ADDITION AND SUBTRACTION.

293. Illustrative Examples. (1) Add 2 mi. 172 rd. 6 ft., 1 mi. 310 rd. 14 ft., and 95 rd. 11 ft. (2) From 5 rd. 3 yd. 1 ft. take 1 rd. 4 yd. 2 ft.

(1) The numbers are written so that units of the same order are expressed in the same column, and the adding begins with the units of the lowest denomination, as in simple addition.

The sum of the feet is 31 feet = 1 rod 14 feet. Writing the 14} feet under the line in the place of feet, and adding 1 rod with the rods of the given numbers, the sum is 578 rods, equal to 1 mile 258 rods. The sum of the miles is 4. Ans. 4 mi. 258 rd. 14 ft. 6 in.

(2) The subtracting begins with the units of the lowest denomination, as in subtraction of simple numbers. As there is but 1 foot in the minuend, 1 of the 3 yards is changed to 3 feet, making with the 1 foot, 4 feet; 4 feet less 2 feet is 2 feet. As there are but 2 yards left in the minuend, 1 of the 5 rods is changed to 51⁄2 yards, making with the 2 yards, 7 yards; 7 yards less 4 yards is 3 yards. 4 rods less 1 rod is 3 rods. Changing the yard to feet we have 1 foot 6 inches, which added to 2 feet makes 3 feet 6 inches or 1 yard 6 inches. Ans. 3 rd. 4 yd. 0 ft. 6 in. NOTE.-The operations upon compound numbers are similar to those upon simple numbers, the difference being that in operations upon compound numbers varying scales are used instead of the uniform scale of tens. Therefore, no special rules are necessary for addition, subtraction, multiplication, and division.

294. Examples for Written Work.

92. How much time is there in 2 h. 40 min., 3 h. 17 min., and 4 h. 45 min. ?

93. Add together 10° 25' 40", 4° 9' 5", and 15° 45′ 18′′.

94. Add together £5 17s. 11d., £8 10s. 4d., 18s. 6d., and £3 7s. 6d.

95. How much wood is there in 3 piles containing, respectively, 5 cords 3 cord feet, 8 cords 4 cord feet, and 10 cords 7 cord feet.

96. How much wheat is there in 1 bu. 3 pk. 7 qt., 2 bu. 1 pk. 5 qt., 1 bu. 6 qt., and 3 bu. 2 pk. 6 qt.?

97. How much land is there in four pastures, the first containing 7 A. 64 sq. rd., the second 15 A. 82 sq. rd. 260 sq. ft., the third 5 A. 17 sq. rd. 160 sq. ft., and the fourth 19 A. 89 sq. rd. 36 sq. ft.?

98. Add 320 cu. yd. 20 cu. ft. 1000 cu. in., 29 cu. yd. 24 cu. ft. 968 cu. in., 500 cu. yd. 728 cu. in.

106. From a firkin of butter containing 44 lb. were sold 18 lb. 10 oz. How much remained?

107. From a cask of oil containing 54 gal. were drawn 5 gal. 2 qt. How much remained?

108. A person who had 7 bu. 3 pk. 2 qt. of grapes sold 3 pk. 4 qt. to one person and 2 pk. 5 qt. to another. What quantity had he left ?

109. How much remains of a journey of 54 mi. after 7 mi. 851⁄2rd. have been traveled?

110. The longest day in Boston is 15 h. 16 min. What is the length of the shortest night?

111. Having 10 sovereigns in my purse, I spent in Liver pool £1 10s. 6d., £2 5s. 10d., and 11s. 6d. How much money had I left?

112. The Hoosac Tunnel is 25,031 ft. long; Mt. Cenis tunnel is 7ğ mi. long. What is the difference in feet?

113. The entire excavation for a cellar was 888.88 cu. yd.; the masonry in the cellar walls measured 111 perches, a perch being 16 ft. by 11 ft. by 1 ft. What was the num

ber of cubic yards inside the walls?

295. How is the difference in latitude found between two places on the same side of the equator? On opposite sides?

Latitude of :

Chicago, Ill., 42° N.

Washington, D.C., 38° 51′ 20′′ N.

San Francisco, 37° 47' 55'' N.

Quebec, 46° 48′ 17′′ N.

Rome, Italy, 41° 5′ 54′′ N.

