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OF CASK GAGING.

To gage a cask in form of the middle fruftum of a spheroid, or thofe much curved.

RULE. First take the difference betwixt the bung and head diameter, and multiply it by 7 tenths, adding the fame to the head, and it will reduce the cask to a cylinder: Then multiply the fquare of the diameter by the length, and divide by the circular divifois for the content.

Give up the content of the following example of a fpheroidical cask, in ale and wine gallons.

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Thus

2334

2058

2760
2646

J140
882

258

The fame by the Slide.

D C
As 18.94: 24:
As 17.14 : 24 :

D C

+

18.5+ 22.8 ale gallons. 18.5: 27.9 wine gall. N. B. There are three forts of casks befide the conical ones, &c.

ift. The middle fruftum of a spheroid. 2d. The middle fruftum of a parabolic fpindle.

Viz. 3d. The middle fruftum of two para

bolic conoids abutting upon one common bafe.

There are rules for finding the content of each fort feverally; but in general practice, and particular that of the excife, fuch casks are refpectively taken in the 1ft. variety (as is reprefented by the figure in the preceding page) fo that one general rule may ferve for bulged casks.

If you wou'd gage each fort feverally, the neareft method is to multiply the difference of the bung and head diameters by 7 for the first form, which are thofe much curved; by 65 for the fecond form, if the ftaves be fomewhat lefs curved; and by .6 for the third form, if the ftaves between the bung and head be very little curved; then add the product to the head diameter, and the fum is a mean dia

meter.

N. B. When you meet with casks reprefenting the lower fruftums of two equal cones, you may either multiply the difference of the bung and head diameters by .55 as above, or you may gage them as fruftums, &c. as in the 9th example.

Note. The diagonal line of the fpheroidical cask in the preceding example will be 21.219 inches. Thus another cask in the fame form will hold 78 gallons wine measure if the dimenfions are as follows; viz. head diameter 24.286 inches, bung diameter 28.334, length 31.225, and diagonal 35.839 inches. Then if you would find the content of any cask in the fame form by the diagonal line only, obferve this proportion; As the cube of 35.839 is to 78 gall. fo is the cube of any given diagonal to the content of its cask. For example; Suppofe a cask whofe diagonal is 53.84 ; fay, as the cube of 35.839 is to 78 gall. fo is the cube of 53.84 to 408 wine gallons for anfwer; and fo with any other cask of like form.

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Again, to gage casks by the Sliding-rule.

Upon the fide of the Rule is plac'd a line of inches, and under it three other lines fignifying the three varieties, the ufe of which is to reduce a cask to a cylinder.

RULE. First fubtract the head from the bung diameter, and find the difference on the faid line of inches; add that number (which you find against fuch difference) to the head diameter and 'twill reduce the cask to a cylinder: Then fet the gage-point to the length, and against the mean diameter is the content.

EXAMPLE. Given the head diameter 24.5 inches, bung diameter 29.7, and length 45, to find the content in ale and wine gallons?

As 18.94 45: 28.14: 99.7 ale gallons. As 17.14: 45: 28.14: 121.2 wine gallons

Another Example by the Rule.

Let the head be 19.6, bung diameter 24.5, and length 28.2; what's the content in wine and ale gallons?

28.2

23.03: 50.8 wine gallons. 23.03: 41.6 ale gallons.

As 17.14: 28.2
As 18.94

of

of ULLAGING of CASKS.

First to ullage a standing cask, being part full.

RULE. Divide the wet or dry inches by the cask's length, and if the quotient exceeds 5000, add to the faid quotient one tenth part of the excefs, but if it be under .5000, fubtract one tenth part of the want; fo will the fum or remainder be a decimal number, by which if you multiply the content of the veffel, the product will be the quantity of liquor therein if your dividend was the wet inches, but the quantity of liquor which is required to fill it up if the dividend was the dry inches.

Obferve in ullaging, that there must be 4 decimal places at least in the quotient.

EXAMPLE. Suppofe the cask's content to be 61 gallons, whofe length is 32 inches, 18 inches wet, and 14 dry; what will be the contained liquor, and alfo the vacuity?

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