ORAL

124. 1. How many cubic feet are there in a block of wood 1 ft. long, 1 foot wide, and 1 foot high? In a block of wood 2 ft. long, 1 ft. wide, and 1 ft. high?

2. How many cubic feet are there in a block of wood 3 ft. long, 1 ft. wide, and 1 ft. high? In a block 3 ft. long, 2 ft. wide, and 1 ft. high? 3 ft. long, 3 ft. wide, and 1 ft. high?

3. If the block of wood is 3 ft. long, 3 ft. wide, and 2 ft. high, how many cubic feet does it contain? If it is 3 ft. long, 3 ft. wide, and 3 ft. high?

The number of cubic feet in each case equals the product of what three numbers?

4. A solid 1 in. long, 1 in. wide, and 1 in. high is a cubic inch. How many cubic inches are there in a solid 12 in. long, 1 in. wide, and 1 in. high?

Make a drawing showing such a solid, marked off into cubic inches.

5. How many cubic inches are there in a solid 12 in. long, 2 in. wide, and 1 in. high? Make a drawing showing such a solid, marked off into cubic inches.

6. If a solid is 12 in. long, 12 in. wide, and 1 in. high, how many cubic inches does it contain, or what is its volume?

7. If a solid is 12 in. long, 12 in. wide, and 2 in. high, how many cubic inches are there in its volume?

8. If a solid is 12 in. long, 12 in. wide, and 12 in. high, how many cubic inches does it contain?

Such a solid being 1 ft. square is a cubic foot. The number expressing its volume in cubic inches is the product of what three numbers?

9. How many cubic inches are there in a brick 8 in. long, 4 in. wide, and 2 in. thick?

SOLUTION: If the brick were 1 in. long, 1 in. wide, and 1 in. thick, it would contain 1 cu. in.; if it were 8 in. long, 1 in. wide, and 1 in. thick, it would contain 8 cu. in.; if it were 8 in. long, 4 in. wide, and 1 in. thick, it would contain 32 cu. in. Since it is 8 in. long, 4 in. wide, and

2 in. thick, it contains 64 cu. in.

The operations performed in the analysis are multiplying 1 cu. in. by 8; multiplying the product 8 cu. in. by 4; multiplying this product, 32 cu. in., by 2; the result is 64 cu. in.

What is the unit of measurement?

In finding the volume of the brick without going through the analysis, what is to be done?

Notice that the dimensions are given in linear inches; the volume is given in cubic inches. If the dimensions had been linear feet, the volume would be expressed in what units?

10. A pile of 2-foot wood is 10 ft. long, 4 ft. high. How many cubic feet are there in the pile? Analyze. Solve without analyzing.

11. How many cubic feet are there in a block of granite 8 ft. long, 3 ft. wide, and 4 ft. high? Analyze. Solve without analyzing.

12. How many cubic feet are there in of a cord of wood? In of a cord?

13. The volume of a brick is 64 in. It is 8 in. long and 2 in. thick. How wide is it?

14. Having the number of cubic units in a rectangular solid, and the number of linear units in its length and thickness, how can you find its width?

15. Having the volume of a rectangular solid and any two dimensions given, how can you find the other dimension?

The solar year, or the time required for the earth to revolve around the sun, is 365 days, 5 hours, 48 minutes, and 46 seconds nearly. This is nearly of a day more than 365 days. This fractional part of the day is omitted each year until the fourth year, when the time lost amounts to nearly a day. In every year, the date number of which is divisible by four, one day is added to the month of February, and that year is called leap year, except in the centennial years, in which case the date number must be divisible by four hundred to be a leap year. This is because, in adding one day every four years, the error amounts to something over three days in four centuries, and is corrected by making the centennial year a leap year once in four hundred years only.

ORAL

126. 1. How many minutes are there in 2 hours? In half an hour? In an hour and a half? In 10 hours?

2. How many minutes are there from 9 A.M. to 11.30 A.M.? From 10 A. M. to 2.30 P.M.?

31

3. How many months are there in 32 years? In 43 years? 4. A man lived 15 years more than half a century. At what age did he die?

5. How many days are there in the spring months? In the winter months of 1908? Of 1909?

CIRCULAR MEASURE

127. 1. Circular measure is used in measuring arcs of circles and angles, and in estimating latitude and longitude.

128. 1. The longitude of a place is its distance east or west from a given meridian. The meridian most commonly used for this purpose is the one passing through the observatory at Greenwich, England. It is called the prime meridian. All places on it have 0° longitude. Longitude is reckoned in degrees, minutes, and seconds, and ranges from 0° to 180° east or west. The earth revolves on its axis from west to east once in every twenty-four hours, and this causes the sun to appear to revolve around the earth from east to west in the same time. Since the sun travels through the entire circumference, or 360°, in twenty-four hours, in one hour it travels 14 of 360°, or 15°; in one minute it travels of 15°, or 15', and in one second it travels of 15', or

15".

Places to the east of any meridian have later time, those to the west, have earlier time, since the sun appears first to those in the east. When the sun is directly overhead, it is

noon on that meridian.

A difference of 15°

TABLE OF LONGITUDE AND TIME

of longitude makes a difference of 1 hour of time. of longitude makes a difference of 1 minute of time. A difference of 15" of longitude makes a difference of 1 second of time.

A difference of 15′

ORAL AND WRITTEN

129. 1. How many degrees of longitude make a difference of 1 hour in time? 12 hours? 30 minutes? 20 seconds?

2. When it is noon at Chicago, what is the time 15° east? 15° west? 30° east? 30° west? 60° east? 60° west?

3. What is the difference in longitude between two cities, if the difference in time is 2 hours? 3 hours, 30 minutes?

4. If I start at Denver and travel until my watch is 1 hr. 30 min. too fast, in what direction and how far do I travel?

5. The first shock of the San Francisco earthquake, April 18, 1906, was recorded at 5.12 A.M. in observatories in 120° W. and at 19 min. 20 sec. past 8 A.M. in 75° W. What length of time was consumed by the shock in passing between the two observatories?

6. The longitude of Philadelphia is 75° 10' 0'' west, and of Vienna 16° 20′ 22′′ east. What is the time in Vienna

when it is 9 A.M. in Philadelphia ?

there are degrees, minutes, and seconds in of the difference in longitude, or 6 hr. 6 min. 17 sec. Since Vienna is in east longitude, and Philadelphia in west longitude, the sun rises earlier in Vienna, and hence we must add the difference in time to 9 A.M., which gives 6 min. 1 sec. past 3 P.M.