Cape Good Hope, 32° 24' 3" S.
Cape Horn, 55° 58′ 4′′ S.

London, 51° 30′ 48′′ N.

Find the difference in latitude between:

114. Washington and San Francisco.

115. Chicago and Rome.

116. London and Quebec.

117. Cape Horn and Cape Good Hope. 118. Cape Horn and San Francisco.

119. Washington and Rome.

120. Select from your map two places on the same side of the equator, and find their difference of latitude.

121. Select two places on opposite sides of the equator, and find their difference of latitude.

296. How is the difference of longitude found between two places on the same side of the meridian of Greenwich? On opposite sides?

NOTE. Whenever the difference of longitude exceeds 180°, it should be subtracted from 360°. Why? Show this by a diagram.

Longitude of :

New York, 74° 0' 3" W.
Boston, 71° 3' 30" W.

London, 0° 5' 48" W.

Paris, Fr., 2° 20′ 22′′ E.

Canton, 113° 14' 0" E.

San Francisco, 122° 26' 48" W.

Find the difference of longitude between :

122. Boston and New York. 123. New York and London.

124. London and Paris.

125. Canton and San Francisco.

297. To find the difference of time between two dates.

Illustrative Example. What is the time in years, months, and days from May 11, 1897, to August 7, 1899 ?

SOLUTION. From May 11, 1897, to May 11, 1899, is 2 years; to July 11 is 2 months more. From July 11 to July 31 is 20 days, and to August 7 is 7 days more. Ans. 2 yr. 2 mo. 27 da.

298. From the preceding illustration may be derived the following

Rule.

To find the number of years, months, and days between two dates: First find the number of entire years between the two dates, then the number of full months remaining, and lastly, the remaining days, including the day of the later date.

NOTE.

The method of finding difference of time by compound subtraction will be found in the Supplement, Art. 15.

Oral Exercises.

299. a. What time elapsed between the birth of Benja min Franklin, Jan. 17, 1706, and that of George Washington, Feb. 22, 1732?

b. America was discovered by Columbus Oct. 12, 1492; the settlement at Jamestown took place May 13, 1607. What time elapsed between these two events?

c. Lafayette was born Sept. 6, 1757, and died May 19, 1834. What was his age at the time of his death?

d. What was Lafayette's age at the time of the Declaration of Independence, July 4, 1776?

e. How old was Washington at the time of his death, which occurred Dec. 14, 1799?

f. How old was Lafayette when Washington died? g. What time elapsed between the landing of the Pilgrims, Dec. 22, 1620, and the Declaration of Independence?

h. How many years have elapsed since the Declaration of Independence?

i. If a man was born March 5, 1856, how old will he be if alive at the close of the nineteenth century?.

300. Illustrative Example. Find the exact number of days from Jan. 7, 1896, to April 10, 1896.

SOLUTION. There are 24 days remaining in January, 29 days in February (leap year), 31 days in March, and 10 days in April.

24 +29 +31 + 10 = 94. Ans. 94 days.

NOTE. — Any year is a leap year when the number denoting the year is divisible by 4 and not by 100, and when it is divisible by 400. (See Supplement, Art. 39.)

Find the exact number of days.

j. From April 10 to July 5.

k. From Sept. 3 to Nov. 12.

7. From Oct. 4 to Jan. 1. m. From Dec. 2 to Feb. 1. 1896.

n. From Dec. 6, 1895, to March 8,
o. From Oct. 24, 1895, to May 12, 1896.

MULTIPLICATION AND DIVISION.

301. Illustrative Examples. (1) Multiply 5 oz. 7 pwt. by 4. (2) Divide 5 A. 8 sq. rd. by 3.

(1) 4 times 7 pwt. equals 28 pwt., which equals 1 oz. 8 pwt. Write 3pwt., and keep the 1 oz. to add to the product of ounces. 4 times i oz. equals 20 oz., which, with the 1 oz. kept, equals 21 oz., or 1 lb. 9 oz. Ans. 1 lb. 9 oz. 8 pwt. (2) 5 acres divided by 3 gives 1 acre, with 2 acres remaining. We write the 1 acre and change the 2 acres to square rods, which equals 320 sq. rd. This, with 8 sq. rd., equals 328 sq. rd. 328 sq. rd. divided by 3 gives 109 sq. rd. Ans. 1 A. 109 sq. rd.