Explanation. The block will contain as much as a cubic block of the same length and breadth.

10. What is the cube root of .00064?

Ans. .04.

11. There is a pile of wood 4 ft. wide, 6 ft. high, and 213 ft. long; how large a cubic pile will it make?

Ans. a cubic pile 8 ft. square.

SPECIFIC GRAVITY.

LESSON 191.

The specific gravity of any substance is the ratio of its weight to the weight of an equal bulk of fresh water; thus, if the substance weighs 2 oz., and an equal bulk of water 1 oz., its specific gravity is 2; if it weighs 1 oz., and an equal bulk of water 2 oz., its specific gravity is, or .5. See Promiscuous Questions after Fractions, lesson 85.

Therefore, to get the specific gravity of any substance, Divide its weight by the weight of an equal bulk of fresh

water.

A cubic foot of pure fresh water, properly distilled, weighs 1,000 ounces, avoirdupois, at the temperature of melting ice.

The table on the following page shows the specific gravity of several of the most common and important substanIt is formed by dividing the weight of a cubic foot of each substance, in ounces, by 1,000. If we omit the point, we get the weight of a cubic foot of each substance

ces.

in ounces.

Note. It is not necessary to commit the table to memory.

What is the specific gravity of any substance? What if the substance weighs 2 oz., and an equal bulk of water 1 oz.? What if it weighs 1 oz., and an equal bulk of water 2 oz.?

How then do we get the specific gravity of any substance?
What is said of the weight of a cubic foot of water?

How is the table formed?

Note. The specific gravity of any solid, liquid, or gas, increases with the cold, and diminishes with the heat. Moreover, there is always some difference in the specific gravity of several varieties of the same substance.

1. I have 16 round bars of hammered copper, 12 ft. long and of a foot in diameter; what do they all weigh if we reckon the circumference 3 times the diameter ? Ans. 800 lbs. 1.6 oz. Explanation. Find the weight of a cubic foot in the table.

What does the specific gravity of any solid, liquid, or gas, increase with? Diminish with? Is the specific gravity of several varieties of the same substance always the same?

2. A man melted a number of pieces of lead, and cast them in a prism 1.5 ft. long, 1 ft. high, and .75 ft. wide ; what did it weigh? Ans. 798 lbs. 2 oz.

3. There is a dish of mercury, or quicksilver, 8 inches square on the top, 6 inches square on the bottom, and 4 inches deep; how much mercury, by weight, does it contain ? Ans. 96 lbs. 121 oz., about.

4. How large a cube will 58,400 ounces of tin make? Ans. a cube 2 ft. square.

5. There is a monument in a grave-yard composed of black marble, in the shape of a cone, 4 ft. in diameter at the base, and 7 ft. high; what is its weight?

Ans. 4,948 lbs., about. 6. What is the weight of a thousand heavy bricks, each being 8 inches long, 4 inches wide, and 2 inches thick ? Ans. 4,629 lbs. 10 oz., about.

7. What is the weight of a coil of 5 inch rope, that is, of rope 5 inches in circumference, containing 45 fathoms, if we reckon the circumference 3 times the diameter ? Ans. 268 lbs. 9 oz., nearly.

1

8, What is the weight of a ball of white oak 1 ft. in diameter ? Ans. 30 lbs. 61 oz., about. 9. What is the weight of a barrel of sea water, the length being 36 inches, head diameter 18 inches, and bung diameter 21 inches, the staves being quite curving? Ans. 421 lbs., about. 10. There is an iron pipe 5 inches in diameter on the outside, and 4 inches on the inside; how much does a piece 100 feet long weigh? Ans. 2,212 lbs., nearly.

LESSON 192.

1. There is a bottle which weighs 6 oz.; when filled with water it weighs 36 oz., and when filled with olive oil it weighs 33 oz. 7 drams; what is the specific gravity of the oil?

Ans. .915.

