EXAMPLES. Divifors. Dividends. Quotients. Sq. Rts. ,7854) 282,0000(359,05 (18,95 Ale gallons 345 In like manner any other divifor, or gauge point, may be found, wher the folid capacity of the integer is given, whether it be a gallon, bufhel, or a foot, &c. and in this manner was the following table computed. PROB. 2. To find factors for circles. RULE. Divide,7854 by the folid capacities of each gallon, bufhel, &c. and the quotients will be proper multipliers for the fquare of the diameter of any circle, to reduce the area of that circle into ale, wine, malt gallons, or bufhels, &c. 7854,00346 Wine gallons Malt bushels Mash tun gallons And in this manner were the other factors found for circles, in the following table. PROB. 3. To find factors for fquares. RULE. Divide unity by the folid capacity of each gallon, bufhek foot, &c. and the quotients will be the proper factors or multipliers. EXAMPLES. 282, 1,000000(,003546 factors for Ale gallons 231, 1,000000(,004329 268,8 1,000000(,003720 2150,42) 1,000000(,000465 Wine gallons Malt gallons Malt bushels Mafh tun gallons. 227, )1,000000(,0044 PROB. 4. To find gauge points for fquares. RÚLE. Extract the fquare roots of the folid capacities of each gallon, Bushel, &c. in inches, and it is done. A TABLE OF FACTORS. Multipliers, Divifors, and Gauge Points, for Squares and Circles. Divifors for Gauge Pints for Factors for Squares Gircles. Squares. Circles. Squares Circles. PROB. 5. To find the area of a fquare tun, back, or cooler, &c. RULE. Multiply one fide of the fquare by itself, and that product multiply or divide by the factor, &c. for fquares, and the product, or quotient, will be equal to the area of the fame kind as the factor or divifor made ufe of. EXAMPLE. What is the area in ale gallons of a square, each of whofe equal fides is 30 inches? Note. In gauging all fuperficies, the areas are always understood to be one inch deep. T. To find the fame by the Rule. Set the proper divifor on A to a fide of the square on B; then against the other fide of the square on A is the area on B, thus: As 282 : 30 :: 30: 3,19, the area in ale gallons as before. Or thus: Set unity on C to the fquare gauge point on D, and against any fide of a fquare on D is the area on C; thus: In like manner may the area of the fquare be found in any of the other denominations mentioned in the Table, by making use of the respective factors, &c. For if, instead of 282, I had divided by 231, 2150,42, the area, would have been found in wine gallons, or malt bushels. PROB. 6. To find the area of a parallelogram. RULE. Multiply the longeft fide by the fhorteft, and that product multiply or divide by the factors or divifors in the Table, and the product or quotient will be the area required. EXAMPLE. The longeft fide of a parallelogram is 40 inches, and the fhorteft fide 20 inches; what is the area in ale gallons? PROB. 7. To find the area of a rhombus. RULE. Multiply the perpendicular by one of the fides, and that product multiply or divide by the factors, &c. for fquares, and the product or quotient will be the area required. 2 Y 2 EXAMPLE. EXAMPLE. The fide of a rhombus is 37 inches, and the perpendicular 30 inches; what is its area in ale gallons? 37 = Side 30 Perpendicular 782)1110(3,93 Area in ale gallons, A 846 2640 1020 846 174 The fame by the Rule. B 37 :: 30: 3,93, area as before. PROB. 8. To find the area of a rhomboides RULE. Multiply the longeft fide by the perpendicular, and that product multiply or divide by the proper factors in the table, and the product or quotient will be the area required. EXAMPLE. Required the area in ale gallons of a rhomboides whofe longeft fide is 60 inches, and perpendicular 37 inches? 37 60 PROB. 9. To find the area of a plain triangle. RULE. Multiply half the longeft fide by the perpendicular, and that product multiply or divide by the factors in the table, and the product or quotient will be the area required, EXAMPLE, EXAMPLE. The length of the base of a triangle is 50 inches, and its perpendicular height 30 inches; what is its area in ale gallons? 30= Perpendicular 25 Half base = As 282 30: 25: 2,65 the area as before, PROB. 10. To find the area of a trapezium. RULE 1. Divide the trapezium into two triangles, then let fall a perpendicular from each of the angles upon the diagonal, which is a common bafe to both triangles. 2. Multiply half the diagonal by the perpendiculars, or half the fum of the perpendiculars by the whole diagonal, and that product multiply or divide by the factors in the table, and the product or quotient will be the area required. EXAMPLE. Required the area in ale gallons of a trapezium whose diagonal is 60 inches, and the two perpendiculars 15 and 27 inches? 151 27 42 } Perpendiculars 1974 46 Note. The are above found is not quite 4,47, but it is nearer to 4,47 than 4,46, and in the practice of gauging, the officers use but two decimal places of figures; therefore they take the nigheft to the fecond place, whether it be more or lefs, The |