The content being thus found, you may proceed to inch the copper by the fame directions which were given for inching tuns in last problem. CASK-GAUGING. CASK-GAUGING is the most difficult part of the art: This difficulty arises from the variety of curves which veffels may be compofed of. It is alfo the most imperfect, and ever will be; because no cask can be made in fuch ftrick conformity to the folid it reprefents, as by the rules of art it is required to be. Gaugers have reduced all kinds of cafks to four forms, or varieties. Variety I. The middle fruftum of a spheroid-Fig. 2. Variety II. The middle fruftum of a parabolic fpindle-Fig. 3. Variety III. The middle fruftun:s of two parabolice onoidsFig. 4. Variety IV. The middle fruftums of two cones-Fig. 5. PROBLEM. PROBLEM IX. To find the content of a cask. RULE I. For Variety I. To the square of the head diameter add twice the fquare of the bung diameter, then multiply the fum by the length, and divide the product by 1077 for ale gallons. and by 882 for wine gallons. RULE II. For Variety II. To 9 times the fquare of the bung diameter add 6 times the fquare of the head diameter, then multiply the fum by the length; divide the product, as above, for ale and wine gallons. RULE III. For variety III. To the sum and half sum of the squares of the head and bung diameters, add of the difference of their fquares, then multiply the fum by the length, and divide the product, as above, for ale and wine gallons. RULE IV. For variety IV. From the fum and half fum of the fquares of the head and bung diameters, fubtract half the fquare of their difference; then multiply the remainder by the length; and divide the product, as above, for ale and wine gallons. A general Rule for reducing cafks to a cylinder. First, confider which of all the four Varieties the propofed cask resembles, then from the bung diameter fubtract the head diameter, and multiply the difference by .7 for the spheroid, by .65 for the spindle, by .6 for the conoids, and by .55 for the cones; add the product to the head diameter, the fum is a mean diameter, or the diameter of a cylinder of equal content and length with the cafk propofed. EXAMPLE. The length of a cafk is 40 inches, bung diameter 32, and head diameter 24 inches; required its content in ale and wine gallons. CASE I. Suppofe the cask of the first form; then, 8 .7 5.6 By RULE I. 1077(104960(98.3 ale gallons. By the General Rule. 5.6+24 29.6 the mean diameter. 29.6 X 29.6X.00278 X 40=97.6 ale gallons. 29.6 X 29.6X.0034X40=119.1 wine gallons. By the fliding rule. Set the length of the cask in inches on C to the gauge-point on D, and against the mean diameter on D you have the con tent on C. CASE II. Suppose the cafk of the fecond form; then, 8x.65 5.2 and 24+5.2=29.2 the mean diameter. 29.2 × 29.2 X.00278×40=94.98 ale gallons. CASE |