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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 30 th 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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
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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 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 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 as Herodian informs us the Greeks anciently wrote 34 putting three 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 's for 30 because each Δ stood for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Ten being the first Letter of that word and each Ι for single
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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 It s 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
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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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
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 wilâ— be 6 which shews that one Ardub iâ— equal to six Ephas Thus this Proportion appears acknowledged wide in the East although I do acknowledg that severaâ— Ardubs of different Capacity from this are mentioned by Kircher as used among the Egyptians and othe◠〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 stated by the Greeks Yeâ— this sense of the word being as full attested and this being determineâ— 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 demonstrabâ—â— 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 sâ—â— 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 aâ— 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 Cubiâ— of five Palms Which differed noâ— much from our Cubit as I formerly shewed And the Cube of that Fooâ— of theirs was probably the Originaâ— of this ancient Measure the Ephâ— which a little exceeds our Foot Solid as also such their Foot and Cubit iâ— length a little exceeded ours However it 's certain that the excess of the Cubic-Root of an Ephâ— above our English Foot is not quit five Centesimals of an Inch or noâ— 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-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-Fountain-water we may well allow about 1747 such Inches to 1000 Ounces of their lighter rain-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. iâ— 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
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 8 th 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 4 th Chap. of Ezechiel to contain four Drachms of the Latin Ounce The Greek Author of Farrier-Weights saith 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ◠which is the Mark for 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Semissis where 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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
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 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 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 It s 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 It s 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