273. SUBTRACTION OF COMPOUND NUMBERS. 117. From 14 gal. 2 qt. 1 pt. 2 gi. take 5 gal. 3 qt. 0 pt. 3 gi. O pt. from 0 pt.=0 pt. as the next term in the remainder; and so on. 120. If of the month of December 17 days, 9 hours, 43 minutes, 27 seconds have passed, how many days, hours, etc., remain? 121. If from a lot of land containing 7 a. 80 sq. rd. 5 sq. ft. there are sold 1 a. 157 sq. rd. 78 sq. ft., how much remains? 274. To find the difference of time between two dates. 122. What is the difference of time between July 15, 1877, and Nov. 8, 1879? Solution. From July 15, 1877, to July 15, 1879, is 2 years; from July 15 to Oct. 15 is 3 months; from Oct. 15 to Oct. 31 is 16 days; and from Oct. 31 to Nov. 8 is 8 days. Hence, from July 15, 1877, to Nov. 8, 1879, is 2 yr. 3 m. 24 d., Ans. Hence, Rule. Find the number of complete years, then the number of complete calendar months, and then the remaining days. 123. How long from the battle of Waterloo, June 18, 1815, to the death of Napoleon, May 5, 1821? Ans. 5 yr. 10 m. 17 d. 124. How long from the battle of Lexington, Apr. 19, 1775, to the surrender of Cornwallis, Oct. 19, 1781 ? 125. How long from the inauguration of Washington, Apr. 30, 1789, to the battle of New Orleans, Jan. 8, 1815? 126. How long from the Declaration of Independence, July 4, 1776, to the present time? 127. Daniel Webster was born Jan. 18, 1782, and died Oct. 24, 1852; at what age did he die? 128. A note given July 6, 1867, was paid Sept. 9, 1871; how long was it on interest? 129. Find the exact number of days passed between April 7, 1871, 9 A. M., and June 13, 1873, 4 P. M. OPERATION. April 7, 1871, 9 A. M., to April 7, 1873, 9 A. M....731 days. hours. "9 A. M. to 4 P. M.... From Apr. 7, 1871, 9 A. M., to Apr. 7, 1873, 9 A. M., there are 2 years, in which there is a leap year; that is, 366 d. + 365 d., or 731 d. From April 7, 1873, 9 A. M., to May 7, 1873, 9 A. M., there are 30 days; and from May 7, 9 A. M., to June 7, 9 A. M., 31 days. 130. Find the exact number of days passed between Feb. 26, 1868, 7 P. M., and Dec. 23, 1875, 3 p. M. 275. MULTIPLICATION OF COMPOUND NUMBERS. 131. Multiply 4 gal. 3 qt. 1 pt. 3 gi. by 7. OPERATION. gal. qt. pt. gi. Multiply 4 3 1 3 By 7 Product, 34 3 0 1 = 7 times 3 gi. 21 gi.=5 pt. and 1 gi. Write the 1 gi. under the gills, and reserve the 5 pt. to be added to the 7 times 1 pt. 7 times 1 pt. plus 5 pt.= 12 pt. Write O under the pints, and re serve the 6 qt. to be added to the 7 times 3 qt. ; and so on. = 6 qt. 134. Bought 5 loads of wood, each measuring 1 cd. 5 cd. ft. 8 cu. ft., at $6 a cord; cost of the whole? what was the quantity bought and the Ans. 8 cd. 3 cd. ft. 8 cu. ft.; $50.62. 135. If a ship sail 2° 30′ 20′′ a day, how far will she sail in 8 days? 276. DIVISION OF COMPOUND NUMBERS. 136. Divide 30 gal. 3 qt. 1 pt. 3 gi. by 7. OPERATION. gal. qt. pt. gi. 7) 30 3 1 3 Ans. 4 1 1 14 7 Proof, 30 3 1 30 gal. 7 gives 4 gal. and a remainder of 2 gal. 2 gal. = 8 qt. which added to the 3 qt. gives 11 qt. 11 qt.÷7 gives 1 gal. and a remainder of 4 qt. 4 qt. 8 pt. which added to the 1 pt. gives 9 pt.; and so on. 137. Divide 3 wk. 6 d. 14 h. 17 min. 57 sec. by 3. 138. Divide 25° 4′ 10′′ by 10. 139. Divide 107 gal. 1 qt. by 12. 140. Divide 98 bush. 3 pk. 2 qt. 1 pt. by 11. = LONGITUDE AND TIME. 277. As the earth turns on its axis from west to east once in 24 hours, the sun appears to go from east to west round the earth, 360°, in 24 hours; consequently in 1 hour it appears to go 24 of 360°, or 15°; in 1 minute, of 15°, or 15'; in 1 second. of 15', or 15". Hence the following 278. TABLE OF LONGITUDE AND TIME. 360° of longitude correspond to 24 hours, or 1 day of time. 141. When it is 12 o'clock, noon, at Washington, what time is it at Greenwich, Washington being 77° 2′ 48′′ west of Greenwich? OPERATION. 15) 77° 2' 48" 5 h. 8 m. 11 sec., Ans. Since 15° of longitude make a difference of 1 hour in time, and the scale for degrees, minutes, and seconds is the same as that for hours, minutes, and seconds, the difference in longitude in degrees, minutes, and seconds divided by 15 will give the difference in time in hours, minutes, and seconds. Hence, 77° 2′ 48′′ divided by 15 gives the difference in time, viz. 5 h. 8 m. 11 sec. between Greenwich and Washington; and as Greenwich is farther east than Washington, the hour of the day is later in Greenwich than in Washington; that is, it is 8 m. 113 sec. past 5 o'clock in the afternoon at Greenwich when it is noon at Washington. Hence, 279. To find the difference of time between two places when their longitude is known, Rule. Divide the difference of longitude in degrees, minutes, and seconds by 15, and the quotient will represent the difference in time in hours, minutes, and seconds. NOTE. At the place most easterly the sun rises first; that is, the day begins first, and hence noon comes first, and the day closes first. Therefore the place most easterly has its hour of the day, at a given moment, latest. 280. For reference the longitude of several places from Greenwich is here given. Albany, 73° 44′ 49′′ W. Oahu, 157° 37' W. 142. What is the difference in the time of Boston and Washington, and when it is 3 o'clock P. M. in Boston what time is it in Washington? 2d Ans. 36 m. 5 sec. past 2 P. M. 143. What is the difference in time between Paris and New York? NOTE 3. Since Paris is in east longitude, and New York in west, their difference in longitude is found by adding 2° 20′ 15′′ to 74° 0′ 3′′. 144. What is the difference in time between Philadelphia and Chicago? 145. What is the difference in time between New Orleans and St. Petersburg? 146. What is the difference in time for 90° in longitude? 281. To find the difference in the longitude of two places, when the difference of time is known. 147. When it is 12 o'clock at Washington, it is 23 m. 543 sec. past 12 at Boston; what is the difference in the longitude of the two places? |