2. A bottle weighs 4 oz. when empty, 20 oz. when filled with water, and 33 oz. 7 drams when filled with sulphuric acid; what is the specific gravity of the acid ?

Ans. 1.840, nearly. 3. There is a piece of dry white pine in the shape of a wedge, weighing 35 oz., the length is i ft., breadth 6 inches, and the thickness of the head 3 inches; what is its specific gravity?

Ans, .560.

4. A large glass bottle, which is found to contain 98 cubic inches of water, weighs 1 lb. when the air is taken out of it by an air pump; when the air is admitted it weighs 1 lb. 30 grains, and when filled with hydrogen gas it weighs 1 lb. 2 grains; what then does a cubic foot of air weigh, what does a cubic foot of hydrogen gas weigh, and what is the specific gravity of air, and of hydrogen gas, as found by the experiment ?

Ans. a cubic ft. of air weighs 529 grs., nearly; a cubic ft. of hydrogen gas weighs 35.27 grs., nearly; the specific gravity of air is .00121, nearly, and of hydrogen gas, .00008, about.

5. There is an ingot composed of gold and copper, the specific gravity of which is 17.800; in what proportion are the gold and copper mixed?

Ans. 9,010 of gold, to 1,460 of copper. Explanation. See Alligation Alternate. Consider the two metals as cast.

6. I wish to make a gallon of proof spirit from some alcohol, or rectified spirit of wine, and some pure water; what quantity of each must I take?

Ans. of a gallon of each. 7. A man has 16 gallons of French brandy, consisting of 10 gallons of alcohol, and 6 gallons of pure water; what is its specific gravity?

Ans. .900.

8. How much water must be mixed with 4 gallons of rum, the specific gravity of which is 890, to reduce it to proof spirit? Ans. 13 gallon.

LESSON 193.

To find the specific gravity of a small irregular shaped body, heavier than water.

First find its weight, then find how much it weighs when suspended by a string fastened to one of the scales of an accurate balance, the body being immersed in pure cold water. In this position it will evidently lose just the weight of an equal bulk of water; because, if it was of the same specific gravity as the water, it would be just buoyed up by it, and lose all its weight.

Now to find its specific gravity,
Divide its weight by the weight lost.

How do we proceed to find the specific gravity of a small irregular body heavier than water?

To find the specific gravity of a small irregular body lighter than water.

First find its weight, then take a piece of lead, or other substance, sufficiently heavy to sink the body in water when attached to it; find how much the lead weighs when immersed in water; then attach the body to it, and immersing both, find the weight, and subtract it from the weight of the lead in the water. The difference added to the weight of the body evidently gives the weight of an equal bulk of water.

Now to find the specific gravity,

Divide the weight of the body by the weight of an equal bulk of water.

We can also find the specific gravity of a small irregular shaped body by dividing its weight by the weight of a quantity of water of the same bulk. The bulk can be found by immersing it in water, as directed in Mensuration, lesson 172. This method is not so accurate as the preceding ones, especially if the body be quite small.

1. What is the specific gravity of a piece of gold money that weighs 216 grains out of the water, and 204 grains when immersed; and if the piece was formed by alloying pure gold with pure silver, what quantity of each ingredient is there in it?

Ans. the specific gravity is 18, and it contains 183 grs. of gold, and 33 grs. of silver, about.

2. A piece of pine charcoal weighs 437.5 grs., and a piece of lead weighs, when immersed in water, 956.25 grs.; attaching the charcoal to the lead and immersing them, they weigh 300 grs. ; what is the specific gravity of the charcoal? Ans. .400.

3. If a piece of marble weighs 180 pounds, and you find the bulk by immersing it in water, as directed in Mensuration, lesson 172, to be 1 cubic foot, what is its specific gravity? Ans. 2.880.

How do we proceed to find the specific gravity of a small irregular body lighter than water?

How, also, can we find the specific gravity of a small irregular body? What is said of the accuracy of this method?