4 or else by 5 to find out the quarter or fift part of their difference Thirdly that quarter of fift part of the difference must bee added to the halfe summe kept to make up a meane diameter Lastly there remaineth a proportion to bee wrought by multiplication and division which is this As the quadrate of 17 ⌊ 15 which Mr Gunter calleth his gauge point is to the quadrate of the meane diameter last found So is the length of the vessell measured in inches to the content of the same vessell in wine gallons Such a deale of paines and such a multiplicitie of worke is undergone in their ordinary gauging and yet when all is done the capacitie or content of the vessell so found is merely conjectural sometimes falser and sometimes truer according as the diameters of the vessell are more or lesse unequall But this way of art which I propose besides that it is constant and universall in all kinds of wine vessells is most easily performed only with one single addition multiplication as shall anon bee declared both by rule and examples Soe that now I hope I have made Mr Gauger amends for the too much difficultie and paines hee thought my booke put him to and that henceforth hee will bee as earnest to vindicate my credit also as hee hath egerly traduced it before he rightly knew me For although I cannot so well excuse his rashnesse in impertinent interposing himselfe in questions hee had small skill in yet I perswade my selfe he had no malice against my person who was then utterly unknowne to him And for my part for ought I remember I had not so much as heard of any such officer about the Citie But I wholly impute his offence at me partly to the high estimation hee had of Mr. Gunter from whom to dissent he thought to be a hainous matter and partly to his dissidence and distrust of my rule how it might hold when it came to tryal And therefore I doe willingly returne againe into favour with him and recommend this my invention and my selfe to his future approbation and friendship assuring him that what I have before written was not intented against him but onely to shew the true occasion how I fell upon this search and disquisition which in regard of my profession seemed to bee very necessary The principles whereon the way Two principles or grounds of this gauging instrument that I teach is grounded are these two First that a wine vessell is in forme of a perfect sphaeroide with the two ends equally cut off The truth of which ground appeareth both by the generall consent of almost all who have written of gauging and by the fabric of such kind of vessels which by the workemen and makers thereof so farreforth as in practise they are able are intended to bee such And now lately by tryal made thereof with the Standard whereunto it is found to hold greater correspondence in all kind of those vessels then could bee hoped for or almost imagined Secondly that a sphaere or spharoide containeth two third parts of a cylinder hauing the same length and thicknesse and consequently that the solid convexitie betweene two cylinders one within the sphaeroide and the other without touching it and having the same center and height is equall to two third parts of the difference of those two cylinders which hath long since beene taught by the ancient Siracusan Archimedes in his first booke of the Sphaere and Cylinder in his booke of Cone-like and sphaere-like magnitudes of late by our English Archimedes Mr Henry Briggs in his Treatice of Arithmetica logarith mica Out of the consideration of these two principles or grounds I framed my rule which I set downe in my booke of the Circles of proportion Chapt. 9. in these words Measure The rule of Gauging framed out of those tvvo grounds the two diameters of the vessell in ynches or else in tenth parts of a foot the one at the bung hole the other at the head and also the length within And by the diameters found find out the circles then adde together two third parts of the greater circle and one third part of the lesse Lastly multiply the aggregate by the length so shall you have the content of the vessell either in cubic ynches or cubic tenth parts of a foot Which afterward in the end of that Chapter having first inquired the quantity of a gallon both Ale and Wine measure in solid ynches the one to bee 272¼ the other 231 I taught how to reduce into gallons and hundreth parts by dividing the whole number of ynches contained in the vessell by either of those two numbers respectively And this is that very rule the worke and practice of which I have by art with an invention not yet thought upon by any other and with divisions calculated for that purpose sitted and applyed to this my new gauging line or rod. It consisteth of two rulers of brasse The gauging rod described and of the severall parts thereof about 32 ynches of length which also are halfe an ynch broad and a quarter of an ynch thick that being set together they may make halfe an ynch square At one end of both those rulers are two little sockets of brasse fastned on strongly by which the rulers are held together and made to move one upon another and to bee drawne out unto any length as occasion shall require and when you have them at the just length there is upon one of the sockets a long Scrue-pin to serue them fast These two little sockets encompasse not both rulers quite round but have each of them a slit about a quarter of an ynch board that they may not hinder the sight