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12. The ball on the top of St. Paul's Cathedral is 6 feet in diameter, what will the gilding of it cost at 24d. per square inch?

13, How many gallons of water will be required to fill a ditch, mile long, 10 feet deep, 25 feet broad at the top and 18 feet at the bottom?

14. What is the surface of a sphere, the volume of which is 480 square yards?

15. Express the side of the cube equivalent in solidity to a sphere 2.5 feet in diameter.

16. Knowing that globes are to each other as the cubes of their diameters; if the diameter of the Earth be 1, that of the Sun is 109.93, of Mercury .39, of Venus .97, of Mars .56, of Jupiter 11.56, of Saturn 9.61, of Uranus 4.26, of Neptune 3.91, of the Moon, .27; it is required to find the solidity of these bodies, the earth's solidity being supposed unity.

17. The Sun weighs 354936 times as much as the Earth, Jupiter 332, Saturn 101, Neptune 29, Uranus 20, Venus .87, Mercury .18, Mars .14, and the Moon ; the solidity of these bodies being determined by the previous example, find their density or their weight under the same bulk.

18. Supposing the weight of a cubic inch of cast iron weighs 4.3 oz. avoirdupois, what is the weight of an iron ball of 10.5 inches diameter.

TO FIND THE MAGNITUDE AND THE WEIGHT OF A BODY BY ITS SPECIFIC GRAVITY.

416 When solids are too irregular to admit of the application of the rules of mensuration, we can find the content and also the weight by reference to their specific gravity.

The specific gravity of a body is its weight as compared with an equal bulk of some other body.

417. A cubic foot of rain water weighs just 1000 ounces avoirdupois, this has been taken in this country, as the specific gravity of one cubic foot of water, and comparing other bodies with it, the following table, determined by careful experiments contains the weight in ounces of a cubic foot of each.

[blocks in formation]

419. Ex. 1. What is the solidity of 1 ton of oak?

By the table. 925 ounces of oak are the weight of one cubic foot.

.. 1 ton or 35840 ounces of oak are the weight of 35840: 31138.

Ex 2. Required the weight of a block of marble whose length is 2.3 yards, the breath 1.25 yards, and the thickness .97 yard.

Here the solidity is 2.3 × 1.25 ×.97 2.78875 cubic yards. .. By the table 1 cubit foot of marble weighs 2700 ounces. .. 1 cubic yard weighs 27 × 2.78875 × 2700 ounces=5 tons, 13 cwt., 1 qr., 22 lb, 4 oz.

420. EXERCISES.

1. A waggon is loaded with 24 bars of iron, 2 yards long, 8 inches, broad and 8 inches thick; find the weight of the load.

2. The weight or pressure of the atmosphere at the earth's surface, is equivalent to the weight of a column of mercury, the height of which is 294 inches. Supposing that the surface of the human body is 3.4 square yards, what is the pressure to which it is subjected? 3. Archimedes discovered the following principle: a body immersed in a fluid, loses as much weight as an equal bulk of the fluid weighs. From this it is required to find the weight of a cast iron ball 6.4 inches in diameter, when immersed in water.

4. What is the weight of the air contained in a room, the dimensions of which are 17 feet 6 inches in length, 14 feet 8 inches in breath, and 10 feet 4 inches in height?

5. What will be the weight of a foot of lead pipe, 3 inches diameter in the bore, and .6 inch in thickness?

6. How many cart loads of clay will there be in a drain 100 feet long, 2 feet broad and 6.4 feet deep, allowing 1 tons for each load?

7. Required the weight of an oak board, 5 yards long, 2.7 feet broad, and 4.4 inches thick?

8. What is the diameter of a gold ball of the same weight as a silver ball whose radius is 1.5 inches?

MISCELLANEOUS EXERCISES.

1. Pestalozzi was born on the 12th of January, 1746, and died February 17th, 1827. How old was he when he died, and how long is that ago?

2. From May 1st to October 15th, 1851, the time that the Great Exhibition was open, the number of visitors was 6167944. How many went on an average daily, Sundays not included?

3. If 17 pieces of cloth, 23.75 yards long and .77 yard wide, are to be lined with stuff, yard wide. How many yards

will be required?

4. There were 3300 iron pillars in the Crystal Palace, on the average 18 feet in length and 8 inches in diameter. If laid side by side, what surface of ground would they cover; and what would be their length, if placed lengthwise?

5. At the opening of a dock, which measures 870 yards by 166 yards, the water was admitted at an average of 4500 gallons per second, and continued to flow in for 12 hours. What was the depth of water?

6. How much further will a man's head travel than his feet, in going round any great circle, supposing his height to be 6 feet?

7. If 100 oranges are bought at 3 a penny, and 100 more at 2 a penny, at what price must they be retailed, so as to gain 25 per cent.?

8. Two travellers sat down to dinner, one had 5 loaves and the other 3; a stranger passing by asked to eat with them, to which they consented. The stranger dined, laid down 8 pieces of money, and departed. How much must each traveller receive?

9. What is the weight of a block of marble, specific gravity 2700, length 63 feet, and breadth and thickness each 12 feet (being the dimensions of one of the stones in the walls of Balbec)?

10. A gentleman dying left in his will a certain amount, to be disposed of as follows: 1st, for funeral expenses £500; 2nd, doctor's bill 150 guineas; 3rd, to each of his two executors £500; 4th, lawyers' bills 300 guineas; 5th, to each of his 13 servants £50: 6th, to his wife he left money for an investment, which, at 4 per cent., would produce her an income of £1000 a year; 7th, the remainder of his property to be divided among his five sons, in such a manner that B shall have 10 per cent. less than A; C, 10 per cent. less than B; D, 10 per cent. less than C; and E, 10 per cent. less than D. Now, E's income, at 4 per cent. from his fortune, was £656.2 per annum. Required, the fortune of each son, and the total amount of property the gentleman left.

11. A could do a work in 16 days, B in 15, and C in 18. Required, the time they will do it in together.

12. How many moidores, guineas, marks, nobles, and crowns are there in £1598. 14s., when there is an equal number of each?

13. If 60 gallons of water, in one hour's time, runs into a cistern, containing 240 gallons, and by a pipe in the same cistern, there runs out 42 gallons per hour. In how many hours will it be filled, supposing there is no water in the cistern, and both taps are open at the same time; the rate of influx and efflux being uniform?

14. The difference of income for one day, between the common and leap year, is 1.346972 farthings. Required, the income per annum.

15. If a solid inch of mould candle will burn 28 minutes, how long will a whole one last, the length of which is 9 inches and diameter .75 inch, supposing the candle to burn uniformly?

16. A body is immersed in a cylindrical vessel of water, the diameter of which is 3 feet 6 inches; and on taking it out, I found the fall of water to be .8 of an inch. solidity of the body?

What was the

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