N. B. I have not any where treated of giving up the content by Scale and Compaffes, nor have I as yet made any mention of the Sliding-Rule, the treating of which I have referved for the following article of Gaging; having each example work'd both by pen and fliding-rule; fo that when a perfon comes to understand the nature of the flide, he may make ufe of it in any other practical cafe as well as in gaging; for the improvements on the flide are now become very ufeful, and are far more expeditious and convenient than that antique method of computing the content by fcale and compaffes. GAGING. ΤΗ GAGING. HAT gaging is included in the science of Stereometry is very plain to be understood, as the capacities or contents of all forts of veffels for liquors, &c. are computed as tho' they were really folid bodies. And herein I prefuppofe that the learner is already well acquainted with the principal rules of arithmetic, efpecially in multiplication and divifion, both in whole numbers and decimal parts; and he fhould like wife understand the rule of proportion. Alfo he ought to have fo much skill in folids as to determine at fight what fort of figure any utenfil is of, or what figure, &c. it may be reduced to, fo that its dimenfions may be taken, and the content thereof computed as near as poffible; for there is not any tun or cask, &c. fo regularly made, as by. the rules of art 'tis requir'd to be. Likewife the learner muft know, that all dimenfions in. gaging are taken in inches and decimal parts of an inch; for the content of a gallon or bu fhel, &c. is known by the ftandard of its kind to be a certain number of cubic inches, &c. which I fhall further acquaint my pupil with. And he muft alfo know that in the bufinefs of gaging, all fuperficies or areas are always understood to be one inch deep, otherwife it could not be faid (as in the gager's language it is,) that the area of fuch a fquare, or fuch a circle, &c. is fo many gallons, &c. Note. The barrel in the excife is reckon'd at 34 gallons, both for ale and beer. 1 fhall I fhall firft begin with finding the areas of fuperficies in ale and wine gallons, and in malt bufhels. EXAMPLE Ift. Suppofe a fquare (which has all its fides equal,) and the fide 45.5 inches ; what will its area be in ale and wine gallons, and in malt bufhels? RULE. Multiply the length or breadth (being here equal) into itfelf, and the product will be the area in inches; then divide by the cubic inches in the refpective gallon, &c. and the quotient will be the area requir'd. 282 in a ale gallon, Cubic inches. 231 in a wine gallon. 2150 in a malt bufhel. 45.5 45.5 2775 2275 1820 282)2070.25(7.34 1974 962 1164 1128 37 See the remainder of the work in the next page. The fame by the Sliding-Rule. Set each proper divifor upon A to a fide of the fquare on B, then against the other side of the fquare on A is the area on B: EXAMPLE 2d. Let the length of a tun, back, cooler, ciftern, couch, &c. be 145.3 inches, and mean breadth 88.6 inches; what is the area in ale, wine, and malt? RULE. Multiply the length by the breadth, and divide by the cubic inches, &c. See the work in the next page. |