2. One gallon, dry measure, contains 268.8 cubic inches; consequently a pint is 33.6, a quart 67.2, a peck 537.6, and a bushel 2150.42 cubic inches. 3. It has been ascertained by experiments, that after the saccharine substance has been extracted from malt, by the opération of mashing, its bulk is diminished a little more than one-sixth part of the whole; in consequence of which the mash-tun gallon is always taken at 227 cubic inches. A Description of THE SLIDING RULE. THIS instrument is in the form of a parallelopipedon; has four sliding pieces, which run in grooves, and is commonly made of box. It was invented by Mr. Thomas Everand, about the year 1683, and is generally called Everand's Sliding Rule; but it has since been much improved by Mr. Verie. It is of various lengths, as, 6, 9, 12, 18 inches, &c.; but 12 inches is the most common length. This rule is much used in Gauging, in consequence of the ease and expedition with which calculations may be made by it. Upon the first face of the Rule, is a line marked A, which is called Gunter's Line, from its inventor Mr. Edmund Gunter; and is numbered from the left ta the right with the figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; and the spaces between each of these figures are graduated into subdivisions. At 2150.42, is a brass pin, marked MB, signifying the cubic inches in a bushel of malt; and at 282, is another brass pin, marked A, denoting the number of cubic inches in a gallon of ale. The second line on this face is upon the slide, and marked B. It is divided exactly in the same manner as that marked A. There is also another slide B, which is used with the former; the two brass ends are then placed together, in which position they form a double radius. At 231, on the second radius, is a brass pin, marked W, denoting the cubic inches in a gallon of wine; and at 3.1416, is another brass pin, marked C, signifying the circumference of a circle whose diameter is 1. By these lines, multiplication, division, proportion, &c. may be performed; and the manner of reading and using them is precisely the same as the lines A and B, upon the Carpenter's Rule. See Section 2, Part IV. Upon the back of the first slide, marked B, are placed the divisors for ale, wine, mash-tun gallons, malt, green starch, dry starch, hard soap hot, hard soap cold, &c. as in the following Table; and the back of the second slide, marked B, contains the gauge-points correspondent to these divisors, where S stands for squares, and C for circles. Upon the same face of the Rule, is another line marked MD, signifying malt-depth; and is numbered from the right to the left, with the figures, 3, 4, 5, 6, 7, 8, 9, 10, 2. The 1, or 10 on this line is placed directly opposite to MB, on the line A; and if it be called 1000, the last division at the left end of the Rule, will denote 2150.42, the cubic inches in a Winchester bushel. This line is used with the lines A and B, in inalt gauging. Upon the second face of the Rule, or that opposite to the one already described, is a line marked D. This line begins on the upper edge of the Rule, and is numbered from the left to the right with the figures 1, 2, 3, 31, 32, which is at the right end of the Rule. The line is then continued from the left end of the other edge, 32, 4, 5, 6, 7, 8, 9, 10. At 17.15 is a brass pin, marked WG, signifying the circular gauge-point for wine gallons; and at 18.95, the circular gauge-point for ale gallons, is another brass pin marked AG, There is also a brass pin at 46.37, marked M'S, which is the square gauge-point for malt-bushels; and at 52.32 is another, marked MR, denoting the round or circular gauge-point for malt bushels. Upon this face of the Rule, is a line marked C. This line is upon the slide; and is numbered and divided in the same way as the lines A and B. Belonging to the Rule, is also another slide C, which is used with the former, in the same manner as the two slides marked B. The line D, on this Rule, is similar to that marked D, on the Carpenter's Rule; and is used with the two slides C, just described; in finding the contents of vessels whose form is that of a cube, a parallelopipedon, a cylinder, &c. &c. By these lines the square root of any number may also be readily extracted; for if 1 on C be set to 1 on D, we have against any proposed number on C, its root on D. The back of the first slide, marked C, is divided, next the upper edge, into inches and tenths; and numbered from the left to the right, with 1, 2, 3, 4, 5, &c.; the second line is marked spheroid, and the third second variety; and both are numbered from the left to the right with the figures 1, 2, 3, 4, &c.; and the spaces between each of these figures are divided into ten equal parts. These three lines are used for finding a mean diameter between the bung and the head of casks of the first and second varieties; which is performed in the following manner: Find the difference between the bung and head diameters, on the first line, or line of inches; then against it, for each variety, is a number, which being added to the head, will give the mean diameter sought; hence the cask is reduced to a cylinder, whose content may be found by Problem III. The back of the second slide, marked C, contains several multipliers for reducing goods of one denomi nation to their equivalent values in those of another: Thus | X to VI 6. | denotes that to reduce strong beer at Ss. per barrel to small beer at 1s. 4d. you must multiply by 6. VI to X. 17 signifies that .17 is the multiplier for reducing small beer at 1s. 4d. per barrel, to strong beer at 8s. per barrel, &c. &c. These multipliers are seldom used. The third face of the Rule contains a line marked Seg. St. or SS, signifying segments standing. This line is numbered from the left to the right, on the upper edge of the Rule, with 1, 2, 3, 4, 5, 6, 7, 8. It is then continued on the other edge, 8, 9, 10, 20, &c. to 100. This line is used with the two slides, marked C, in finding the ullage of a standing cask, or the quantity of liquor it contains when it is not full. Upon the fourth face of the Rule, or the one opposite to that last described, is a line marked Seg. Ly. or SL, denoting segments lying. This line is numbered nearly in the same manner as the last; and is used with the slides C, in ullaging lying casks. These are all the lines that are upon this Rule, which is, in my opinion, better adapted for practice, than any other with which I am acquainted. Note. There are various kinds of Sliding Rules, some of which have a line marked E, for extracting the cube roots of numbers; and others a line for the third variety of casks; they are, however, all upon the same principle, and may be easily understood from the foregoing description. The Method of finding the MULTIPLIERS, DIVISORS, & GAUGE-POINTS, Contained in the subsequent Table. THE multipliers and divisors are chiefly obtained by division in the following manner : Divisors for squares. Multipliers for squares. 282)1.00 &c. (.003546 ale gallons. Divisors for squares. Multipliers for circles. 282).785398 &c. (.002785 ale gallons. 231).785398 &c. (.003399 wine gallons. 268.8).785398 &c. (.002922 malt gallons. 227).785398 &c. (.003460 mash-tun gallons. 2150.42).785398 &c. (.000365 malt bushels. Divisors for circles. .785398) 282.00 &c. ( 359.05 ale gallons. The gauge-points are found by extracting the square roots of the divisors. |