weight or Mony with them. I find also in Cleopatra, that the Obolus Atticus is called the Drachma Aegyptiaca, and is there affirmed to be the sixth part of the Attic Drachma; and consequently hence we may learn to reduce to ours most other Greek Weights, whose proportion to the Drachm is given us in Galen, Dioscorides, and several other Greek Writers.

The Attic Drachm by this reckoning, must be in our Troy Weight 66 Grains; the Learned Greaves hath stated it 67. The difference of one Grain in so many, is so small, as not to be worth contending about; but I count my Reckoning sufficiently confirmed by its near approach to his.

But to return to our Gerah, or Obolus. The determination thereof is useful, because it's proved by Arias Montanus, Waser and Hottinger, out of the Rabbins and Talmudists, that this is of the same Weight and Value with the ancient Coin called Keshitah, sometimes translated a Lamb, probably because either of its Impress, or its old Value, being when Mony was rare, sufficient to buy a Lamb. This is mentioned Gen. 33.19 Jos. 24.32. Job 42.11 but is expressed by St. Stephen, Acts 7.16. to be a piece of Mony.

To this Head also belongs the Investigation of the Darchmon or Adarcon, both which words, by the Septuagint, are translated 〈 in non-Latin alphabet 〉 , as both signifying the same Coin. They are mentioned 1 Chron. 29.7. Ezra 2.69 Nehem. 7.69, 70. Our Learned Brerewood hath suggested, that the Septuagint understands by 〈 in non-Latin alphabet 〉 , not that of Athens, bùt of Alexandria, which was double thereunto, and therefore is known by its help: but he adds also, that both these names of Coin, relate to those Golden Pieces coined by Darius, and thence named by the Greeks 〈 in non-Latin alphabet 〉 .

But our best help to understand these Pieces, is from the Scholiast on Aristophanes, and Harpocration, who both affirm, that they weighed as much as the Attick 〈 in non-Latin alphabet 〉 , which Pollux and Hesychius assure us weighed two Attick Drachms; that is, by our Account 132, or by Greaves's 134 Grains Troy. The forenamed Scholiast saith, that the Darius who coined these Pieces, was elder than that Darius who was Xerxes his Father. Now I find no Darius elder than him but Darius the Mede, whom Daniel mentions twice; but I find him not mentioned by this Name among the Ancients any where else, save in this Passage of the Scholiast, and consequently in these Coins, which he explains. And besides, this evinceth it possible and probable, that the chief Fathers of the Jews returning under Cyrus, might bring with them much of that Mony, which had been coined by Cyrus his immediate Predecessor, to make an Offering to Sacred Uses, as is mentioned Ezra 2.69. where we translate it Drachms; but are to understand, such as Brer wood calls Alexandrian Drachms, or double Attick Drachms. For each Daric contained more than two of our Drachms Troy, which are but 120 Grains; whereas we have shewed these to be about 132, or more.

Now the Weight being stated, the Reduction to the present Value of our Mony, is not difficult: but it must be remembred, that this is not so constant as Weight, but is altered for Reasons of State, more frequently, both in our Kingdom, and in others. However, it's fit to be known, that now, out of every Ounce Troy of Gold, taken with its appointed Alloy, there is coined in Gold Coins, the Value of 3 Pounds Sterling, 14 Shillings, and 2 Pence: which is expressed in Shillings, and Decimals thereof, thus, sh. 74.1664. Wherefore supposing the Daric Gold, and ours of the same goodness, we may find its Value in our Mony by this Analogism: As the Ounce Troy, which is 480 Grains, is to the Doric, which is 132 Grains. So is sh. 74.166, to sh. 20.395. The fourth term shews, that the Daric amounts to 20 Shillings, and about 4 Pence, which is about a third part of a Shilling. And by the same method, the whole Sum of Darics, which we translate Drachms in Ezra may be computed.

Hottinger hath suggested, that Darchemon, is derived from an ancient Persian word Dram, signifying both a Coin, and a Weight of twelve Cherats: what those were he informs us not; but I find, in Arias Montanus de Siclo, the Arabian Cherat, to be derived from the Hebrew Gerah, by a usual change of G into Ch, and that it signifies a Siliqua, or the Fruit of the Carob Tree; and that he weighed twenty such against his Shekel, and found them equal thereunto. Hence I gather that each Cherat weighed 11 Grains Troy, and therefore twelve of them amounted to 132 Grains; which agrees with our former Investigation of the Daric, and shews the Persian Drachm to be just double to the Attick. Now, though I know such a Cherat differs much from the Greek 〈 in non-Latin alphabet 〉 , in Dioscorides and Cleopatra; yet in this estimate of an Eastern Coin, I prefer Arias Montanus his Eyes, and his Scales, attesting the Weight of a Siliqua, or Cherat, before the Testimony of those Fragments, which in many Instances are corrupted.

