COMPARATIVE VIEW OF DENOMINATE NUM. BERS AND FRACTIONS. The common fraction may be reduced to a decimal; thus, B = .2864583. = 55 19 The denominate numbers are all reduced to the lowest denomination, and the whole number and fractions are all reduced to a common denominator. Cor. 1.—As the number of each denomination may properly be regarded as units, so the number expressing the numerator of any fraction may be regarded as units, and used accordingly. TIME. PROBLEM T. To find the difference of time between two given dates, subtract the former date from the latter. EXAMPLES. 1. What is the time from the 10th April, 1845, to the 15th July, 1850 ? yr. da. 1850 ny 15 1845 4 10 mo. mo. 2. What is the time between 15th July, 1850, and the 10th April, 1856 ? yr. da. 1856 4 10 1850 ng 15 Ans. 5 8 25 3. What is the time from the 15th May, 1856, to the 1st January, 1860 ? Ans. 3 yr. 7 mo. 16 da. 4. How many years, months and days from March 10th, 1872, to June 20th, 1874 ? Ans. 2 yr. 3 mo. 10 da. 5. What is the time from Sept. 13th, 1865, to April 10th, 1870 ? Ans. 4 yr. 6 mo. 27 da. 6. What is the time from Dec. 25th, 1870, to Jan,13th, 1875? How many days ? 1st Ans. 4 yr. 18 da. 360 x 4 = 1440 18 2d Ans. 1458 days. PROBLEM 11. To find the difference of time of two places whose longitudes are given. REM.-Divide the difference of longitude by 15, and in the quotient regard degrees, minutes and seconds as hours, minutes and seconds of time. The time must be rated from the fixed meridian, which for the world is Greenwich, England, and as the sun appears to move west, every place west of this meridian must have earlier time, at the rate of 1 hour for every 15 degrees ; that is, when it is 9 o'clock A.M., at Greenwich, it is 8 A.M. 15 degrees west of Greenwich. EXAMPLES, 1. The longitude of New York is 74° 1' 6" west, and that of Cincinnati is 84° 24' west. What is the time at Cincinnati, when it is 12 o'clock, noon, at New York. 84° 24' 0" 74 1 6 ܙ 60 622 ( 41 60 12 00 00 41 314 Ans. 11 18 28%, A.M. 22 15 ng 60 474 ( 31% 45 24 15 ਤ *= 2. Longitude of New York is 74° 1' 6" and St. Louis 90° 15' 10". When it is noon at New York, what is the time at St. Louis ? 90° 15' 10" 174 1 6 15 3. The longitude of Dublin is 6° 20' 30" west, and of Louisville 85° 30' west. What is the time at Louisville, when it is 2 A.M. at Dublin ? sec. 85° 6 19° 30' 00" hr. min. 30 2 00 00 30 ; 15 = 5 16 38 Ans. 8 43 22 P.M. Of the previous day. PROBLEM III. To find the difference of longitude of two places, the difference in their time being given. Multiply the difference of time by 15, and regard the hours, minutes and seconds of the product as degrees, minutes and seconds of longitude. EXAMPLES. 1. The difference in time of two places is 3 hr. 45 min 30 sec.; what is the difference in longitude ? 2. The difference in time between New York and Cincinnati is 41 min. 31% sec.; the longitude of New York is 74° 1' 6" west. What is the longitude of Cincinnati. 84° 24', west long. of Cincinnati. |