ing?

GUAGING.

GUAGING is taking the dimen

What is Guag- sions of the capacity of a cask in inches, and finding the contents in gallons.

How

are the

Cubic

found?

How are the gallons found?

What is the mean diameter ?

The cubic inches are found Inches by multiplying half the mean diameter by half the circumference, and this product by the length. The gallons are found by dividing the cubic inches by the number of inches in a gallon. The mean diameter is that which the cask would average throughout its whole length; and is found by addHow is it found? ing of the difference between the head and bung diameters to the head diameter, for the mean diameter. But if the staves be but little curving from the head to the bung, add only six tenths of this difference.

EXAMPLES.

1. How many ale or beer gallons will a cask hold, whose bung diameter is 31 inches, head diameter 25 inches, and whose length is 36 inches? Operation.

31 bung diam.

25 head diam.

25 head diameter.

4 two thirds difference.

29 mean diameterX34-circumference.

6 difference. circumference X by

diameter

area. Area X by

=

length == cubic inches. Cubic inches by 282 number of gallons.

NOTE 1. In taking the length of the casks, an allowance must be made for the thickness for both heads of 1 inch, 14 inches, or 2 inches, according to the size of the 'cask.

NOTE 2. The head diameter must be taken close to the chimes, and for small casks add three tenths of an inch; for casks of 40 or 50 gallons, 4 tenths; and for larger casks, 5 or 6 tenths, and the sum will be very nearly the head diameter within.

2. A had a cask of cider, whose internal dimensions were, head diameter 22 inches, bung diameter 28 inches, length 42 inches; and B had another cask measuring 26 inches in diameter at the head, 33 inches at the bung, and is 41 inches in length. How much is the difference in contents of the two casks? and how many pounds of raisins at 9 cents per pound, must A give B for the excess of his cask, admitting 28 pounds of raisins to be worth 3 gallons of B's cider?

3. A gentleman having a cask of beer in a leaky condition, which measured 46 inches in length, 35 inches in diameter at the bung, and 29 inches at the head; and being obliged to draw it off into casks of 20 inches in length, 16 inches bung diameter, and 13 head diameter, I demand the number of such casks necessary to hold his beer.

4. I demand the difference, in wine and beer gallons, between the capacity of 2 casks, the largest measures 40 inches in length, 34 in diameter at the bung, and 28 at the head; and the other is just half the dimensions of the largest, taken in inches.

Q

QUESTIONS FOR EXERCISE.

1. A goldsmith sold 1lb of gold at a farthing for the first ounce, a penny for the second, 4d. for the third, &c. in quadruple proportion geometrical. I demand what he sold the whole for also how much he gained by the sale, supposing gave for it £4 per ounce.

he

Answer, {

He sold it for £5825 8 5
And gained £5777 8 5

2. A cunning servant agreed with a master (unskilled in numbers) to serve him 11 years, without any other reward for his service but the produce of 1 wheat-corn for the first year; and that product to be sown the second year, and so on from year to year, until the end of the time, allowing the increase to be but in tenfold proportion; that 7680 wheat-corns make a pint, and is sold at 3s. per bushel. Ans. £33908 8 4

3. A thresher worked 20 days at a farmer's, and received for the first day's work 4 barleycorns, for the second 12 barley-corns, for the third 36 barley-corns, and so on in triple proportion geometrical. I demand what the 20 days' labour came to, supposing the pint to contain 7680 corns, and the whole quantity to be sold at 2s. 6d. per bushel.

half

Ăns. £1773 7 6, rejecting remainders. 4. A school-master being asked how many scholars he had, answered, if I had as many, as many, and one fourth as many as I now have, the number would be 99. How many had he? 144÷3×2-60-Ans

5. A B and C, discoursing on their ages, B says to A, I am as old, and half as old again as you; says C to B, I am twice as old as you; and A affirms that the sum of their three ages amount to 165. What was each man's age?

Ans. A 30, B 45, and C 90 years of age. How many parts of 165 was C ?

How many was B?

6. A gentleman bought a chaise, horse, and harness, for £55; the horse came to twice the price of the chaise, and the harness cost one third the price of the horse. What did he pay for each? Ans. For the chaise £15, for the horse £30, and for the harness £10.

7. What is the difference of

and ?
Ans..

8.

What differs from ?

Ans. I

9. What is the difference between 10 and

12

10.

Ans. 14.

What differs from 48? Ans. 47. 11. Bought a piece of cloth containing 47 yards, off which I cut 2415 yards. I demand how much I have by me. Ans. 2212 yards.

.12. A man had 4 bags of money, containing in all £500. In the first was £1303; in the second £9711; in the third £1107. 1 want to know what was in the fourth. Ans. £161.

13. A person dying left his widow £1780; and £1250 to each of his 4 children; 30 guineas apiece to 15 of his poor relations; and £150 in

charities. He had been 25 at an average had cleared had he to begin with?

years in trade, and £126 a year. What Ans. £4347.

14. The globe of the earth, under the line, is 360 degrees in circumference, each degree 691 miles; and this body being turned on its own axis in 23 hours 56 minutes-at what rate an hour are the inhabitants of Bencoolen, situated under the equator, carried about from west to east by this rotation ? Ans. 1045 miles.

15. A fellow was saying that when he told over his basket of chesnuts 2 by 2, 3 by 3, 4 by 4, 5 by 5 or 6 by 6, there still came an odd one; but when he told them 7 by 7 they came even. How many had he Ans. 721. What number multiplied by 57 will produce just what 134 multiplied by 71 will do? Ans. 166.

16.

17. There are two numbers, whose product is 1610, the greater is given 46. What is the sum of their squares, and what the cube of their Ans. Sum of squares 3341. cube of their difference 1331.

difference?

The

18. A B and C trade in company; and at making up their accounts, it appears that A and B together gained £13 10s. B and C together £12 12s.; and A and C together gained £11 16s. 6d. What did they severally gain?

Ans. A £6 7 3, B £7 2 9, and C £5 9 3.

19. There is a mast or pole of its length stands in the ground, 12 feet of it in the water, and of its length in the air, or above water. Í demand the whole length. Ans. 216 ft.