Because the Roman Coins mentioned in the New Testament, had some relation to the Shekel, being several of them often exchanged for it, and all of them parts of the Roman Ounce, which we have shewed to be two Shekels. I shall briefly on this occasion state their Weight and Value reduced to ours. The only Silver Coin of the Romans, there spoken of, is the Denarius, which under the Caesars, in whose time Christ and the Apostles lived, was a little less than the Consular Denarius, of which Greaves hath writ very learnedly. By help of some of them which have fallen under my examination, and by taking half the Weight of the Aurei of such Caesars, which Greaves hath given us, and prov'd that their Denarii were subduple thereunto; I estimate their Weight to be about 60 Grains of our Troy Ounce. Hence their Value in proportion to our Mony (which now hath 62 Pence in an Ounce Troy) is 7 Pence 3 Farthings.

The other Roman Coins mentioned in Scripture, were Copper, and are all known parts of the Roman, As, or Assis, which before, and long after Christ's Time, was just half a Roman Ounce, and so equal in weight to the Shekel: but its Value was but the tenth part of the Denarius, which is in our Mony but three Farthings, and a tenth of a Farthing, thus written f 3 1. Hence it follows, that the Assarium, mentioned Matth. 10.29. which is determined by Cleopatra to be ¼ of the Ounce, must in value of our Coin be f. 1.55 a Farthing and an half. Hence also Quadrans, mentioned Matth. 5.26. which is ¼ of As: or 1/ •• of their Ounce, is little above three quarters of our Farthing, exactly .77 Centesimals of it. And half this 〈 in non-Latin alphabet 〉 , which we translate a Mite, is .38 Centesimals of a Farthing, or about a third part of a Farthing; yet was in weight half a Drachm of their Ounce, mentioned Mark. 12.42.

The Weights less than Shekel being thus stated, thereby we shall, secondly, pass to the determination of those which are greater, and may be called Sums of Shekels.

I. The Talent. II.The Maneh.

I. A Talent was 3000 Shekels, as may be collected by halving the Number of the Israelites (because each one brought half a Shekel) which half of their Number is 301775, and is the Sum of the Shekels which they all contributed. Now Moses assures us, Exod. 38.25, 26. that these amounted to 100 Talents, with 1775 Shekels more: wherefore that Number which dividing 301775, will quote 100, and leave 1775 in remainder, is the number of Shekels in a Talent: but only 3000 will do this; therefore 3000 Shekels are a Talent.

Hence we may easily reduce the Talent to Ounces, or Pounds Averdupoise, used in Weight among us; for we have shewed two Shekels to be our Ounce Averdupoise; therefore 1500 Ounces are in a Talent; which Number divided by 16, the Ounces of a Pound Averdupoise, gives the Pounds Averdupoise in a Talent, thus 16 ) 1500 ( 93.75. The Quote shews that 93 Pounds and three quarters of a Pound Averdupoise, are in a Talent. This Weight is the same now, and in former Ages: but the Value of this Weight of Silver or Gold, alters in several Ages considerably, as Coins do every where.

However, the Value of a Talent; 1. Of Silver. 2. Of Gold. In Mony now used, may be thus stated.

1. Every Shekel is in Pence of our present Silver Mony 28.2875, for I now compleat the Decimals of a Penny, formerly omitted in estimate of a single Shekel, as inconsiderable; but now, being to be multiplied by 3000, they will grow considerable, and give the Pence of a Talent to be 84862.5: These divided by 12, give the Shillings thereof 7071.875: The Shillings and Decimals thereof divided by 20, give the Pounds Sterling, and parts thereof, l. 353.59375; the Decimals are equal to 11 Shillings 10 Pence half-penny.

2. A Talent of Gold may hence be valued compendiously thus. Gold is now to Silver of the same Weight, As 14.356 to 1: Wherefore multiply the Silver Talent l. 353.59375 By 14.356 The Product will be 5076.191875 Which is 5067 l. 3 s. 10 d.
The Value of Gold above Silver hath grown, since the Roman Consuls Time, from 10 to above 14 and a third; and I guess it will grow still higher.

Secondly, and lastly; By help of the Shekel, we come to understand the Jewish Maneh, which was a round Number of Shekels; but with some variety in the Numbers thereof.

The best result of my search into this is, in these two Propositions.

