Note The old Ale Gallon contained 282 cubic inches, and the old X 98324 = old Ale Gallons. X 1.20032 = old Wine Gallops. X 1.01704 = Imperial Gallons. Old Wine Gallons ........... X .83311 s Imperial Gallons. Cubic feet.... x 6.232 = Imperial Gallons. Cubic inches x .003607 = Imperial Gallons. ... IMPERIAL DRY MEASURE. 4 Gills 2 Pints 4 Quarts 2 Gallons 4 Pecks.... 8 Bushels 82 Bushels 40 Bushels .. 80 Bushels . I Gill I Chaldron 1 Last 8.665 cubic inches. 1.2837 cubic feet. .. Note.-The Winchester bushel contained 2150.42 cubic inches, and to Imperial bushel contains 2218.192 cubic inches,-hence, Imperial bushels X 1.0315157 Winchester bushels. and Winchester bushels X .969447 Imperial bushels. The Imperial bushel is now the standard measure of capa. city for all dry goods, but in measuring lime, fish, fruit, or potatoes, it must be heaped up in the form of a cone, to the height of at least 6 inches, the diameter of the bushel to be the base of the cone, which determines all bushels to be of one uniform dimensions, namely, 194 inches diameter inside, and 7.4275 inches deep nearly. A bushel of wheat is reckoned = 60 libs. Avoirdupois. Do. barley 47 Do. oats = 38 Do. peas ....... 64 Do. beans, 63 Coals were formerly sold by the heaped bushel ; 3 bushels being 1 sack, and 12 sacks | chaldron, 2 London chaldrons were equal to 1 Newcastle chaldron, the average weight of the Newcastle cbaldron being 53 cwt. ;-but that system is nearly abolished, and coals are now generally sold by the ewt. of 112 pounds, or ton of 20 cwt. Dimensions of Drawing Paper in feet and inches. Wove Antiquarian 4 feet 4 inches by 2 feet 7 inches. Double Elephant .. 3 4 by 2 2 Atlas 2 9 by 2 2 Columbier 2 9 by 1 11 Elephant 2 34 by .. 104 Imperial ... 2 5 by Super royal 2 3 by Royal 0 by Medium 10 by Demy -73 by :::: 2 DECIMAL FRACTIONS. A Decimal Fraction derives its name from the Latin, decem, “ten,” wbich denotes the nature of its numbers, representing the parts of an integral quantity, divided into a tenfold proportion. NUMERATION Teacheth to read or write any number proposed, either by words or characters. In Decimal Fractions, the integer, or whole thing, as a gallon, a pound, a yard, &c. is supposed to be divided into ten equal parts, called tenths; those tenths into ten equal parts, called hundredths; and those hundredths into ten equal parts, called thousandths; and so on, without end. So that the denominator of a decimal being always known to consist of a unit, with as many ciphers as the numerator has places, is, therefore, never expressed, being understood to be 10, 100, 1000, 10000, &c. according as the numerator consists of 1, 2, 3, 4, or more figures; thus, instead of o, o, 2006, the numerators only are written with a dot or comma before them, thus, .2, .24, .211. If a unit of any kind, as a gallon, a pound, &c., be divided into ten equal parts, then the decimal represents as many of those parts as the decimal figure expresses,—thus, 7 means seven of those parts, or seven-tenths; but if the decimal consisted of two figures, unity would be understood to be divided into a hundred equal parts, of which the decimal represents as many as the figure expresses,—thus, .65 means sixty-five of those parts, or sixty-five hundredths; and if the decimal consisted of three figures, unity would be supposed to be divided into a thou. sund equal parts, of which the decimal represents as mądy as the number expresses,- thus, .625 is six hundred and twenty-five of those parts; or, if the decimal .0625, unity would be understood to be divided into 10,000 equal parts : but the value of figures is made more plain by the following TABLE. Tenths .56 .567 Ten thousandths .5678 Hundred thousandths, &c. ... .56789 Thus, .5 is read five-tenths; .56 is read five-tenths and six-hundredths, or fifty-six-hundredths; .567 is read five-tenths, six-hundredths, and seven-thousandths, or, five hundred and sixty-seven thousandths; and so on, as in the table. Ciphers, to the right hand of decimals cause no difference in their value; for .5,.50, .500 are decimals of the same value, being each equal to a ; that is, .6=to, .50=13, .500=H. But if ciphers are placed on the left hand of decimals, they diminish their value in a tenfold proportion; thus, 3, .03, .003, are three-tenths, three-hundredths, and three-thousands, and answer to the vulgar fractions to, tšos Toco respectively, A whole number and decimal are thus expressed, 85.75, 85.04, &c. REDUCTION OF DECIMALS. By reduction we change vulgar fractions, and the lesser parts of coin, weight, méasure, &c. into decimals, and find the value of any decimal given. Because decimals increase their value towards the left hand, and decrease their value towards the right 96 hand, in the same tenfold proportion with integers, or whole numbers, they may be annexed to whole numbers, and worked in all respects as whole numbers; and if simple arithmetic be well understood, there is little more to be learned than the placing of the separating point,-the rule for which ought to be well attended to. 1.-To reduce a vulgar fraction to a decimal of an equal value. RULE. -Add a cipher, or ciphers, to the numerator, and divide by the denominator, the quotient will be the decimal required. EXAMPLE.-Reduce 14 to a decimal. 32) 14.0000(.4375 Thus you may take any number 128 of ciphers at pleasure, but their number will be best aseertained 120 when the work is finished ; then you must have as many decimal 240 figures as you have taken annexed 224 ciphers in dividing; and if there are not so many in the quotient, 160 160 you must prefix ciphers to the left hand of it, thus, = .03125. Sometimes the quotient figures will repeat continually, as , thus, = .666, then it is called a re. petend, and the last figure may be dashed or marked, to distinguish it from a terminate decimal. Sometimes two, three, or more figures will repeat, as {}, thus, =.3636; such are called compound repetends or circulates, and the first and last figure may be dashed or marked. 2.-To reduce the lesser parts of coin, weight, measure, &c. to decimals. RULE.—Divide the least name by such number as will reduce it to the next greater; to the decimal so obtained prefix the given number of the same 1.0000 32 2.000 3 12.000 33 |