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Ez. 1. Required the content of a spheroidal cask, whose length is 40, and bung and head diameters 32 and 24 inches.

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By the Gauging Rule.
Having set 40 on C, to the ale gauge 32.82 on D, against

24 on D, stands 21:3 on C
32 on D, stands 38.0 on C

the same 380

sum 97'3 ale gallons.

And having set 40 on C, to the wine gauge 29 7 on D, against

24 on D, stands 26.1 on C
32 on D, stands 46.5 on C

the same 46:5

sum 119-1 wine gallons.

Er. 2. Required the content of the spheroidal cask, whose length is 20, and diameters 12 and 16 inches.

Answer { 14:869 wine gallons.

12:136 ale gallons, Prob. 13. To find the content of a cask of the second form.

To the square of the head diameter, add double the square of the bung diameter, and from the sum take 2-5ths or 1-401h of the square of the difference of the diameters ; then multiply the remainder by the length, and the product again by '000gł for ale gallons, or by 0011tor wine gallons.

Er. 1. The length being 40, and diameters 24 and 32, required the content.

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By the Gauging Rule. Having set 40 on C, to 3282 on D, against 8 on D, stands 2:4 on C; the 4-10th of which is 0:96. This taken from the 97'3 in the last form, leaves 96'3 ale gallons.

And having set 40 on C, to 29:7 on D, against 8 on D, stands 2.9 on C; the 4-10th of which is 1'16. This taken from the 119 1 in the last form, leaves 117 9 wine gallons.

Er. 2. Required the content when the length is 20, and the diameters 12 and 16

Answer

5 12.018 gallons,

14:724 wine gallons Prob. 14. To find the content of a cask of the third form.

To the square of the bung diameter, add the square of the head diameter ; multiply the sum by the lengtk, and the product again by the length, and the product again by .0014 for ale gallons, or by 0017 for wine gallons.

Er. 1. Required the content of a cusk of the third form, when the length is 40, and the diameters 24 and 32.

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108 8 wine.

By the Gauging Rule.
Set 40 ou C, to 26 8 on D, then against

24 on D, stands 32 0 on C
32 on D, stands 57.3 on C

sum 89 3 ale gallons. And having set 40 on C, to 24:25 on D, then against

24 on D, stands 39•1 on C
32 un D, stands 69:8 on C

sum 108:9 wine gallons. Er. 2. Required the content when the length is 20, and the diameters 12 and 16.

S112 ale gallons. Answer

13:6 wine gallons. Prob. 15. To find the content of a cask of the fourth form.

Add the square of the difference of the diameters, to 3 times the square of their sum; then multiply the sum by the length, and the product again by 00023} for ale gallons, or by .00028 for wine gallons.

Ex. 1. Required the content, when the length is 40, and the diameters 24 and 32 inches. 56

8
56
8
378980

378880
336
64
*000235

*00028;
280 9408

1136640

303 1040
3136
9472 757760

757760
3
40
75776

* 126293

9408

378880 ale

87'90016 gallons 10734933 wine.

By the Sliding Rule.
Set 40 on C, to 6564 on D; then against

8 on D, stands 0:6 on C
56 on D, stands 29•1 on C

29.1

29-1

sum 879 ale gallons.
And set 40 on C, to 59:41 on D; then against

8 on D, stands 0:7
66 on D, stands 35.6

35.6 35.6

sum 107.5 wine gallons.

Ex. 2. What is the content of a conical cask, the length being 20, and the bung and head diameters 16 and 12 inches ?

Answer { 19:98752 ale galloris,

13'41866 wine gallons. Prob. 16. To find the content of a cask by four ditensions.

Add together, the squares of the bung and head diameters, and the square of double the diameter taken in the middle between the bung and head; then multiply the sum by the length of the cask, and the product again by '00041 for ale gallons, or by .00053 for wine gallons.

Ex. 1. Required the content of any cask whose length is 40, the bung diameter being 32, the lead diameter 24, and the middle diameter between the bung and head 28 inches.

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Set 40 on C, to 42:0 on D; then against

24 on D, stands 13:0
32 on D, stands 23.2
57] on D, stands 75.0

sum 111'2 wine gallons.

Ex. 2. What is the content of a cask, whose length is 20, the bung diameter being 16, the head diameter 12, and the diameter in the middle between them 148?

5 11.4479 ale gallons,

{ 13.9010 wine gallons. Prob. 17. To find the content of any cask from three dimensions only.

Add into one sum, 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the product of the two diameters : then multiply the sum by the length, and the 00034

00034 product again by for wine gallons, or by or '000037's 9

11 for ale gallons.

Ex. 1. Required the content of a cask, whose length is 40, and the bung and head diameters 32 and 24 ? 32 24

32
32
24

24

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2972160
*00034

2972160

0000374
11888640
8916480

8916480

270196 9)1010-53440

112-2816 wine gallons 9186676 ale gallons

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