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CASE INI. Suppose the calk of the third form; then,

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8X.6=4.3 and 24+4.8=28.8 the mean diameter
28.8 x 28.8 x .00278 x 40= 92.4 ale gallons.
28.8 X 28.8 x.0034 x 40=112.8 wine gallons.

Case IV. Suppose the cask of the fourth variety:

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By the general rule.

8*.55=4.4 and 24+4.4523.4 the mean diameter.

28.4 * 28.4*.00278 X 40=89.8 ale gallons.
28.4 X 28.4x.0034 X 40=109.69 wine gallons.

A cask of the ist variety is the most capacious, and one of the 4th the least capacious. The spindle is most used.

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We have now shewn the method by which calks (when full) may be gauged, both by the pen and rule. It now remains to point out a method by which cafks, that are not full, may be gauged, and this is called ullaging.

PROBLEM X.

To find the ullage of a cask.

A cask may either stand on its end, with its axis perpendicular to the horizon, fig. 6. or ly with its axis parallel to the horizon, fig. 7.

RULE I.

When sanding—Divide the wet inches by the length of the calk; and, if the quotient exceeds -5, add i'r of the excess to the said quotient: but, if it be less than 15, subtract a part of the deficiency, fo will the sum or remainder be a multiplicand, by which if you multiply the content, the product will be the quantity of liquor.

RULE IL.

IP'len lying-Divide the wet inches by the bung diame

ter;

ter *; find the quotient among the versed fines in the table of circular segments, and multiply the corresponding area by the whole content of the calk, and the product gives the liquor in the calk.

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32)18.00(-5025 -5625–5=.0625 excess.

.00625 1 's of which is .00625 the multiplicand .56875

60.96

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If, infiead of the wet inches, you divide by the dry, and proceed as the rule directs, the Icsult will be vacuity,

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Let the length be 32.5 Dry inches

21 Bung diameter

3!

Content
Wet inches

Required the ullage lying.
Anf. 20.97 ale gallons A.G.

75-37 A. G.

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EXAMPLE IV.

Let the bung diameter be
The dry inches
The content 108 gallons.

33

How many gallons are I 2 wanting to fill up

the vessel ? Anf. 35 gallons.

Note. The nearer the form of the cask approaches to a cy: linder, the more exact will the tables give the ullage ; but when the bung diameter is much greater than the head diame ter, the line of segments is truer than the tables.

By the Sliding rules

When lying. 1), Set the bung diameter upon the line of numbers to 100 upon the line of segments; then against the wet inches on the line of numbers is a fourth number; which reserve.

2d, Set 100 upon B to the whole content upon A, and against the reserved number is the answer.

When

When fandiug. 1, Set the length of the cask on the line of numbers, to 100 on the line of segments; then against the wet inches on the line of numbers is a fourth proportional, which reserve.

2d, Set 100 on B to the whole content on A; then against the reserved number on B is the ullage required.

To gauge a floor of malt.

RULE I.

Measure the length and breadth of the floor, and take a num, ber of depths by your gauging-rod, and divide their fum by their number, the quotient will give a mean depth,

RULE II.

Multiply the length, breadth, and depth continually, and divide the product by 2150; the quotient gives the number of bushels.

EXAMPLE

A rectangular malt floor is 490 inches long, 368 inches broad; the depths, taken in several places, are as follow;

Inches.

5

Inches.

3.2
4
4
4.5

6.2

6.7 Required the content.

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