Note. The two upper contents in gallons are found by removing the dot in the areas one place farther to the right hand; the last content is found by multiplying its correfpondent area by the depth 7. To find the content upon every inch of the copper's depth. RULE. From the whole content of the copper reduced into barrels, &c. fubtract the area of the first 10 inches, and the remainder will be the content, when one inch is dry; and fo continue fubtracting that area from the remainder, until 10 inches are dry, and you will gain the contents of the firft 10 dry inches. See the whole operation. 17 0 2,516 Note. When I have finished the fubtraction with the firft area, which is at the 10th dry inch, I add the content of the first 10 inches to the remainder, in order to prove my work, whofe fum, if right, will be equal to the content of the copper. Then PROB. 15. To gauge a back or cooler, and to find the content at every tenth of an inch. RULE 1. Find the area at one inch deep, by the foregoing rules, which reduce to barrels, firkins, and gallons; then find the one-tenth of that area by removing the dot one place farther to the left hand, which also reduce to barrels, &c. 2. To find the content at every tenth, add the area or content of the first tenth to itself, and you will have the content at two tenths; again, add the content of the first tenth to the content of the second tenth, and you will have the content of three tenths; and thus by continually adding the content of the first tenth for every tenth, you may tenth a back to what depth you please. EXAMPLE. Suppose I found the length of a back 272 inches, and breadth 90,8 inches; what is the content at every tenth of the first 3 inches of the back's depth ? 282)24697,6(87,58 = Area at 1 inch in gallons. 2256 I The area of 1 inch being 87,58 gallons, the tenth part of that fum is 8,758 gallons, which reduced is ob. 1f. 2,58g. and fo much will the back hold on every tenth of an inch of its depth. To find the content at every tenth of an inch, till you come to the depth required, proceed as follows. Thus, when I come to 1 inch of the back's depth, I find the content to be equal to that before found, which proves the work to be true; and in this manner I proceed to make the following table, to three inches of the back's depth, where all the contents are placed to the nearest even allon. TABLE PROB. 16. To find the folidity of the ungula, or hoofs, of the fruftum of a cone, having the length of the greatest and leaft diameters, and also the depth given in inches. RULE 1. For the greater hoof. Multiply the product of the greater diameter and the fruftum's height by the fquare of the greater diameter, made lefs by the product of the leffer diameter into a mean proportional between the two diameters; and this last product divide by three times the circular divifors in Page 346, multiplied into the difference of the diameters, and the quotient will be the folidity of the greater hoof. RULE 2. For the leffer baof. Multiply the product of the leffer diameter and height by the product of the greater diameter, into a mean proportional between the two diameters, made lefs by the fquare of the lefs diameter; and this laft product divide by three times the circular divifors for ale, wine, malt, &c. in Page Page 346, multiplied into the difference of the diameters, and the quotient will be the folidity of the leffer hoof. EXAMPLE. Let the following figure reprefent the fruftum of a cone, whofe greater diameter A B= 36 inches, the leffer diameter DC 30 inches, and the height = 20 inches; what is the folidity of the greater hoof A C B, and also the leffer hoof A DC, in ale gallons. 36= A B 20 b 1. For the greater hoof AC B. 36 32 Mean dia. 36 30=Less DC D 720 1ft pro. 216 960 2d prod.' 108 60,82 = Content in ale gallons of the whole fruftum. LXXII. CASK GAUGING. N order to have a right understanding in this matter, it is neceffary are generally compared to folids, generated by one or other of those fections; which would enable him the better to diftinguish to which of thefe folids the cask's curve bears the nearest resemblance. 3 B Gaugers |