By the Sliding Rule. 1. As the bung diameter on the line of numbers on the little slider, marked N, is to 100 on the line of fegment, marked SL, fo is the wet ́or dry inches on the line of numbers N, to a fegment upon SL; which referve. 2. As 100 upon A, is to the cask's content upon B, fo is the referved fegment upon A, to the quantity of liquor in the cask. N SL N Α SL As 31: 100: 21: 73,8; which referve. And as 100 B A B 75,37 :: 73,8: 56,6, ullage of liquor in the cask. To find the vacuity by the rule, you must work in all refpects as you did for the ullage, only, inftead of the wet inches, you must make ufe of the dry inches: Thus, N SL N SL 100:10: 26,2 which reserve. B Then as 100 In the cask 75,37 :: 26,2 : 19,7, the vacuity of cask. 55,6 Content of the cask = 75,3, nearly the fame as before. PROB. 2. To find the content of the ullage of a flanding cafk, by the pen. RULE. Divide the wet or dry inches by the length of the cask, and if the quotient exceeds ,500, add to the faid quotient one tenth part of the excefs; but if it be under,500, fubtract one tenth part of what it wants of,500; then let this fum or difference be multiplied by the content of the cask, and the product will be equal to the quantity of liquor therein, if the dividend was the wet inches; but if it was the dry inches, it gives the vacuity, or what it wants to fill it up. EXAMPLE. Let us fuppofe a fpheroidal cask pofited as above, the -length 32,5 inches, the bung 27, the head 23, the content of this cask will be 59,95 ale gallons: then let the wet inches be 8,5, I demand how much liquor there is in the cask, and alfo the vacuity? ,5000 32,5)8,50000(,2615=under,500 10),2385(,02385 of the wants of,5000 ,2615 the wet quotient 59,9 Content of the cafk. Note. The difference between the fum of the feparate parts thus found, and the whole content of the cafk, is occafioned by the line of fegments being adapted to one particular fort of calk only; which is not material, and near enough the truth in practice. LXXIV. MALT GAUGING." PROB. 1. To gauge a maltfter's fquare, or oblong ciftern. I. RULE 1. EASURE the length and breadth of the ciftern, in feveral places, and in cafe you find any variation, add the lengths or breadths together, and divide their fum by the number of dimenfions taken of each, and the quotient will be a mean length or breadth; and at the fame time alfo, the depth of the cistern. 2. To find the area of the cistern, multiply the length by the breadth, and that product multiply or divide by the proper factors for fquares malt bufhels, in page 346; and the product or quotient will be equal to the area. EXAMPLE. EXAMPLE. There is a ciftern, whofe length is 114 inches, breadth 58,5 inches, and the depth 36 inches; what is the area át one inck deep? A B 2698 By the Rule. A B Ás 2150,42 : 114 :: 58,5 : 3,1 = Area as before. Note. If any depth in inches be multiplied by the area, the product will be equal to the content of the malt in the cistern. PROB. 2. To gauge a maltfter's round ciftern RULE 1. Take mean diameters between every fix, or ten inches of the depth, and at the fame time take the depth. 2. Find the area of each mean diameter; then fquare the diameters, and multiply or divide each fquare by the circular factors for malt bufhels, in Page 346, and the product or quotient will be equal to the feveral areas required. EXAMPLE. Suppofe the depth of the ciftern be 30 inches, and the diameter at 5 inches from the bafe 29,6 inches, at 15 inches from the bafe the diameter is 33 inches, and 25 inches from the base the diameter is 36,2 inches; required the refpective areas of the mean diameters in malt bufhels. And in this manner the other areas are found to be ,40, and ,48. Note. All depths that are taken in this ciftern, must be multiplied by the respective areas to which they belong. PROB. 3. To a couch of malt, in a square or oblong frame, and find the content of the Jame. RULE. Multiply the length, breadth, and depth together, and that product divide by the fquare divifor for malt bufhels, in Page 346, and the quotient will be the content of malt in the couch. EXAMPLE. What is the content of a couch in malt bufhels, whofe length is 105 inches, breadth 104 inches, and depth zo inches? 105 = Length 104 Breadth 420 1050 10920 20 2150,42)218400,00(101,5 Content is bufhels. A As 20 •PROB. 4: To find the content of a couch, or floor of malt, having the length, breadth, and depth given in inches. RULE. Multiply half the length of the floor by the breadth, and that product by the depth; from this laft product cut off three figures to the right hand, and it will give the content of the floor seven-bufhels too much in every 100; which excefs may be deducted, either by fubtraction or multiplication. If the malt divifor had been 2000, this method would have answered without any deduction; but fince it is 2150, the multiplying by half the length or breadth, will give too much; to remedy this, if you multiply the product of the length, breadth, and depth, by 93, you will find the true content. Or, if you fubtract feven bushels for every 100, and 17 for every 10 bufhels, or ,07 for every fingle bufhel, you will have the content. EXAMPLE. Suppofe the length of a floor be 400 inches, breadth 215, and depth 4 inches; what is the content in malt bufhels? 379 159,96 Content in Bufhels. CUT LXXV. MONEYING OF CHARGES. PROBLEM I. Te money Goods at 1d. per pound. RULE. NUT off the right hand figure, which count fo many pence and farthings, and those on the left hand will be so many shillings and half-pence. EXAMPLE. What is the duty of 364 pounds of sheep-skins, at 14d. per pound? 364 = 365. 36 half-pence, and four times five farthings. 36 fhillings 4 times 1d. ·£. si d. I 16 0 PROB. 2. Το money goods at the rate of 30l. per cent. RULE. Divide the value of the goods by 5, and to the quotient add its half, whofe fum will be the duty required. EXAMPLE. Suppose the value be fix pounds, ten fhillings, and ten pence; what will the duty of the fame amount to? d. £• s. Anfwer Or the fame may be found by multiplying the value of the goods by 3C 2 PROB. 3 |