THE ROYAL GAPER; Or, Gauging made Perfectly Eafy, Ast is actually practifed by the Officers of his Majesty's Revenue of Excife. In Two Parts. PART I. Containing the practical Methods of finding the Area's and Contents of fuch Superficies and Solids, as are the Foundation of Gauging. Alfo the Established Rules for finding the Contents of all Sorts of Cisterns, Coppers, Backs, Coolers, Tuns, Stills and Cafks, when full, or Part empty: The Examples being performed here both by the PEN AND SLIDING RULE: And this not in Ale, Beer, Wine and Malt only; but in Made-Wines, Soap, Starch, Candles, Hops, Coffee, Tea, Chocolate, all Sorts of Leather, Paper, &c. which have been very confiderable Branches of the Revenue, as well as of every Excife Officer's Duty for above thirty Years paft, though yet never treated of by any Author. With the Officer's Duty in the Distillery. Freed from the Obfcurities and Errors of other Writers. PART II. Shewing the neceffary Steps to be taken for obtaining Employment in the Excife, with authentic Forms of fuch Certificates, Petitions, Oaths, &c. as are requifite for that Purpose. Together with Such Directions for the Officer's Conduct as are neceffary for afcertaining and fecuring the Duties, to which the refpective Traders are fubject; and very advan tageous to thofe Traders, who are defirous to afcertain the Amount of their respective Duties, without entirely depending upon the Skill and Integrity of the King's Officer. To which is added, Cafk-Gauging, &c. as practifed in the Port of London. The Whole illuftrated with many New Copper-Plates adapted to the Subject. The THIRD EDITION, very much enlarged and improved, By CHARLES LEAD BETTER. LONDON: Printed for E. WICKSTEED, at the Black-Swan in Newgat.-freet, near Newgate Market. 1750. © 3-1-2.3 8.m OFFICERS OF HIS MAJESTY's Royal Revenue OF EXCISE, (Who are the best Judges of the Subject here treated of;) AND ALSO TO THE BREWERS, MALTSTERS, DISTILLERS, &c. OF GREAT BRITAIN, The following TREATISE OF GAUGING Is Humbly Inscribed, BY Their Faithful And Obedient Servant, Charles Leadbetter. 418433 (iv) INCE GAUGING is one of the most useful Branches of the Mathematicks, and as the Author has had the Credit of an Employment under the Honourable the Commiffioners of his Majesty's Royal Revenue of Excife, He prefumes that his Brother Officers will expect no Apology for the prefent Undertaking. For, The Compiler of the following Sheets, far from taking a malicious Satisfaction in laying before the World the Errors and Defects of the Treatifes already extant upon the Subject of Practical Gauging, rather chufes to join with those, who have long complained, that an ufeful and general Treatife, relating to the Business of a Gauger in the Excife, has been extreamly wanted, which should treat of those Matters, after a natural and authentic Manner. Every Officer of Experience, who has had the forming of Probationers for the Excife, will concur in this Opinion, That the main Difficulty to bring young Pupils to confider thofe Things, which are to be the Subject of their future Conduct, in a proper Light, has received its Influence from the Direction of blind Guides, who have given their Minds a wrong Turn; and this Complaint, which every one must acknowledge to be well grounded, the Author apprehends, will be removed for the future, by means of the enfuing Treatife; which may furnish every Writing-Mafter and Accomptant with fuch an Infight into the Business and Duty of an Excife Officer, as their Scholars must neceffarily reap the Advantage of. And As fome Writers have attempted to perfuade the Publick, that Tables ready calculated are far more exa and ready in Practical Gauging, than the Sliding Rule; it may not be unfeafonable to obferve, That if Tables happen to be false printed, as we frequently find moft Tables are, the Officer must act at random, not knowing whether he is right, or whether he is wrong: Whereas, by the Sliding Rule, 'tis impoffible he fhould ever err; for the Ufe of that Inftrument being but once well understood, which by the Directions I have given in the following Treatife, it very easily may; the Officer, with the greatest Dispatch and Certainty, may, on all Occafions, come to the Exactnefs of the tenth Part of an Unit, which is as near as is ever required in Practice in the Excife; and therefore he is perfuaded, that those who have taken the most Pains to decry the Sliding Rule, are truly ignorant of its Excellency and Ufe. To those who understand how far the Operations in Divifion, if fet down at large, would have extended this Treatise, and of how little Service it would be to the Reader, there needs no Excufe for omitting them. Being fenfible that the Officers of Excife have little Leifure to apply their Minds to the Speculative Part of Geometry, for that Reason the Demonftration of fome of the Rules are omitted. For, notwithstanding the unneceffary Noife and Buftle fome Gentlemen have made of late about Algebra and Fluxions *, it The Rev. Dr. Ifaac Watts, a Gent. long diftinguished for his great Candor and good Senfe, having treated thefe Matters with a becoming Freedom and Judgment, (in his late Treatife of The Improvement of the Mind, Part I. Chap. XX) I fhall give the Reader an Extract of fome Part of it. Though I have fo often commended Mathematical Studies, (fays the Doctor,) and particularly the Speculations of Geometry, &c. as a Means to fix a wavering Mind, to beget an Habit of Attention, and to improve the Faculty of Reafon; yet I would by no means be understood to recommend a Pursuit of thefe Sciences, to thofe extenfive Lengths to which fome Moderns ⚫ have advanced them, this is neither neceffary nor proper for any Man, but thofe few who fhall make thefe Studies their Profeffion and Support. • The general Principles of Algebra, Geometry, &c. have their valuable and excellent Ufes, but a Penetration into the abftrufe Difficulties and Depths of ⚫ modern Algebra and Fluxions, the various Methods of Quadratures, the Menfuration of all manner of Curves, and their mutual Transformation, and twenty other things that some modern Mathematicians deal in, are not worth our Attention. And this is the Sentence of no less a Man than Dr. George Cheyne, who was a very good Proficient and Writer on these Subjects: He has not only affirmed, "That they are barren and airy Studies for a Man to "fubfift upon, but he has also had the Ingenuity to own this great but grievous "Truth, viz. That though they may quicken and fharpen the Invention, ftrengthen and extend the Imagination, improve and refine the Reasoning "Faculty, and are of ufe both in the neceffary and the luxurious Refinement A 3 "of |