Ray's New Higher Arithmetic · Art. 225 · Unit 11: Compound Denominate Numbers
57. Longitude and time
Goal: Your student finds the difference of longitude from a difference of time and the reverse, and works out the time in another city.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Two cases: difference of time to longitude (multiply by 15) and longitude to time (divide by 15), with worked examples, a table of longitudes of American and world cities, and 11 practical examples (New York and Cincinnati, a ship's chronometer, and others). Answers are printed.
The lesson, step by step
Warm-up
Ask: The earth turns 360° in 24 hours. How many degrees in one hour? (15.)
The two cases
Read:
To find the difference of longitude between two places when the difference of time is given.
To find the difference of time when their longitudes are given.
Rules: multiply the difference of time by 15 for longitude; divide the difference of longitude by 15 for time.
Work the book's examples
Time to longitude: 4 hr. 18 min. 26 sec. × 15 = 64° 36' 30". Longitude to time: 81° 39' 22" ÷ 15 = 5 hr. 26 min. 37 7/15 sec.
Local time
Before standard time zones (adopted by U. S. railroads in 1883, a few years after this book), every town kept its own sun time. Places east have later time. Use the book's table of longitudes.
Guided practice
Together:
It is six o'clock A. M. at New York; what is the time at Cincinnati?
Find both longitudes in the table, subtract, divide by 15, and subtract that time from 6:00. (The book: 18 min. 2.6 sec. after 5 A. M.)
Independent practice
Your student works the rest of the 11 examples.
Wrap-up
Ask: A ship's clock set to Greenwich time shows 4 P. M. when it is noon on board. Is the ship east or west of Greenwich, and how far? (West; 4 hours × 15 = 60°.)