1. That Maneh being set for a meer Weight, without respect to Coinage, contained just 100 Shekels. This seems clear, by comparing 1 Kings 10.17. (where it's said, that in each of Solomon's Shields, were three Manehs, or, as we translate it, Pounds of Gold) with 2 Chron. 9.16. where our Translation affirms, that 3000 Shekels of Gold, went to one of those Shields. And indeed, although the word Shekel be not in the Original exprest, yet it must be understood; because Ezekiel assures us, Ezek. 45.12 that by the Shekel, the Maneh was adjusted. And Pollux, lib 9 c. 6. affirms, that when we say a Golden One, we understand a 〈 in non-Latin alphabet 〉 ; as when we say a Silver piece, we mean a Shekel, although we express it not.

2. When the Maneh is set for a sum of Mony, or Coin, it contains but 60 Shekels To this number the parts of a Maneh, in Ezek. 45.12. added together, do amount. And Josephus, lib. 14.12. affirms, the Jews 〈 in non-Latin alphabet 〉 (which is derived from Maneh) to be two Pounds and an half, which reckoning 12 Ounces to the pounds, as the Greeks and Romans in his time did, is just 30 Ounces, which we have shewed to be just 60 Shekels: and Rabbi Gedaliah, in Schalsh agrees with him. Neither is it unusual to take the same word in one sense, when it relates to meer Weight, as we do a Pound (meaning thereby the Pound Troy, used in weighing Silver) for 12 Ounces; and in another sense, the same word Pound, when it relates to Mony, meaning thereby the Pound Sterling, which of Silver Coin contains not quite four Ounces; and of Gold contains not quite the third part of an Ounce.

I will not digress to consider the great variety of Minae, used among the Greeks and Romans, but only suggest that the various import of the word in these Nations, seems to have proceeded from the inconstancy of its signification in the Oriental Tongues, from whence it its derived.

I will conclude with an observation of the Harmony or good Correspondence of the Measures and Weights thus stated. The Cubit will lead to all the Measures, and to the Shekel, with the other Weights thence derived: and reciprocally the Shekel will lead, not only to the Weights, but to all the other Measures. Thus take the Cubit from the Egyptian Standard; its Cube is Ardob: the sixth of that is Epha, whose tenth is Homer, its tenth Cotyla, its tenth gives an Ounce Averd. of Water, half that gives the Shekel's weight precisely. So reciprocally take a true Shekel (as divers still remain) that doubled gives an Ounce of Water, this ten times is Cotyla, this ten times Homer, ten such are Epha, six Ephas an Ardub. Its Cube Root will agree with the Standard-Cubit of Egypt.

I will conclude this Discourse with the Proposal of a Method, whereby this Doctrine may be made useful to all Nations, most of which are unacquainted with our English Standards of Measure, or Weight, to which only I have made my Principal Reduction in this Book.

This I shall do, by shewing, that either the Jewish Cubit, or our English Foot, may be expressed and understood by a known Proportion to an universal measure, which is either already known, or may easily be found by the diligent enquirer in any Nation: such is a Thread with a Bullet annexed, adjusted by carefull tryals to that length, that every single vibration of it, will spend just a second Minute; so that it will vibrate 60 times in a first minute. This length will be the same in all Nations and Ages, and may easily enough be found, either by help of a true Pendulum-Clock, or otherwise exactly enough for humane uses. And as its Motion will serve to measure all Time, so its Length, by the help of Arithmetical Operations, and application, may be employ'd to measure all other continued Quantities. Its whole length may be called the Horary Yard, as a third part of it is denominated the Horary Foot, by the Learned Proposer of it, Hugenius, in his Treatise de Horologio Oscillatorio.

This Length being found in any Nation, may be applied to their usual Measures, whereby it will appear to the Eyes, how it must be expressed in that Nation, as in ours it is expressed by 1 Yard, 3 Inches, 25 Centesimals of an Inch; or by 39 Inches, 25 Centesimals, whereas the Jewish Cubit was found by us to be shorter, viz. 21.888.

Wherefore to find what Proportion, or Rate the Universal Measure hath to the Jewish Cubit, it will be conveniet to suppose this Measure divided into Decimal Parts, 10000; and then we may find how many such parts of that Length are in their Cubit, by this Analogy.

As the Pendulum Length in our known Measure, 39.25, is to the Jews Cubit in the same Measure, 21.888, so is the Pendulum's Length in Decimal Parts, 10000, to the Jews Cubit in such Parts, 5576 : 5. This fourth Proportion gives the Jews Cubit in its Rate to 10000, which are Terms most fit for general use; which was the thing sought for. Now, the Cubit being so determined, the Proportion of the side of an Epha answering thereunto, may be found by the Method intimated in the Harmony of Measures lately delivered. And the Epha being made 1000 part thereof, will give the Ounce, whose half is the Shekel.

