Denominate Numbers-Time. 352. The standard units in the measurement of time are the day and the year. NOTE 1.-The solar day is the interval between the time when the sun is on a given meridian and the time when it appears on that meridian again. These intervals (solar days) are not perfectly uniform. The average of these intervals is the mean solar day—the day noted by our watches and our clocks-the day, one twenty-fourth of which is called an hour. NOTE 2.-The solar year is the time of one revolution of the earth around the sun, or nearly 3651 mean solar days. The calendar year of 365 days is nearly 6 hours less than the solar year. Four years of 365 days each, would lack nearly 24 hours (4 times da.) of being equal to 4 solar years. Hence 1 day is added to 365 every fourth year, with the exception noted below. NOTE 3.-The exact length of a solar year is 365 da. 5 hr. 48 min. 48 sec. Since this lacks 11 min. 12 sec. of being 365 days, it follows that if every fourth year should contain 366 days, in 400 years the calendar years would amount to 3 days (400 times 11 min. 12 sec.) more than the solar years. Hence three of the years that would otherwise contain 366 days, are made to contain 365 days. The years thus changed to 365 days are those ending the centuries (1800, 1900, 2000, 2100, etc.) unless the number denoting the year is exactly divisible by 400. Denominate Numbers-Time. EXERCISES. 1. If Jan. 1 of a common year is Monday, Feb. 1 is ; April 1 is -; May 1 is ; June 1 March 1 is is; July 1 is; August 1 is; September 1 is ; November 1 is -; December 1 -; October 1 is is 2. Jan. 1, 1899, was Sunday. Tell the day of the week for each of the following dates: 1900, January 1; February 1; February 8. PROBLEMS. 1. How many days from Jan. 1, 1900, to Aug. 17, 1900 2. Jan. 1, 1900, falls on Monday. Upon what day of the week does Aug. 17, 1900, fall? 3. What month begins on the same day of the week as January in every common year? 4. What months begin on the same day of the week as February in every common year? 5. If January begins on Sunday, (a) how many Sundays in the month? (b) How many Mondays? (c) How many Tuesdays? (d) How many Wednesdays? 6. If a common year begins on Sunday, (a) how many Sundays in the year? (b) How many Mondays? 7. (a) How many days old are you? (b) How many weeks old? (c) Upon what day of the week were you born? Denominate Numbers Circular Measure. 353. For the purpose of measurement, every circumference is supposed to be divided into 360 equal parts. Each of these parts is called an arc of 1 degree. 354. An angle is measured by regarding its vertex as the center of a circle, its sides being extended until they cut the circumference. The angle is measured by the arc lying between its sides. If the intercepted arc is an arc of 45 degrees, the angle is an angle of 45 degrees; if the arc is 20 degrees, the angle is 20 degrees, etc. 355. In geography, a meridian is a north and south line on the surface of the earth, extending from pole to pole. 356. Longitude is distance east or west in degrees (or parts of degrees) from a given meridian. Longitude is usually measured from the meridian that passes through Greenwich. PROBLEMS. Find difference in longitude between 1. Rome, 12° 27' east, and Washington, 70° 2' 48" west. 2. Washington and Chicago, 87° 37' 30" west. 3. Chicago and Denver, 104° 59′ 23′′ west. 4. Denver and San Francisco, 122° 24′ 15′′ west. 5. San Francisco and Berlin, 13° 23' 53" east. Denominate Numbers-Longitude and Time. 357. One degree of longitude corresponds to 4 minutes of time. EXPLANATORY.-The sun seems to move over 360 degrees of longitude in 24 hours; over 1 degree in of 24 hours = 4 minutes. PROBLEMS.* 1. When it is noon at Greenwich, what is the time at Washington, 77° 2' 48" ? 2. When it is noon at Washington, what is the time at Greenwich? 3. When it is noon at Portland, Maine, 70° 15′ 40′′, what is the time at San Francisco, 122° 24' 15"? 4. When it is noon at San Francisco, what is the time at Portland, Maine? 358. Standard Railroad Time. Every railroad train in North America is run on the time of some one of the following meridians: 60th meridian (passing through Labrador). 75th meridian (passing near Philadelphia). 90th meridian (passing near St. Louis). 105th meridian (passing near Denver). 120th meridian (passing near Carson City). Observe that each of the above numbers after the first is 15 greater than the one preceding it; and that 15 degrees of longitude correspond to 1 hour of time. *At first the pupil should give an approximate answer to these problems, considering integral degrees only. Later, if thought advisable, he may take into the account the parts of degrees. One arc minute corresponds to of 4 minutes of time, or seconds of time. One arc second corresponds to go of 4 minutes of time, or of one second of time. That is, each arc degree corresponds to 4 minutes of time; each arc minute, to 4 seconds of time; each arc second, to of a second of time. Hence, multiplying by 4 the figures standing for degrees, minutes, and seconds, of longitude will give the figures standing for minutes, seconds, and 60ths of seconds, of time. Denominate Numbers-Value. 359. The standard unit of value in the United States is 360. The standard unit of value in Great Britain and Ireland is the pound. Its value, reckoned in United States money, is $4.8661. ENGLISH, OR STERLING, MONEY. 4 farthings (far.) = 1 penny (d.). 361. The standard unit of value in France is the franc. Its value, reckoned in United States money, is 19.34. 362. The standard unit of value in Germany is the mark. Its value, reckoned in United States money, is 23.854. 363. The standard unit of value in Russia is the ruble. Its value, reckoned in United States money, is $.772. PROBLEMS. 1. Find the value of a guinea in United States money. 2. Find the value of $1000 in English money. 3. Find the value of £5000 in United States money. 4. Find the value of £1000 in Russian money. 5. Find the value of 4000 marks in English money. 6. Find the value of 8000 francs in United States money. |