PROB. 11. To find the duty of any number of barrels of common brewers ftrong beer, at eight fhillings per barrel, with the allowance of 21 in every 23 barrels. RULE. This may be done by finding a factor, thus : The duty of 23 barrels, at 8s. per barrel. = Duty of 23 barrels of common brewers X beer = Bar. Bar. Decimal. As 23 8,2 :: 1,35652, the common factor. Therefore, if any number of barrels, and quarters of a barrel, reduced to a decimal, be multiplied by it, the product will be equal to the duty in pounds, and decimal parts of a pound. EXAMPLE. What is the duty of 150 barrels of common brewers ftrong beer, at eight fhillings per barrel, with the allowance of 24 barrels in 23? factor for ftrong beer ,35652 150,5 given number of barrels PROB. 12. 35652 53,656260531. 135. 1d. the duty. To find the duty of any number of barrels of common brewers Small beer, at one filling and four-pence per barrel, the allowance being 24 in every 23 barrels. There must be a factor found for common brewers small beer, as well as ftrong, in the following manner : The duty of 23 barrels at 1s. 4d. per barrel The allowance of 2 barrels The duty of 23 barrels of common brewers fmall beer = Bar. As 23 Then the proportion for the factor is, £. s. d. I 10 8 Bar. Deci. of £oo 1,366 :: 1 05942, the factor. Therefore, if any number of barrels and quarters of a barrel, reduced to a decimal, be multiplied by it, the product will be equal to the duty in pounds, and decimal parts of a pound. 3D EXAMPLE EXAMPLE. What will the duty of 152 barrels of common brewers fmall beer amount to, at one fhilling and four-pence per barrel? PROB. 13. To find the duty of any number of barrels of common brew. ers table beer, at three billings per barrel, with the allowance of 2 in every 23 barrels. By reafon of this allowance there will be alfo a fraction in the price of one barrel; fo there must be a factor found for common brewers table beer, as well as for strong and finall. The factor is found in the following manner : The duty of 23 barrels at 3s. per barrel is 3 89016 £. s. d. 9 7 The duty of 23 barrels of common brewers table beer is Therefore, if any number of barrels, and quarters of a barrel, of common brewers table beer, reduced to a decimal, be multiplied by the above factor, the product will be equal to the duty in pounds, and decimal parts of a pound. EXAMPLE. What will the duty of 40 barrels of common brewers table beer amount to, at 3s. per barrel? The common rule by which tables for that purpose are made, is thus: Bar. £ s. d. 20 Bar. 23(61(25: 8d. gr. the duty of 1 barrel; therefore, 46 15 12 23)-186(8 2 4 8 all the fractional parts in common brewers tables for beer, are fo many parts of 23 of a farthing. PROB. 14. To find factors for reducing the odd gallons of one denomination to their equivalent value in that of another denomination, fo that they may produce the fame duty. . RULE 1. If the odd gallons to be reduced only differ in duty, and there be the fame number of gallons to the barrel, hogfhead, &c. then the factor may be found by dividing the pence that one fort is charged per barrel or hogfhead, &c. by the pence that the other denomination is charged at, vice verfa, and the quotient will be the factor required. 2. When the odd gallons to be reduced not only differ in duty, but alfo in the number of gallons to a barrel, hogfhead, &c. then the factor will be found by multiplying the pence that one fort is charged with duty, by the number of gallons in a barrel, hogshead, &c. of the other. for a dividend; which divided by the product of the number of gallons to the barrel, hogfhead, hogfhead, &c. and the duty of the other, vice verfa, the quotient will be the factor required. E. I. Required to find a factor to reduce ftrong beer, at eight fhillings per barrel to small, at one fhilling and four-pence per barrel? By Rule 1.-Firft 8s. = 96d. ÷ 16= 6, the factor required. E. 2. It is required to find a factor for reducing fmall beer to ftrong. See the first example. By Rule 1.—96) 16,000 (,166, the factor required. E. 3. It is required to find a factor to reduce odd gallons of cyder, at 18s. 9d. o qrs. 9 per hogfhead, containing 63 gallons, to its equiva lent value in gallons of fmall beer, at 1s. per barrel, whose barrel contain 34 gallons? By Rule 2. The duty of a hogfhead of cyder, 185, 9d. 0 qr.,8 = 900,8 qrs. Alfo 48 qrs. X 63 gallons 3024, the divifor ..30627,2 3024 10,128, the factor required. 3 D 2 And And in this manner you may find factors to reduce any number of odd gallons of one denomination, to their equivalent value in those of another. Note. The drawback muft be taken out of both strong and finall beer before it be reduced, as in the above example. PROB. 15. To find factors for reducing ale measure to wine and corn meajure; and e'contra, corn to ale and wine measure. To perform which, oblerve the following proportions, which are wrought by the Rule of Three Inverfe. 1,220779 factor for ale to wine. ,819148 2150,42 231 2150,42 2150,42 • 131137 7,625602 The USE of the foregoing FACTORS -wine to ale. -ale to corn. -corn to ale. -wine to corn. corn to wine, Multiply any number of gallons of ale, wine, or corn meafure, by its proper factor; the product will be the number of gallons, reduced to the meafure required. EXAMPLE. Required to reduce 63 gallons of wine to ale measure? ,819148 Factor for wine to ale. 63 2457444 4914888 Anfwer 51,606324 gallons, ale measure. And thus may any number of gallons of ale measure be reduced to corn or wine measure by the help of the foregoing factors. The way to find any FACTOR is as follows: Let a number of gallons, a hogfhead, &c. b = number of gallons in a barrel, &c. c = duty of a hogfhead, &c. d = duty of a barrel, &c. and the factor required. When the number of gallons in each are the fame, and the difference is only in the price, then ab and x = C d. PROB. 16. To find factors for falaries, both for common and leap years, at any rate per annum. RULE. As the number of days in a year is to the falary per annum, fo is one day to its falary; which decimal of the falary, for one day, will be a proper factor to find the falary of any number of days at that rate. EXAMPLE. EXAMPLE. If the falary be 51. per annum, what will the factors be at that rate, both for a common and leap year? As 366 I £. 5 Decimal. 013699, the factor for a common year. Decimals. 013661, the factor for a leap year. And in this manner was the following Table of Factors computed. A TABLE OF FACTORS FOR SALARIES. By the above table the falary due for any number of days at any rate therein mentioned may be found, both for a common or leap year; for if you take the factor of the rate, and multiply it by the number of days, the product will be equal to the falary due in pounds, and decimal parts of a pound. E. 1. Suppofe the falary to be forty pounds per annum; how much would be due to a perfon for fixty days? The factor for a common year, at 40l. per ann. is,109589 60 f. s. d. Anfwer 6,575340 6 11 6 E. 2. Suppofe the falary was fifty pounds per annum; how much would be due to an officer for 80 days? The factor for 50%. =,136986 Anfwer .80 10,958880 10l. 19s. 2d. Note. If any of the factors in the table are reduced, they will fhew the amount of a day's falary, at any rate therein mentioned. |