GAU
( 127 )
GAU
terbiiry, and one Egelfine, an Abbot, who commanded the Forces in that County • ordering every Man, fit to bear Arms, to inarch and cover themfelves, with green Boughs in rheir Hands : In this Diiguife they met the Conqueror un- aware at S-wainfcomb ; where, difcovering themfelves, the Archbifhop and Abbot acquainted him with their Refolu- tion of ftanding and falling in defence of the Law of their Country. Upon this the Conqueror, imagining himfelfen- compafs'd in a Wood, granted, that they, and their Pofle- rity, fhould enjoy their Rights, Liberties, and Laws : Some of which, as particularly that of Gavelkind, continues to their Defcendents to this Day.
GAVELMAN, a Tenant, who is liable to Tribute.— Villani de Terring, qui vocantur Gavelmanni. Somner, Gavelkind.
GAVELET, in Law, a fpecial, and antient kind ofCef- favit, us'd in Kent, where the Cuflom of Gavel-kind con- tinues ; whereby the Tenant mall forfeit his Lands and Te- nements to the Lord, if he withdraw from him his due Rents and Services. See Fee, Service, and Gavel- kind.
The Procefs of the Gavelet is thus : The Lord is firfl: to feek by the Steward of his Court, from three Weeks to three Weeks, to find fome Diftrefs upon the Tenement ; till the fourth Court ; and if in that time he find none, at this fourth Court, it is awarded, that he take the Tene- ment into his hand in name of a Diftrefs, and keep it a Year and a Day without manuring ; within which time, if the Tenant pay his Arrears, and make realbnable Amends for the Withholding, he fhall have and enjoy his Tenement as before : If he come not before the Year and Day be paft, the Lord is to go to the next County Court, with Witneffes of what pals'd at his own Court, and pronounce there his Procefs, to have futther Witneffes ; and then by the Award of his ownCourr, he fhall enter and manure the Tenement as his own : So that if the Tenant defire afterwards to have and hold it as before, he mult agree with the Lord, ac- cording to this old Saying :
Has he not fince any thing given, or any thing paid, Then let him fay five 'Pound for his Were, e're he become Hcalder again.
Other Copies have the firft Part with fome Variation ;
Let him nine times fay, and nine times repay.
GAUGF.~<Point, of a filid Meafiire, is the Diameter of a Circle, whofe Area is equal to the folid Content of the fame Meafure. See Measure, and Content.
Thus, the Solidity of a Wine Gallon being 231 Cubic Inches ; if you conceive a Circle to contain fo many Inches, the Diameter of it will be 17. 15; and that will be the Gauge Point of Wine Meafure.
And an Ale Gallon containing 288 Cubic Inches ; by the fame Rule, the Gauge Point for Ale-meafure will be found to be 19. 15 : And after the fame manner may the Gauge- Point of any other Meafure be determined.
Hence we deduce, that when the Diameter of a Cylinder in Inches is equal to the Gauge-Vomt in any Meafure, (given likewife in Inches) every Inch in length thereof will contain an Integer of the fame Meafure. In a Cylinder, whofe Diameter is 17. 1 5 Inches, every Inch in Height con- tains one intire Gallon in Wine-meafure ; and in another, whofe Diameter is 10. 15, every Inch in length contains one Ale Gallon. ,
Gauge Line, a Line on the common Gauging Rod, whofe Defcription and Ufe fee under the Article Gauging.
GAUGER, an Officer of the King's Excife, whole Bufinefs it is to gauge, i. e. to examine, furvcy, or meafure all Calls of Beer, Wine, Oil,£i?c. and to give them a Mark of Allowance (which is a Circle burnt with an Iron, before they be fold in any Place within the Extent of this Office. See Excise, and Gauging.
GAUGING, the Art, or Afl of meafuring the Capaci- ties, or Contents of all kinds of Veffels ; and determining the Quantity of Fluids, or other Matters, contain'd therein. See Measuring, Content, (Sic.
Or Gauging is the Art of reducing the unknown Capa- city of Veffels of divers Forms ; cubical, parallelipipedal, cylindrical, fpheroidal, conical, i£c. to fome known cubic Meafure ; and of computing, for inftance, how many Gal- lons, Quarts, Pints, or the like, of any Liquor, e. gr. Ale, Beer, Wine, Brandy, Sic. are contain'd thctein. See Cube, Parallelipited, &c.
Gauging is a Branch of Stereometry. See Stereome- try.
The principal Veffels that come under its Operation, are "Pipes, 'Barrels, Rundlets, and other Casks ; Sacks, Coolers, Fats, &c. See Barrel, &c.
The folid Content of cubical, parallelipipedal and prilma- tical Veffels, we have already obferv'd, is eafily lound in
Cubic Inches, or the like, by multiplying the Area of the Bafe by the perpendicular Altitude. SeeSor.iD, Prism^C'
And for cylindrical Veffels, the fame is found by multi- plying the Area of the circular Bafe, by the perpendicular Altitude, as before. See Cylinder.