Wherefore by this Method, my labour in reducing these to our English Standard, may become useful to those that know not our Standard, and consequently to all that understand the Language in which it's now written, or into which it may be translated, if it find acceptance.

Corollaries shewing the Uses of this Discourse of Measures and Weights.

1. THese are sensible Instances of God's care of Justice among Men. These determine every Man's Property, the Bounds of his Land, the Quantity of the Fruits thereof, and the Value of his Mony. Wherefore they are used, both in the first setting out of all Estates, and in all Traffic succeeding thereunto.

2. The fit Measures of the Tabernacle and Temple, to the uses of the whole Nation of the Jews, demonstrate God's early care to settle his People Israel, in the form of one entire National Church, under Moses, Aaron, and the other Priests, who were general officers for all Israel. The Church in the Wilderness, mentioned by St. Stephen, Acts 7.38. was thus National, and is the first collective Body of Men, called a Church in the Scripture-Language, by a Man full of the Evangelical Spirit.

Synagogues for particular Neighbourhoods convenience, in the publick Exercise of Religion, were introduced long after, by the pious prudence of the National Governours of the Jewish Church and State, and accordingly were all subordinate to them. It's to be observed also, that this Limited Place for publick National Worship, was within their own Nation, in the midst of their Camp in the Wilderness, in their own Land in Canaan. No recourse from it to a Foreign Church by Appeals, but all Differences finally decided within their own Nation, and therein all, even Aaron, although the High Priest, and elder Brother to Moses, yet was subject to Moses, who was King in Jesurun. By these means all Schismatical setting up of one Altar against another was prevented; National Communion in solemn and decent Piety, with perfect Charity, was promoted, which being no Shadows, but the most substantial Concerns of Religion, are to be preserved in the Gospel-Times.

3. Hereby is more evidently prov'd the Magnificence, Symmetry, and Beauty that was in the Structure of the Temple; and the liberal Maintenance which God provided for the Levites his Ministers. For if the Cubit by me proposed, determine the Area, both of the Temple, and of the Priests Suburbs (as the Scripture sets them both out by Cubits) they must be much longer, than if they were set out by so many shorter Cubits (suppose Cubits of 18 inches) in such proportion as the Squares of these different Cubits bear to each other: by the 19 & 20 Prop. of Euclid's 6th Book. But the Squares of these different Cubits are in foot-measure, which is here more convenient, as 3.82 to 2.25: the bigger of which, is near half as much more as the less. Therefore the Areas of the Temple, and of the Priests Suburbs, are according to my Measure, near half as big again, as they would be if determined by that shorter Cubit.

Such greatness of the Temple Solomon intimates to the King of Tyre to be requisite, as best suiting with the Greatness of God, 2 Chron. 2.5. This Reason alledged by Solomon to a Heathen, must be of moral or natural, and therefore perpetual Force, continuing to Evangelical Times; and therefore intimating to us, that even now magnificent and stately Buildings are usefull meanes to signify what great and honourable Thoughts we have of God, and design to promote in those that come to the Places of his Publick Worship. And from God's liberal provision of Land in the Levites Suburbs, besides other Advantages, we are taught, by St. Paul, that even so those that preach the Gospel, should live of the Gospel, 1 Cor. 9.14.

4. The Fitness, Safety, and Honour, of keeping constantly to the use of such indifferent Things, as have been determined by Law or Custom, is clearly proved by the constancy of Israel's using those Measures (altho others might be assigned, as the Greek or Roman Measures, to serve the same Ends) from the Time of Moses, and probably before, to the Captivity and after. And this notwithstanding they were used by the Egyptians and Canaanites, which altered not their Nature in the least. And this Instance proves undeniably, that such indifferent practices, as the use of these Measures, may be highly useful to the greatest Moral Duties, the Publick Honour of God, and the Preservation of Justice among men.

These Corollaries hold useful (excepting the Third, which bears upon the largeness which I have assigned) notwithstanding there may be supposed some mistake in my Determination of the Bigness of these Measures. But I hope my Reasons will justify that also.

