Note. According to the observation in Note 2, of the Gauging, the deduction, in the last Example, becomes exactly 3 barrels.

T3

SECTION III.

XI:5:0

OF GAUGING AND ULLAGING CASS AS PRACTISED IN THE EXCISE.

CASK GAUGING.

PROBLEM III

Is gunge and fix a cask of the first variety, u practised in the Excise.

Also, 39301.79067294.12 183.625, the conent in wine gallons.

BY THE SLIDING RULE.

The difference between the head and bung diame ters is 6.3 inches; against this number on the line of inches, we have 4.4 on the line marked spheroid, which being added to 24.6, the head diameter, gives 29 inches, for the mean diameter.

Then,

On C.

S109.4 ale gallons. 123.6 wine gallons.

26.2 inches.

21.4 inches.

4.8 inches.

.68

384

288

3.264

21.4

Head diameter

Mean diameter

24.664 inches.

The areas answering to the mean diameter 24.7 inches, are 1.6991 ale, and 2.0743 wine gallons; then 1.6991 × 32.5 = 55.220, the content in ale gallons; and 2.0743 x 32.5 = 67.414, the content in wine gallons.

BY THE SLIDING RULE.

The difference of the diameters is 4.8 inches;

against this number on the line of inches, we fod 3.34 on the line marked spheroid, which being addei to 21.4, the head diameter, gives 2474 inches, for the mean diameter. Then,

Here 23.4 — 19.5 = 3.8 inches, the diference of the diameters; and 3.8 x .08 2.584; then 1952584 = 22.184 inches, the mean diameter. Tx areas corresponding to 29.2 inches, are 1.3726 ale, md 1.575 wine gallons; then 1.8720 x 27.7 = 98.2 the content in aie gallons; and 1.575T X MT 46.416, the content in wine gallons.

BY THE SLIDING RULE.

Here the ference of the diameters is 3.8 incha: against this number on the line of inches, we have 9.65 on the line marked spheroid; and 19.6 + 26 = 22.25 inches, the mean diameter. Then,

PROBLEM IV.

To guage and fix a cask of the second variety, as practised in the Excise.

Then (28.632 × 28.632 × 46.7) 359.05 = (819.791424 × 46.7) 359.05 = 38284.2595008 ÷ 359.05 = 106.62654, the content in ale gallons; and 38284.2595008294.12130.16544, the content

in wine gallons.

BY THE SLIDING RULE.

Here the difference of the diameters is 6.3 inches; against this number on the line of inches, we find 4.0 on the line marked 2nd Variety; and 24.6 + 4.0 = 28.6 inches, the mean diameter.

Then,