Calks of the ufual Form of Hoglheads, Kilderkins, &c. may be confider'd as Segments of a Spheroid cut oft" by two Planes, perpendicular to the Axis ; which brings them to Ol/ghtred's Theorem, for meafuring Ale and Wine Calks ; which is thus: Add twice the Area of the Circle at the Bung, to the Area of the Circle of the Head . Multiply the Sum by one third of the Length of the Caflt : The Product is the Content of the Veffel in Cubic Inches.
But, for Accuracy, Dr.lVallis, Mr. Cafitrl, &c. think, that moft of our C.ifks had better be confider'd as Frufta of pa- rabolic Spindles ; which are left than the Frufla of Sphe- roids of the fame Bafe, and Height; and give the Capacity of Veffels nearer the Truth, than cither Ougbtred'sbicthoA, which fuppofes them Spheroids; or than that of multiply- ing the Circles at the Bung and Head, into half the Length oftheCafk, which fuppofes them parabolic Conoids; or than that of Clavius, &c. who takes them for two trun- cated Cones ; which is furtheit off of all.
The common Rule for all Wine or Ale Calks, is to take the Diameters at the Bung, and at the Head ; by which you may find the Areas of the Circle there : Then taking two Thirds of the Area of the Circle at the Bung, and one Third of the Area of the Circle at the Head; and adding' them together into one Sum ; this Sum multiplied by the internal Length of the Caflt, gives the Content in folid In- ches : Which are converted into Gallons, by dividing by 282 for Ale, and by 2 5 1 for Wine Gallons.
But Gauging, as now practifed, is chiefly done by means of Inftruments, call'd Gauging Rods, or Rules, which do the Bufinels at once, and anfwer the Queftion without fo much Calculation ; which is no inconfiderable Addition, both to the Eafe and Difpatch of the Work. This Inflrumental way of Gauging, therefore, we ftiall here chiefly infitt upon. — ■
ConftruBion of a Gauging Rod, whereby the Content of any Cylindrical, or other common Veffel is eafily had.
Take the Diameter A B of a Cylindrical Veffel, A B D A, Tab. Surveying, Fig. 2<f. that holds one of the Meafures wherein the Fluid is eflimated, e.gr. Gallons; and at the Extremity A, erect an indefinite Perpendicular, A 7. From A to 1, fet off a Right Line, equal to A B ; then will B 1 be the Diameter of a Veffel, that holds two Meafures, or Gallons, of the fame Height as the former.
Again, let A 2=B 2 ; then, B 3 will be the Diameter of a Veffel that holds three Meafures,but of the fame Height as that which only holds one : And, after the fame manner, find the Diameters of other larger Veffels, A 4, A 5, A 6,
Laflly, fet off the feveral Divifions thus found, A 1, A 2, A 3,&c. upon one Side of a Rod, or Rule ; and on the other the Height, or Depth of a Cylinder, that holds one Mea- fure or Gallon, repeated, as oft as it will go. Thus is the Gauging Rod comfleat.
'Demonflration. For Cylinders, that have the fame Al- titude, are to each other as the Squares of their Diame- ters ; confequently the Square of rhe Diameter that holds 2, 3, or 4. Gallons, muft be double, triple, or quadruple of that which only holds one. And fince in the firft, A B— A 1, the Square of B 1 is double, that of B 2 triple, that of B 3 quadruple, &c ; it is evident, that the Right Lines A 2, A 3, A 4, &c. are the Diameters of the Veffels re- quired.
Thefe Divifions, therefore, being applied to the Side of a cylindrical Veffel, it will immediately appear how many Meafures, e. gr. Gallons, a cylindrical Veflel of that Bafe and of the Height of that which holds one Gallon, will contain.
Wherefore, finding by the Divifions on the other Side of the Rod, how often the Height of one Gallon is contained in the Height of the given Veffel ; and multiplying the Dia- meter before found by this Number : The Product will be the Number of Gallons the Veffel contains.
Thus, v. gr. if the Diameter of the cylindrical Veffel be 8, and its Height 12, its Content will be 96 Gallons.
Note, i° The lefs you take the Height of the Cylinder, containing one Gallon, the greater will the Diameter of the 1 " Bafe be : Whence both that, and the Diameters of the Cy- linders, containing feveral Gallons, will be the more eafily divifible into leffer Parts. Sayer directs fuch Height to be only one Digit, or Tenth of an Inch.
2 The Diameters of Veffels holding one or more deci- mal Parts of a Gallon, will be had by dividing one or more decimal Parts of the Veffel holding a whole Gallon, by its Height ; which gives us the Area of the circular Bafe 5 from whence the Diameter is eafily found by the Rules de-
liver'dt
