TABLE OF QUOTIENTS FOR THE FOUR VARIETIES OF CASKS IN ALE AND WINE MEASURES.

To illustrate the use of the Table we shall give two examples, which we think will be amply sufficient.

EXAMPLE 1.

Required the content of a Cask of the 2nd Variety, in wine gallons, the length of the Cask being 50 inches, the head diameter 25 inches, and bung diameter 32.5 inches.

SOLUTION.

Bung Diameter Head Diameter

32.5)

25.0

Quotient
(77 nearly.

Now entering the Table with 77, we find the decimal corresponding to this quotient in the Second Variety, under WINE GALLONS to be 29146, wherefore we have

⚫0029146 tabular decimal divided by 100

32.5 x 32.5 1056-25 square of the bung diameter

Product 3.078 area of a cylinder
Multiply by 50 length of the cask

Product 153.9 wine galls. content required.

The content thus found differs 3 gallons from the content of the same Cask found in PROBLEM II., but this is partly owing to 77 in the quotient being too great.

EXAMPLE 2.

Required the content of a Cask of the First Variety, in ale gallons, the bung diameter being 40 inches, the head diameter 30 inches, and the length of the Cask 48 inches.

SOLUTION.

Bung Diameter Head Diameter Quotient

40)

30.00

(75

Now entering the Table with 75, we find the

decimal corresponding to this quotient in the First Variety under ALE GALLONS to be 23789, wherefore we have

40 x 40

⚫0023789 tabular decimal divided by 100

1600 square of the bung diameter

142734

23789

Product 3.80624 area of a cylinder
Multiply by 48 length of the cask

3044992 1522496

Product 182-69952 ale gallons, content required.

PROBLEM V.

To determine the Content of a Cask of the FIRST VARIETY, in Wine Gallons, by a Table of Diameters for the Head and Bung.

With the head diameter in inches and tenths enter the Table, and take out the area corresponding to the Head Diameter: in like manner, with the bung diameter enter the Table, and take out the area corresponding to the Bung Diameter; then add the first area to twice the second, and multiply the sum by the length of the Cask: the product will be the content in wine gallons.

NOTE. If Wine Gallons be multiplied by 9, and divided by 11, the quotient will be the equivalent in Ale Gallons very nearly.

0.5094 0.5142

0.5190

0.5585 0.5636

0.5687

21 0.4998 0.5046 22 0.5485 0.5535 23 0.5995 0.6047 24 0.6528 0.6582 25 0.7083 0.7140 0.7197 0.7254 0.7312

0.6100 0.6153 0.6206 0.6637 0.6692

0.6747

26 0.7959 0.8019 0.8079 0.8140 27 0.8571 0.8633 0.8696 0.8759 28 0.9205 0.9270

0.8201

0.8822

0.9335 0.9400

0.9466

32
1.1971 1.2044
33 1.2719 1.2795
34
1.3489 1.3568
35 1.4283 1.4363 1.4444 1.4525

1.2118

1.2193

1.2267

1.2871 1.2948

1.3024

1.3646

1.3725

1.3804

1.4606