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# Modern Arithmetic III, Article 81

To complete this lesson, complete the following tasks:

1.   Study the lesson for mastery.
2.  Memorize the lesson that it may be recited.
3.  Complete the lesson assessment.

## Lesson

Before beginning this lesson, be sure you are familiar with Circular Measure in Article 72 and the rule for the Division of Compound Numbers in Article 80.

1. On what is our ability to calculate time based?
Our ability to calculate time is based on our knowledge of the sun’s movement around the circumference of the earth.

2.  Do the speed of the sun’s movement or the circumference of the earth ever change?
No.  The speed of the sun’s movement and the circumference of the eartgh are always the same.

3. What are we able to do since the sun’s movement and the circumference of the earth are always the same?
Since both the size of the earth, and the speed of the sun’s movement are always the same, we are able to compare longitude and time.

4. How is the circumference of the earth divided?
The circumference of the earth, like other circles, is divided into 360 equal parts.

5.  What do we call these 360 parts into which the circumference of the earth is divided?
The 360 parts into which the circumference of the earth are divided are called
degrees of longitude.

6.  What is the speed of the sun’s movement relative to the earth?
The sun appears to pass entirely round the earth, all 360°, once in 24 hours, or one day.

7. Over how much of the earth’s surface does the sun pass in 1 hour of time?
If we divide the 360° of longitude by 24 hours of time, we find that the sun passes over 15° of the earth’s circumference every hour. (360° ÷ 24 hrs. = 15°).

8.  Why do we use degrees rather than distance to measure time on the earth?
The distance the sun travels on the earth’s surface in one hour differs based on where a place is located.  In one hour, the sun covers a greater distance on the earth’s surface at the equator than it does to the north or south of it.  This is why we use degrees rather than distance to measure time.

9.  Over how much of the earth’s surface does the sun pass in 1 minute of time?
As 15° equals 900’ (that is, 900
minutes of longitude), and 1 hour equals 60 minutes of time, therefore, in 1 minute of time the sun passes over 15’ of a degree. (900’ ÷ 60 min. = 15’).

10.  Over how much of the earth’s surface does the sun pass in 1 second of time?
As 15’ equal 900” (that is, 900
seconds of longitude), and 1 minute of time equals 60 seconds of time, therefore, in 1 second of time the sun passes over 15” of a degree. (900” ÷ 60 = 15”).

11.  How are degrees of longitude converted to hours of time?
Degrees (°) of longitude, divided by 15, give hours of time.

12. How are minutes of longitude converted to minutes of time?
Minutes () of longitude, divided by 15, give minutes of time.

13. How are seconds of longitude converted to seconds of time?
Seconds (“) of longitude, divided by 15, give seconds of time.

14. What is the rule to find the time corresponding to any difference of longitude?
Divide the longitude by 15, according to the rule for Division of Compound Numbers, and mark the quotient hours, minutes and seconds of time, instead of degrees, minutes and seconds of longitude.

15.  What is the rule to find the longitude corresponding to any difference of time?
Multiply the time by 15, according to the rule for multiplication of compound numbers, and mark the product in degrees, minutes and seconds of longitude, instead of hours, minutes and seconds of time.

## Assignment

Modern Arithmetic III, Article 81 Assessment