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Of Calk Gauging. There is a great variety in gauging calks ; but the following methods will be near enough truth for all common casks; such as barrels, butts, &c. that are pretty much bulged.

First, Having taken the bung and head diameters, the rule is, to the sum and the sum of the squares of the bung, and head diameters add the difference of the said squares: this sum multiply by the length, and divide by 1077 for beer, or 882 for wine gallons.

2. Rule, which is as true, and much easier.

To the double square of the bung diameter add the square of the head diameter; then multiply this sum by the length of the cask, and divide by 1077 for beer, or 882 for wine.

Queft. 23. There is a cask, whose bung diameter is 28 inches, head diameter 25 inches, length 36: I demand the content in ale gallons ?

First, The square of the bung diameter 28 is 784; which doubled is 1568. Then the square of the head, viz. 25*25=625; which added to 1568, is 2193; this X 36, the length is 78941, which divided by 1077, gives 73. gallons, 2 pints for beer, and divided by 882, give 893 gallons, wine or brandy.

Note, If you find the area of the bung, and head diameters (by Question 20.) and add twice the area of the bung, viz. 2.184 to the area of the head 1.741, it is 6.109, which multiplied by į of the cask's length, viz. 12, gives 73:308 gallons, as before.

These methods holding good for molt casks, I shall give no more examples.

Note If one of the head diameters be larger than the other, and the cask is straight in the sides, like some churns, then (by Questions 21) find a mean diameter throughout, and proceed as therein directed.

6. Of

2.

6. Of Cross MULTIPLICATION.

There are two Methods.

1. By Multiplication only. 1. Rule. Feet multiplied by feet produce feet.

2. Inches multiplied by feet, or feet by inches, produce inches.

3. Inches multiplied by inches produce parts.

Note, 12 seconds make i part, 12 parts make 1 inch, and 12 inches make i foot.

2. By Multiplication and Division, Rule 2. Having placed the lefser fum for the Multiplier, multiply the very last place of the Multiplicand towards the right hand by the first place or name of the Multiplier, and carry i for every 12, serting down what is over 12 under the part you multiplied, then take the parts of the Multiplier as in Practice, carrying as before i for every 12.

But an example will render it more easy, if I give it

both ways.

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First, I begin and multiply the top 4 feet, 3 inches, and 6 parts, by 4 feet, (carrying r for every 12) saying, 4 times 6 is 24 parts, that is o and carry 2; then 4 times 3 is 12, and 2 I carried is 14 inches, that is 2 inches, and carry i to the feet; then 4 times 4 is 16 feet, and i is 17.

Secondly, I multiply now 4 feet, 3 inches, 6 parts, by the lower 3 inches, saying 3 times 4 is 12 inches (because feet multiplied by inches are inches) then 3 times 3 inches is 9 parts (for inches by inches produce parts) and lastly, 3 times 6 parts is 18 parts, viz, i part, 6 seconds.

The second Method.

I first multiply the first or top line as before, and find it as before, 17-2-0; and now I take the parts as in Practice, saying, 3 inches is of a foot, &c. See the work,

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I say 3 inches iš of a foot, and take the parts from 4 feet, 3 inches, 6 parts, saying the 4th of 4 is I foot; then the 4th of 3 inches 6 parts, (viz. 42 parts) is io times (4 is 40) and 2 parts over ; lastly, I say the 4th of 2 parts (viz. 24 seconds) is 6 seconds; which is now done in two lines only.

And now, Tyro, I must bid you farewell, and I hope you will take care to improve yourself in them, rather than trifling away your time with idle fancies : for it is evident, that the knowledge of Arithmetic is ne. Q

cessary

cessary in every station of life, since almost all manner of business depends upon it: and not only this, Tyro, but it is a great help to protect us against the frowns of fortune, and keep us (by being qualified for some lawful post, or employment) from those common temptations and misfortunes, to which those, who know the want of it, so often fall into and pay for so dearly.

Tyro. I return you thanks for this advice, and hope I mall make such use of it as may not frustrate your good designs. Philo. I make no doubt but

you

will. And therefore I once more bid you an hearty farewell. Tyro. Sir, I am your humble servant.

FINI S.

Looking-Glass, in Pater-Nofter-Row.

This Day is published, (Price bound 1 s.) The Tenth Edition, with large and useful Additions, : recommended by several eminent Clergymen, School

masters, and others, as the moit useful book of the

kind extant. The UNIVERSAL SPELLING-BOOK: Or, A new and easy Guide to the English Language.

By DANIEL FENNING, Late School-master of Bures in Suffolk, and Author of

the Use of the Globes, Practical Arithmetic, Treatise

of Algebra, Royal Dictionary, &c. Printed for S. CROWDER, at the Looking-glass in PaterNofter-Row, and B. COLLINS, at Salisbury. 1765.

This Day is published, (Price 1s. 6 d.) Elegantly printed on a fine Paper, calculated in so

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tain many Thousand Calculations more than in any other Book of the like Kind: Allo several instructive and useful Tables, necessary for Persons in every Branch of Life and Business,)

By DANIEL FENNING, Author of a New Treatise of Arithmetic, Use of the

Globes, the Universal Spelling-Book, Royal Dictionary, and others.

This Day is published, The POLITE ACADEMY ; or, School of Beha.

viour for Young Gentlemen and Ladies, with 12 Copper-Plate Cuts neatly engraved, Price is. bound and gilt.

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