Besides these Uses, it seems to me considerable, that the knowledg of Weights, Measures, and Coins, together with that of Numbers of all their Parts and Proportions to each other, is the prime and most obvious Instance of something peculiar to Mankind above all other living Creatures, enabling Men more than them, to civil Society, mutual Commerce and Aid to each other thereby, above all that is found in the low Correspondencies of Brutes. And agreeably to this peculiar Skill of Mankind in Numbers and Measures, we may remark, that the best Sciences which we have, viz. Arithmetick and Geometry, and our most perfect Arts, I mean, the Geometrical Doctrines of Mechanicks and Staticks, are all employ'd in this Matter, founded in the Principles of Numeration, and Mensuration, and built up by a close order and coherence of Demonstrations, such as no where else are to be found. This was, I confess, the first Motive that made me take so much pains to retrieve these Scripture-Numbers, Measures, and Weights, which are the most ancient of all whereof we have any Memoires.

Lastly; The Harmony of these Measures and Weights, so stated, will evince the Wisdom of the Ancients (probably Noah, or the Antediluvian Men) in the first constitution of them, confirms the Truth of our investigation of them, and will ease all our Memories in retaining them, and shews that some degree of Mathematical Learning was requisite, or highly commendable in the Mosaical Priests, who were to be Overseers of their Measures and Weights.

A Table of the Principal Measures, &c. herein contained.
I. Of Length. Inch Decim. 21.888 Hence are deduced; 10.944 3.648 .912 7.296 Eng. Feet & Dec. 7.296 10.944 14.592 145.92 3648

  Feet. Mil. Engl. The Eastern Mile 4000 Cubits 7296 1.3816 The Parasang, — 12000 Cubits 21888 4.1454 The 30th part thereof is a Stadium, as Herod. and Hesychius witness, — 400 Cubits, the 11th part of an Eastern Mile ,13816   The 30th part thereof is a Stadium, as Herod. and Hesychius witness, — 400 Cubits, the 11th part of an Eastern Mile 729.6 feet Eng.   Their days Journey not always equal, but set by Abulfeda at a middle rate, eight Parasangs, or 96000 Cubits 33.1632  

II. Table of Measures of Capacity.

  Sol. Inches. Wine Gal. P. Sol. Inch. Epha, or Bath, 1747.7 7 4 15.2 Corus, or Chomer, viz. 10 Epha's 17477 75 5 7 Seah the third of Epha 582.5 2 4 3 Hin the sixth 291.25 1 2 1.5 Homer the tenth 174.77 0 6 0.5 Cab the eighteenth 97.03 0 3 10 Log the seventy-second 24.25 0 0 24.2

Add the Syrian 〈 in non-Latin alphabet 〉 Congio Romano — in solid Inches — 207.06 — 7 Pints English Wine-measure, and about half a quarter of a Pint.

III. A Table of Weights and Coins.

The Shekel of Silver just half a Roman Ounce—to half our Averdupoise Ounce in Troy Grains—219, in value of our Mony, pence 28.28, that is, 2 Shillings, 4 Pence Farthing, with three Centesimals of a Peny above it, which are near ⅛th part of a Farthing.

Hence the half and quarter of Shekel are known.

Half a Shekel is called Bekah.

Its twentieth part, called Gerah and Agurah (well translated by Obolus Atticus) and Keshitah.

Hence a Talent of Silver—3000 Shekels, is in our Silver Coin, l. 353.59375, or 353 l. 11s. 10d. ob.

Talent of Gold, 5076 l. 3s. 10d.

Hence Maneh in meer Weight, 100 Shekels, in Coin 60.

The Golden Darics, or Persian Darchemons, 12 Gerahs, value 1 l. 0.4 d.

The Roman Silver Denarii—7 d. 3 far. Gold Coins double in Weight.

Their Brazen or Copper Asses, ½ ounce Weight, in value 3 Farthings, and 1 tenth of a Farthing.

Half this was Assarium, 1 Farthing, and 55 Centesimals of a Farthing.

Hence Quadrans is little above 3 quarters of our Farthing in value: And half this, called 〈 in non-Latin alphabet 〉 , translated a Mite, is about 1 third of our Farthing in value.

POSTSCRIPT.

BEcause my exactest determination of the Epha is founded in the proportion of ⅙ which it bore to the Egyptian Ardub, the Cube of their Cubit; I entreated my Learned Friend, Dr. John Moore, to enquire of Dr. Pocock, the great Oracle in Eastern Learning, whether or no he had met with any other Authority, besides what I have before mentioned, whereby that proportion may be proved. In his obliging Answer, which came after my Book was finish'd, I find that he hath confirmed it, from the chief Arabian Lexicographer, the Author of the Dictionary called Kamus; who expresly affirms Ardob to be a great Egyptian Measure, containing six Waibahs. And he hath also confirmed my Judgment, that Waibah, or Oeba, is the same with Epha, by the Authority of Abu Walid the great Grammarian.

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