TABLE. .45 1.4364 .46.4491 Quot. Mult. Quot. Mult. Quot. Mult. Quot. Mult. Quot. Mult. .01.0017 .11 .0598 .21 .1527 .31.2640 .41 1.3860 .02.0048 .12 .0680 .22.1631 .32 .2759 .42.3986 .03.0087 .13 .0767 .23.1738 .33 .2878 .43 .4110 .04.0134 .14 .0851 .24 .1845 .34.2998 .44 .4238 .05.0187 .15 .0941 .25.1955 .35 .3119 .06.0245 .16 .1033 .26 .2066 .36 .3241 .07.0308 .17 .1127 .27 .2178 .37 .3364 .47.4618 .08.0375 .18.1224 .28 .2292 .38.3487 .48 .4745 .09.0446 .19 .1336 .29 .2407 .39 .3611 .49.4873 .0520 .2 .1454 .3 .2523 .4 .3735 .5 1.5000 To find the multiplier for any quotient from this table. .1 RULE. Take the multiplier answering to the two first quotient figures; take also the difference between this multiplier and the next greater, and multiply this difference by the given number, exclusive of the first two figures, crop off at the right hand of the product as many figures as you had figures of the given number, to multiply by, then add the remaining left hand figures of this product to the multiplier taken from the table. Examples. 1. Required the multiplier answering to the quotient .176452. .1224 next greater multiplier. .1127 given multiplier. 97 difference. x.6452 given number, exclusive of the first two figures. 625844 product. and .1127+63=.1190 multiplier. Answer. Here 63 is added because 625844 is nearer 630000 than 620000. 2. Required the multiplier answering to the quotient .3861. Ans. .3687. 3. Required the multiplier answering to the quotient .4875. Ans. .4841. 4. Required the multiplier answering to the quotient .2567. Ans. .2029. 5. Required the multiplier when the bung diameter is 30 inches, dry inches 10. Ans. .2918. 6. Suppose the bung diameter of a cask to be 31.4 inches, of which 7.8 inches were dry, whole capacity 122.4 gallons; required the ullage, and also the quantity of liquor in the cask. 7.8÷31.4=.2484 quot., and .1937-multiplier. and 122.4—23.70833=98.63112 galls. of liquor. Ans. 7. The bung diameter of a cask is 32 inches, of which 12 inches are dry, whole capacity 100 gallons; I wish to know how many gallons are contained in the cask. Ans. 65 galls. 3 qts. 8. The bung diameter of a cask is 21 inches, of which 7 inches are dry, whole capacity 32 gallons-I wish to know the quantity of liquor in the cask. Ans. 22.6624 galls. Note. If more than one half of the bung diameter be dry, use the wet inches the same as directed for the dry in the rule, and the result will be the quantity of liquor in the cask. 9. Suppose the burg diameter of a cask be 28 inches, of which 17 are dry, whole capacity 80 gallons—I wish to know the quantity of liquor in the cask. Ans. 27.4 galls. To ullage a standing Cask. RULE. Multiply the square of the distance of the liquor's surface from the middle of the cask, by the difference between the squares of the bung and head diameters, and divide the product by the square of half the length of the cask; subtract one-third of the quotient from the square of the bung diameter, and multiply the remainder by the distance of the liquor's surface from the middle of the cask. The last product divided by 294.12, will give the quantity above or under half the content of the cask, according as the wet inches exceed or fall short of half the length of the cask. Examples. 1. Suppose the length of a cask to be 40 inches, the bung diameter 32 inches, the head diameter 24 inches, the wet inches 26, and content 117 gallons; how many gallons are in the cask? 32x32=1024 square of the bung diameter. 24x24 576 square of the head diameter. 448 difference of the squares of the diameters. 40÷2=20, and 26-20-6 distance of the liquor's surface from the middle of the cask. 6×6=36, and 36×448-16128. 20×20=400, and 16128÷400-40.32 quotient. 40.32-3-13.44 of the quotient. 1024-13.44-1010.56, and 1010.56×6=6063.36 6063.36-294.12=20.615 gallons above the half content. 117÷2-59.5, and 59.5+20.615-80.115 Answer. 2. The bung diameter of a standing cask is 35 inches, head diameter 28.7, length 40, wet inches 10, content 148.5 gallons-required the content in the cask. Ans. 33.74 galls. 3. The length of a standing cask is 48 inches, the bung diameter 36 inches, the head diameter 33 inches, whole capacity 195.376 gallons, and 40 wet inches-I wish to know how many gallons are in the cask. Ans. 166.521 gallons. TABLE Showing the weight, contents in pure gold, old value, and new value of the principal gold coins throughout the world, as established by act of Congress of session 1833-24. Old standard, 22 carats-New standard, 21 carats 21 grs. by which the actual value of the Eagle coined prior to July 31st, 1834, is $10.668; that coined since, $10. Note.-The tables at pages 54, 55 and 130 were prepared previous to the passage of this act, and were inadvertently put to press without the necessary alterations being made. The pupil is requested to compute the gold coins according this table. |