of the divisions which are upon the broad or flat sides of the rulers Which divisions are indeed of most principall use being properly the gauge-divisions and are now first of all invented and accommodated to the mensuration of vessels The gauge-divisions are in all two hundred and thirtie of which every particular division standeth for one hundreth part of a wine gallon so that they are in all a wine gallons and 30 hundred parts And for the more perspicuous distinguishing of them they are figured by tens thus 0 ⌊ 10 0 ⌊ 20 0 ⌊ 30 0 ⌊ 40 0 ⌊ 50 0 ⌊ 60 0 ⌊ 70 0 ⌊ 80 0 ⌊ 90 1 ⌊ 00 1 ⌊ 10 1 ⌊ 20 1 ⌊ 30 1 ⌊ 40 1 ⌊ 50 1 ⌊ 60 1 ⌊ 70 1 ⌊ 80 1 ⌊ 90 2 ⌊ 00 2 ⌊ 10 2 ⌊ 20 2 ⌊ 30 there being betweene every one of those figures ten divisions or ten hundreth parts At the other end of both the rulers is a hooke framed into right or square angles to be scrued on the one with a Scrue-pin the other with a matrix or Scrue-plate And above these hookes the edge of both rulers is divided into ynches beginning exactly equall with the ends of the hookes and figured with
5 10 15 20 25 27 30 c. And each ynch is subdivided into ten equall parts Which division of ynches together with the hookes serve to take the length of all vessels that the ends of the barrell boards overreaching the bottoms may not bee an impediment to the measuring thereof Vpon the other edge of each ruler is set the the line of Numbers which is the very same in both though some what differently figured For that on the ruler next the socket with the long Scrue-pin is noted with the figures 1 2 3 4 5 6 7 8 9 10 20 which I therefore call the line of digit numbers and that on the other ruler is figured with tens as 10 20 30 40 50 60 70 80 90 100 200 300 and I call it the line of denarie numbers Wherein you are to remember that from 1 to 5 and from 10 to 50 and also above 100 every space is subdivided into one hundred parts but above 5 unto 10 and above 50 unto 100 because the spaces are too small to receive an hundred parts they are subdivided but into fiftie Thus having shewed the description The use of the gauging rod taught in foure rules of the severall parts of the gauging rod I now come to the use thereof in measuring any kind of vessel by the wine gallon For which I will set downe these fower rules Rule I. How to take the length of a Vessell HAving first sitted the two hookes upon the ends of the two rulers so that the line of ynches may be uppermost draw out the rulers in length and apply them to the vessell long wise so that the two hookes may embrace the two bottoms thereof at that length scrue them fast together with the long Scrue-pin in the socket then take off the hooke which hath the Scrue-pin and looke how many ynches the socket of the ruler which hath the hooke on doth cut in the ruler without the hooke for that shall be the length of the vessell from out side to out side in ynches wherefore if out of that measure you take the thicknes of the two bottoms which may bee easily estimated by a spigot hole you shall have the true length of the vessell within But if the length of the vessell be lesse then 27 ynches you cannot use both hookes as before was done Wherefore apply the ruler which hath the matrix or Scrue-plate to the vessell setting that hooke against one of the bottoms and where the divisions of ynches in that ruler beginneth stick up a knife then remove that same hooke to the other bottome and the ynches which the knife cutteth shall give the length of the vessell from out side to outside Rule II. How to take the Diameters of a Vessell at the Bunge and at the Head and how to adde them together that you may finde the summe of them THe Diameters are not measured by ynches as the length is but by Wine gallons and hundreth parts in this maner Take off the hook which hath the scrue-pinne and dipp that end of the Ruler into the Vessell at the bung and looke how many parts of the divisions of Gallons the inside of the bung-hole doth cut the same shall bee the Diameter at the bung In like maner apply the same end of the Ruler to the head of the Vessell without and looke how many parts of the divisions of Gallons it is broad over the midd'st or center thereof the same shall be the Diameter at the head But if the Diameter at the bung be greater then that Ruler is long draw out the rulers and scrue them at their whole length and so measure therewith the Diameters as was before shewed The two Diameters being found out must bee added together thus Write downe the Diameter at the bung twice and under it the Diameter at the head onely once setting like places one under another in the same rowes that is all the unites in one rowe all the tenth parts which are they next the units in another row and all the hundreth parts in the last row and draw a long line betweene the unites and the parts then adde them all three together into one summe by the way of ordinary Addition As in example Suppose a Vessel that hath the diameter at the bung gallon 1 8 hundreth parts viz. 1 ⌊ 08 and the diameter at the head onely 96 hundreth parts of a Gallon viz. 0 ⌊ 96. you shall write downe the Diameter at the bung twice the diameter at the head once and adde them altogether as you see done in the side and the summe of the diameters shall bee found 3 ⌊ 12 that is gallons 3 and 12 hundreth parts And thus shall you doe in all Vessels Rule III. How to multiply the summe of the Diameters of a Vessell by the length