the dimensions of the two cisterns thus formed, when the content of the less is 380 ale gallons.

Ans. The length of each cistern is 64 inches, the breadth of the greater 51.118 inches, and that of the less 34.882 inches.

79. The sides of a triangular cooler are 60, 70, and 80 inches, respectively. Now, if it be cut by a plane parallel to the longest side; required the dimensions of the remaining triangle, when the area of the portion parted off is three ale gallons.

Ans. The three sides of the remaining triangle are 45.849, 53.490, and 61.132 inches, respectively.

80. The sides of a triangular cooler are 60, 70, and 80 inches, respectively. Now, if it be cut by a plane passing from the opposite angle to the middle of the longest side; required the areas, in ale gallons, of the two vessels thus formed.

Ans. The area of each vessel is 3.605 ale gullons. 81. If the length of a cistern be 94, and its breadth 72 inches; what must be its depth, in order that it may contain 16 quarters of barley? Ans. 40.669 inches.

82. The perpendicular depth of a cistern is 42, its breadth 108, and the diagonal of its bottom 180 inches; how many bushels of barley can be steeped in this cistern at one time, allowing of the whole content for the swell of the grain? Ans. 242.997 bushels.

83. The content of a cylindrical vessel is 9743 ale gallons, and the diameter of its base 147 inches; required its perpendicular depth. Ans. 161.888 inches. 84. The diagonal of the base of a cubical vessel, is 72 inches; required the content in wine gallons.

Ans. 571.268 wine gallons. 85. The diameter of the legal Winchester bushel is 18 inches, and its depth 8 inches; what is the diameter of that bushel whose depth is 9 inches?

Ans. 17.441 inches. 86. The bottom diameter of a vessel, in the form of the frustum of a cone, is 150 inches, the top diameter 86 inches, and the slant height 68 inches; what is the content in ale gallons? Ans. 2383.846 ale gallons. 87. The slant height of a cistern in the form of the frustum of a square pyramid, is 85 inches, the perpendi

cular height 75, and the side of the base 195 inches; what is the content in malt bushels?

Ans. 513.883 malt bushels. 88. The content of a vessel in the form of a pentagonal prism, is 3834 wine gallons, and the side of its base is 74 inches; required its perpendicular depth.

Ans. 94.005 inches.

89. A reservoir measures 182 inches in length, 112 in breadth, and 74 in depth; how long will a person be in filling it with water, by means of a pump; supposing he makes 26 strokes in a minnte, and lifts 3 pints of water at each stroke? Ans. 9 hours, 8.614 minutes.

90. The bottom diameter of a vessel, in the form of the frustum of a cone, is 86 inches, the top diameter 62 inches, and the perpendicular depth 58 inches; how many gallons of ale are contained in the vessel, when the depth of the liquor is 40 inches?

Ans. 615.401 ale gallons. 91. The perpendicular depth of a vessel, in the form of the frustum of a square pyramid, is 65 inches, the side of the top 68 inches, and the side of the bottom 94 inches; how many wine gallons does the vessel contain, when the depth of the liquor is 45 inches?

Ans. 1412.725 wine gallons.

92. The perpendicular depth of a vessel, in the form of the frustum of an elliptical cone, is 65 inches; the transverse and conjugate diameters of the bottom measure 86 and 58 inches; the transverse and conjugate diameters of the top, 62 and 42 inches; how many ale gallons does the vessel contain, when the depth of the liquor is 42 inches? Ans. 485.1191 ale gallons.

93. The perpendicular altitude of a conical vessel, is 87 inches, and the diameter of its base 64 inches. Now, if this vessel be cut by a horizontal plane; required the contents of the two vessels thus formed, in ale gallons, when the content of the frustum is to that of the segment, as two to one.

Ans. The content of the pustum is 220.552, and the content of the segment 110.276 ale gallons.

94. The side of the base of a vessel, in the form of the frustum of a square pyramid, is 60 inches, the side of the top 40 inches, and the perpendicular depth 84 in

ches. Now, if this vessel be cut by a plane parallel to the base; required the contents of the two vessels thus formed, in wine gallous, when the content of the greater is to that of the less, as five to four.

