232. The great ocean steamers. Some idea of the great shipping industry may be obtained by thinking that in one year 857,000 immigrants (steerage or third-cabin passengers) came to our country, besides the first- and secondcabin passengers. A large ocean steamer has a capacity of over 2,000,000 cu. ft., perhaps a thousand times the capacity of your recitation room.

WRITTEN EXERCISE

1. One of the fastest day's runs recorded for a steamer is 601 knots. How many statute miles is this?

2. A certain ocean steamer can carry 3192 persons, including the crew. The crew number 12% as many as the passengers. How many are there of each?

3. Prior to 1860 the best steamship record between New York and Queenstown was 9 da. 2 hr. When it was reduced to 5 da. 7 hr., what was the per cent of reduction?

4. To build one of the large Atlantic steamers, 1400 plates of steel were used in the hull alone. They weighed 4 long tons each. How many tons did they all weigh? How many pounds?

5. A steamer carries 350 first-cabin passengers, 48% as many in the second cabin, and 400% as many in the third cabin (steerage) as in the other two together. How many passengers does it carry?

6. A 20,000-ton boat carries 12 times as much freight as the old-style ocean steamers, makes 25% better time, and the expenses are only 4 times as much. In one year such a modern boat will do how many times the work of the old kind? At the same cost, it will carry how many times as much freight?

233. Problems in meteorology. Problems concerning rainfall, temperature, and the general state of the weather are called problems in meteorology. They are so related to agriculture as to have a place among industrial problems.

WRITTEN EXERCISE

1. What is the weight of an inch of rainfall upon an acre, taking the weight of 1 cu. ft. of water as 1000 oz.? What is it on a 200-acre farm? Answer in tons.

2. The lowest daily temperatures registered during a certain week in January, in Buffalo, were 7°, 3.6°, — 9° (9° below zero), 6°, - 3°, 0°, 8°. What is the average of these readings?

3. In our common Fahrenheit (F.) thermometer the freezing point of water, 32°, is the 0° in the Centigrade (C.) thermometer, and the boiling point, 212°, is the 100° in the Centigrade. Express 4° C. in Fahrenheit, and 62° F. in Centigrade. Draw each thermometer to scale.

4. A barometer registered 29.024 in. on Monday. In the next 4 days it rose 0.135 in., 0.044 in., 0.095 in., and 0.573 in. On Saturday and Sunday it fell 0.021 in. and 0.417 in. What was the Friday reading? the Sunday reading? What were the weather indications on Friday? on Sunday?

A rising barometer indicates fair weather. When the mercury falls rapidly a storm is indicated.

5. The mean (average) annual rainfall at Mobile is 62.2 in. ; at Sacramento, 20.9 in.; at Denver, 14.5 in.; at Indianapolis, 43 in.; at Des Moines, 33.1 in.; at St. Paul, 27.5 in.; at St. Louis, 41.1 in.; and at Portland, Oregon, 46.8 in. Taking the weight of 1 cu. ft. of water as 62.5 lb., what is the weight of water annually falling on a square mile in each of these cities? Answer in tons.

6. If light travels 186,000 mi. per second, and it takes it 8.158 sec. to come from the sun to the earth, what is the distance traveled?

7. Water is composed of two gases, oxygen and hydrogen, 88.89% by weight being oxygen. What is the weight of the hydrogen in a cubic foot of water?

8. The air is composed of two gases, oxygen and nitrogen. In every cubic foot of air there are 345.6 cu. in. of oxygen. What per cent of the volume of the air is nitrogen?

9. A certain cirrus cloud is observed to be 6 mi. above the earth, or 240% higher than a certain rain cloud observed a few hours before. How high was the rain cloud?

10. At the temperature when sound travels 1120 ft. per second, what is the distance of a thunder cloud in which lightning is seen 17 sec. before the thunder is heard?

11. If a large drop of rain falls at the rate of 20 ft. per second, and a small one, blown by the wind, only 25% as fast, how long will it take the small one to reach the earth from a cloud 24 mi. high?

12. The wind pressure in a hurricane has been known to be as great as 49.2 lb. per square foot. In such a storm how many tons pressure on the side of a large office building 104 ft. long and 308 ft. high?

13. In a great storm the velocity of the wind often reaches 88 ft. per second. What is then its velocity per minute? In a hurricane it has been known to be 66%% greater. What is then its velocity per hour?

14. When the mercury in the barometer is at 30 in., the pressure of air on every square inch of surface is 15 lb. What is the pressure on a pane of glass 2 ft. by 3 ft., when the increased air pressure forces the mercury up to 31 in.? Why does the glass not break?

POWERS AND ROOTS

234. Square numbers and square roots. If a square has a side 4 units, it has an area 16 square units. Therefore 16 is called the square of 4, and 4 the square root of 16.

235. Square roots of areas. sidering the abstract numbers

sides and area,

Therefore, conrepresenting the

The side of a square is the square root of its area.

236. Writing squares and roots. The square of 4 is written 42; the square root of 16 is written √16.

237. Perfect squares. A number like 16 is a perfect square, but 10 is not a perfect square. We speak, however, of √103.16+, because 3.162 nearly equals 10.

238. Square roots of perfect squares. Square roots of perfect squares may often be found by factoring.

3)441

3)147

7)49

7

ORAL EXERCISE

State the square roots of the numbers in Exs. 1–8 :

What are the sides of squares whose areas are as follows?

WRITTEN EXERCISE

By factoring, find the square roots of the following:

Find the sides of squares whose areas are as follows:

25. 19,600 sq. ft. 28. 16,384 sq. in.

26.

15. 2.25 sq. ft.

18. 15,625 sq. in.

21. 0.1225 sq. ft.

areas are as follows:

24. 11,025 sq. ft.

27. 20,736 sq. in.

29. 16,900 sq. ft. 30. 129,600 sq. in.

31. From the corner of a square piece of land containing 576 sq. rd. a small square lot containing 64 sq. rd. is cut out. Draw the plan of the lots and find the perimeter of each.

32. A square lot has an area of 169 sq. rd. How far is it around the lot? How far is it around a lot of four times this area? The second perimeter is how many times the first? Plot each lot to a scale.

33. A man has two adjacent building lots fronting on the street, each lot being square. The area of the two together is 89 sq. rd., that of the larger being 64 sq. rd. What is the frontage of the lots?

34. A square lot has an area of 289 sq. rd. How far is it around the lot? (Try the prime numbers between 10 and 20.) How far is it around a lot of nine times this area? The second perimeter is how many times the first?