To Gage and Inch a Round Mash-Tun To Gage and Inch a Square Mash-Tun To Gage and Inch an Oval Mash-Tun To Gage and Inch a Square Jack-Back To Gage and Inch a Round Hop-Tun To Gage and Inch an Oval Hop-Back To Gage and Tenth a Rectangular Cooler To Gage and Tenth a Multilateral Cooler To Gage and Tenth an Under-Back To Gage and Inch a Square Guile-Tun To Gage and Inch a Round Guile-Tun To Gage and Inch a Guile-Tun with Tapering Sides To Gage a Spheroidal Cask by a Table of Quotients TABLES OF QUOTIENTS FOR FOUR VARIETIES THE NEW PRACTICAL GAGER. AS all instruments used in gaging are decimally divided, and as the dimensions of every utensil are taken in inches and tenths, the best introduction to Practical Gaging must evidently be a succinct account of decimal fractions. OF DECIMALS. In decimal arithmetic the unit is supposed to be divided into parts, which are first, tenths; then hundredths; then thousandths; &c. of the whole. The half of any thing is therefore expressed as fivetenths, since, if in the whole there be ten equal parts, there must in the half be five. In like manner the quarter of any thing will be twenty-five hundredthparts, since, as the whole is conceived to consist of 100 equal parts, the quarter must consist of 25 of those parts. So an eighth part is equivalent to 125 thousandth-parts, because, if in the whole there be 1000 equal parts, it follows that in an eighth there will be B 125 such parts. To write these as vulgar fractions, 25 125 it would be, 100, 1000, which are respectively equal to,,. The denominators of all decimal fractions being manifestly either 10, 100, 1000, 10000, &c., they are not written but understood: for five-tenths are denoted by the figure 5 preceded by a dot, thus, 5, which dot is called the decimal point. The figure next to the decimal point always expresses tenths; the second figure, hundredths; the third, thousandth-parts; and so on. Hence 01 will represent the hundredth part of a unit, and 001 the thousandth part: wherefore ⚫378 signifies three-tenths plus seven hundredths plus eight thousandth-parts; that is in all. From this it is apparent that any finite decimal fraction may be converted into a vulgar fraction by setting under the point the figure 1, annexing to it as many ciphers as there are places in the decimal, and then expunging the point. For example, 087 will become 10009 87 and 0009 will become 10 Whereby it is evident that in decimal arithmetic, ciphers on the left of significant figures between them and the point decrease their value in the same ratio that they increase the value of integers when written after them: at the same time, it appears that a cipher annexed to a decimal cannot alter its value, inasmuch as 50 or are precisely equal to 5 or 1. 5 50 100 When a number is partly integer and partly decimal, the integer is written, as in whole numbers, before the |