Ans. The content of the greater vessel is 511.784, and the content of the less 409.4272 wine gallons.

95. The diameter of the base of a conical vessel, is 60 inches, and its perpendicular altitude 72 inches. Now, if this vessel be cut by a plane parallel to the base; required the dimensions of the two vessels thus formed, when their contents are equal.

Ans. The diameter of the section made by the cutting plane is 47.622 inches, the altitude of the segment 57.146 inches, and that of the frustum 14.854 inches.

96. The side of the base of a vessel in the form of the frustum of a square pyramid, is 60 inches, the side of the top 40 inches, and the perpendicular height 50 inches. Now, if this vessel be cut by a plane parallel to the base; required the dimensions of the two vessels thus formed, when their contents are equal.

Ans. The side of the section made by the cutting plane, is 51.924 inches, the altitude of one of the vessels 29.812 inches, and that of the other 20.188 inches.

97. The internal diameter of a spherical vessel is 74 inches; and if it be cut by a horizontal plane, which makes the depth of the less segment 25 inches; required the contents, in ale gallons, of the two vessels thus formed. Ans. The content of the greater segment is 552.794, and that of the less 199.599 ale gallons.

98. The diameter of the base of a vessel, in the form of a prolate semi-spheroid, is 50, and its perpendicular altitude 60 inches. Now, if this vessel be cut by a hori zontal plane, at the distance of 30 inches from the base; required the contents, in wine gallons, of the two vessels thus formed.

Ans. The content of the frustum is 233.748, and the content of the segment 106.249 wine gallons.

99. The diameter of the base of a vessel, in the form of a paraboloid, is 50, and its perpendicular altitude 60 inches. Now, if this vessel be cut by a horizontal plane, at the distance of 30 inches from the base; required the

contents, in wine gallons, of the two vessels thus formed?

Ans. The content of the frustum is 191.248, and the content of the segment 63.748 wine gallons.

100. At Konigstein, near Dresden, in Germany, is a cask whose head diameter is 25 feet or 300 inches, bung diameter 26 feet or 312 inches, and perpendicular altitude 28 feet or 336 inches; how many gallons of wine will it contain, admitting it to be of the third variety?

Ans. The content of this enormous cask, is 107010 wine gallons, which exceeds the content of the cask at Heidelberg, by 370543 gallons. (See Example 5, Prob. IV., Part V.

Note. The Konigstein cask was begun in the year 1722, and finished in 1725, under the direction of General Kyaw; and is considered to be the largest cask in the world. It consists of 157 staves, each 8 inches in thickness; and one of its heads is composed of 26, and the other of 28 boards. The top or upper head of this enormous cask is railed round, and affords sufficient room for twenty persons to regale themselves.

REMARK.

Having given copious directions for finding the Areas and Contents of all Vessels that can possibly be met with in Practice, and illustrated those directions by numerous Examples, we come now to describe the methods of gauging and fixing the Utensils of Victuallers, Common Brewers, Distillers, Maltsters, Starch-makers, Soap-makers, Glassmakers, &c. &c. as practised in the Excise.

PART VI.

The Method of Gauging and Fixing Victuallers' Utensils; of Gauging and Inching Common Brewers' Utensils; and of Gauging and Ullaging Casks. Also, the Method of Gauging and Fixing Maltsters' Utensils; and of Gauging and Inching a Still, and a Distiller's Wash-Back. Likewise, the Method of Gauging and Fixing the Utensils of Starch Makers, Soap Makers, and Glass Makers, as practised in the Excise.

SECTION I.

THE METHOD OF GAUGING AND FIXING VICTUALLERS UTENSILS, AS PRACTISED IN THE EXCISE.

PROBLEM I.

To gauge and fix a mash-tun, in the form of the frus tum of a cone.

To take the dimensions.

With the Dimension Cane, or any other convenient instrument, take the perpendicular depth of the vessel.

Also, with the Diameter Rule, take two cross diameters of the top, at right-angles to each other; and likewise two cross diameters of the bottom. Add these diameters together; divide the sum by 4, and take the quotient for a mean diameter.

Note 1. A mean diameter may also be found by taking two cross