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 4 seconds of time. One arc second corresponds to so 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 the dollar. 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 23.85¢. 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. SHORT METHODS. Multiplication and Division. Art. 1. To multiply a number by 50: Multiply of the number by 100. Why? (a) Find the sum of the fifteen products. Art. 2. To multiply a number by 51: Take 50 times the number, to which add the number itself. Why? (b) Find the sum of the fifteen products. Art. 3. To multiply a number by 52: Take 50 times the number, to which add twice the number. 34 × 52 50 times 34 = 1700 Why? 1700 + 68 = 1768 (c) Find the sum of the twelve products. Art. 4. To multiply a number by 49: Take 50 times the number, from which subtract the number itself. Why? 24 × 49 50 times 24 = 1200 1200 24 = 1176 (d) Find the sum of the nine products. Art. 5. To multiply a number by 331: Multiply of the number by 100. Why? Art. 6. To multiply a number by 341: the number, to which add the number itself. Take 331⁄2 times Why? (f) Find the sum of the twelve products. Art. 7. To multiply a number by 35: the number, to which add twice the number. Take 331⁄2 times Why? (g) Find the sum of the nine products. Art. 8. To multiply a number by 321: Take 331⁄2 times the number, from which subtract the number itself. Why? |