THe length of a Vessell being measured in ynches and tenth parts and the Diameters being found out in Gallons and hundreth parts and also added together as hath beene declared The summe of the Diameters is to bee reconed in the line of digit numbers which is noted with the figures 1 2 3 4 5 c. and the length in the other line of denarie numbers which is noted with the figures 10 20 30 40 50 c. In both which lines of numbers you are to consider that in the spaces betweene the figures every tenth division is distinguished with a long line and every single division with a short line and every fift with a line of a length betweene both and in the line of digit numbers they signifie so many hundreth parts of a gallon But in the line of denarie numbers as also in the line of digit numbers beyond 10 every tenth division is for unites and every single division is for tenth parts and beyond 100 every tenth division is for ten and every single division for one unite Where note that in those spaces which by reason of their smalnesse have but 50 yet they are understood to bee 100 by imagining every one to containe two The nature and valuation of both the lines of numbers the digit and the denarie being understood multiplication is thus to be wrought Set the unite place of the line of digit numbers marked with 1 to the place of the length of the Vessell reconed in the line of denary numbers there scrue the Rulers fast then in the line of digit numbers recon the summe of the Diameters found out that at the Bung being doubled as was taught before and looke what space and division it poynteth out in the line of denary numbers the same being reasonably aestimated shall bee the product sought for By aestimating reasonably I understand that you consider whether the figure of that space is to bee taken for tenns or for hundreds which is done very easily for no man is so simple as to mistake a Vessell of ten or twenty Gallons for one or two hundred or of one or two
proposed in wine gallons upon the ruler figured with denarie numbers as hath before beene taught and thereto set the marke w and so shall the other marke a point to the number of beere gallons contained in the same vessell I will shew the practice of this Rule by the vessells measured in the three last examples First The Canarie pipe whose length was ynches 48 ⌊ 5 and the diameter at the bung gallon 0 ⌊ 93 and the diameter at the head gallon 0 ⌊ 54 the measure whereof was by Example V found to be gallons 116 ⌊ 4 how many beere gallons will it containe Set the marke w unto the wine measure 116 ⌊ 4 reconed upon the ruler figured with denarie numbers scruing it there fast and the marke a shall in the same ruler point out 98 ⌊ 76 that is gallons 98 and 76 hundreth parts the content thereof in beere measure Againe The Graves hogshead whose length was ynches 31 ⌊ 2 and the diameter at the bung gallon 0 ⌊ 73 and the diameter at the head gallon 0 ⌊ 57 the measure whereof was by Example VI found to bee gallons 63 ⌊ â—4 how many beere gallons will it containe Set the marke w unto the wine measure 63 ⌊ 34 reconed upon the ruler figured with denarie numbers scruing it there fast and the marke a shall in the same Ruler point out 53 ⌊ 74 that is gallons 53 and 74 hundreth parts the content thereof in beere measure Lastly the High countrey hogges-head whose length was ynches 30 ⌊ 82 and the diameter at the bung gallon 0 ⌊ 63 and the diameter at the head gallon 0 ⌊ 51 the measure whereof was by Example VII found to bee gallons 54 ⌊ 55 how many beere gallons will it containe Set the marke w unto the wine measure 54 ⌊ â—5 reconed upon the ruler figured with denarie numbers scruing it there fast and the marke a shall in the same ruler point out 46 ⌊ 28 that is gallons 46 and â—8 hundreth parts the content thereof in beere measure And now I have finished what I determined to write concerning the use of this my new Gauging line or rod and have made it so plaine and easie that I doubt not but every meane capacitie will bee able with a little care to apprehend the meaning and practice I have also delivered the Rule which I follow and whereupon I ground this worke only the maner of computing the Gauge-divisions I have concealed both because that speculation is impertinent to the managing and hand-working therewith and also that because unto men of art by comparing the rule with the performance it will not bee difficult to find out the reason but especially because I intend and wish the benefit of making and fabricating this Instrument unto Mr. Elias Allen who gave the occasion of it and at whose request I invented it And if it shall bee serviceable to this most illustrious Citie as a meanes of keeping truth and equitie in that kind and acceptable to you Right Honourable LL and to you Right Worshipfull to whom I present it and conducing unto the glory of Almighty God the author of every good abilitie it hath obtayned the desired END PErlegi hoc opus Mathematicum cui titulus est The new artificiall Gauging Line or Rod in quo nihil reperio quod non cum utilitate publica imprimatur modò intra tres menses proximè sequentes Typis mandetur Ex aedibus Lambethanis Octob. 10. 1633. Guil. Bray THese Instruments are made in brasse by Elias Allen over against St. Clements Church without Temple-barre where also those who are desirous may bee instructed in the practicall use thereof and such as shall have occasion may have vessels gauged