Ray's New Higher Arithmetic · Arts. 205–208 · Unit 11: Compound Denominate Numbers
51. Time, longitude and other tables
Goal: Your student uses the table of time, applies the leap-year rule, knows that 15° of longitude make 1 hour, and reads the paper and counting tables.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Measure of time (solar, mean solar, civil and astronomical days; the table; the length of the solar year), the rule for leap years with a note on the Julian and Gregorian calendars, the comparison of time and longitude, and miscellaneous tables (books and paper, counting, barrels and other units).
The lesson, step by step
Warm-up
Ask: How many seconds in a day? (86400.)
Days
Read:
Time is a measured portion of duration.
The Solar Day is the interval of time between two successive passages of the sun over the same meridian.
The Civil Day, used for ordinary purposes, commences at midnight and closes at the next midnight.
The book gives the solar year as 365 da. 5 hr. 48 min. 46.05 sec., or about 365¼ days.
Leap years
Read:
Every year that is divisible by 4 is a leap year, unless it ends with two ciphers
and a year ending in two ciphers is a leap year only if it divides by 400. The book's note: Pope Gregory XIII corrected the calendar in 1582, and England adopted it in 1752. Ask: Were 1900 and 2000 leap years? (1900 no; 2000 yes.)
Time and longitude
Read:
The longitude of a place is its distance in degrees, minutes, and seconds, east or west of an established meridian.
The earth turns 360° in 24 hours, so 15° of longitude = 1 hour of time, 15' = 1 minute, 15" = 1 second.
Other tables
Read:
The words folio, quarto, octavo, etc., used in speaking of books, show how many leaves a sheet of paper makes.
Also: 24 sheets = 1 quire, 20 quires = 1 ream; 12 = 1 dozen, 144 = 1 gross, 20 = 1 score.
Practice
Your student finds: minutes in a week; which of 1800, 1880, 1896 and 2100 are leap years; how many sheets in a ream.
Wrap-up
Ask: If the sun is overhead here, where on earth is it overhead one hour later? (15° farther west.)
Answers to the book's problems
Practice: 1 week = 10080 minutes; leap years: 1880 and 1896 (1800 and 2100 are not); 1 ream = 480 sheets.
Worked out for this site from the scan. If a number in your copy differs, trust the book.