They also sold on commission, at 10%, 5 chairs, at $8; 12 chairs, at $1.70; 1 bureau, at $18; 1 table, at $8; 1 lounge, at $12; 1 stove, at $17. What were their net proceeds from the above sales?

97. How many bricks 8 in. by 4 in. by 2 in. in the walls of a building 29 ft. long by 24 ft. wide and 20 ft. high, outside measurement, having 10 windows 6 ft. by 4 ft. and 2 doors 7 ft. by 4 ft., the thickness of the walls being 1 foot, and of the entire wall being mortar?

NOTE. In estimating the number of bricks required, masons reckon by outside measurements, and make no allowance for corners.

98. The circular outlet to a cistern being 4 inches in diameter, what must be the width of a rectangular receivingpipe, whose depth is 2 inches, that its capacity may be the same as that of the discharging-pipe?

99. When it is 10 A. M. in X, which is 44° 15′ 2′′ W. long., what is the time in Y, which is 8° 4' 40" E. long.?

100. A, B, and C shipped goods by the same vessel. The value of A's goods was $50000; of B's, $40000; of C's, $30000. During a storm half of A's goods and one fifth of B's were thrown overboard. What should be each man's share of the loss, and how much should be paid to A by C and by B to adjust the losses?

101. I sold 6 sewing-machines at $72 each. On two of them I gained 20%, on two others 33%, and on the rest I lost 25%. What was the balance of gain or loss?

102. A grocer imported 75 gallons of oil, which cost him $2 a gallon and a duty of 10%. Suppose 5 gallons to leak out, for what must he sell the remainder per gallon to gain 10% on the money spent?

103. At 1 cent per cubic foot, what will be the cost of dig ging a ditch outside a square garden containing 12.75 square rods, the ditch to be 7 feet wide and 5 feet deep?

104. How many gallons in a cylindrical jar 2 feet across and 4 feet high?

105. I found, on going to Gile & Walcott's dry-goods store, that they had that morning marked up their goods 15%. What did I save by purchasing the day before the following goods: 18 yds. blk. silk, at $1.12; 13 yds. de laine, at $0.27; 9 yds. cambric, at $0.15; 3 yds. silesia, at $ 0.25; 1 waterproof, at $8? 106. A grocer paid 21 cents a gallon for a cask containing 27 gallons of kerosene, 10 % of which leaked out. If the remainder was sold 25% on the gallon higher than it cost, what was the gain or loss on the money invested?

107. Supposing a cubic foot of snow to weigh 21 lbs., what will be the pressure of a body of snow 9 inches deep upon a flat roof 100 ft. by 25 ft.?

108. If an elephant's tusk 9 feet long and 8 inches in diameter at the base weighs 214 pounds, what would be the dimensions of a similar tusk weighing 75 pounds?

109. An engineer, having placed a mortar near the bank of a river, wished to find its distance from a fort on the opposite

shore. To do this he marked off a line from the mortar towards the fort; went 8 rods up the river, where he drove a stake; and 6 feet farther on took his station. Then he told his assistant to

start from the stake and mark off a line parallel with the first line, till he came in range between him and the fort. This line measured 480 feet. What was the distance sought? (See Art. 735, note.)

For other miscellaneous examples, see Appendix, page 315.

APPENDIX.

Names of Numbers (Art. 2).

1. The only compound names of numbers that do not show plainly how they are made up are Eleven, Twelve, Twenty, and the other names ending in -ty.

Eleven (in Old English endlif, in Gothic âinlif) is a compound of end or en, meaning one, and lif, meaning ten. So eleven means one and ten. Twelve (in Old English twelf, in Gothic twa-lif) is a compound of twa, meaning two, and lif, meaning ten. So twelve means two and ten.

Twenty (in Old English twentig) is a compound of twen, meaning twain or two, and tig, meaning ten. So twenty means two tens, thirty means three tens, and so on.

Roman Numerals (Art. 12).

2. The Roman Numerals are so called because they were used by the ancient Romans. They were in general use in Europe as late as the twelfth and thirteenth centuries for keeping accounts and other purposes of common life. They were not used as the Arabic numerals are, to make computations with, but merely to record the results. The computations were made mostly with counters.

By the Roman method of writing, seven letters are used to denote numbers, as follows:

I.

V.

X.

L.

One.

Five.

C.

D.

M.
Ten. Fifty. One hundred. Five hundred. One thousand.

The method of using these letters to denote numbers is shown in the following table:

3. Names of Numbers higher than Trillions (Arts. 22, 23).

The names of the groups used to express numbers higher than trillions are, in their order from trillions, quadrillions, quintillions, sextillions, septillions, octillions, nonillions, decillions, undecillions, duo. decillions, tredecillions, quatuordecillions, quindecillions, sexdecillions, septendecillions, octodecillions, novemdecillions, vigintillions, etc.

4. To Read Decimals (Art. 35).

The following method of reading decimals is recommended by its simplicity and its conformity to the method of reading whole numbers.

ILLUSTRATIVE EXAMPLE. Read the number 0.279036205. Begin at the decimal point, and point off three figures at the right of the point for the thousandths' group, three more for the millionths' group, and so on; thus,

0.279,036,205.

Then read the number expressed in each group separately, pronouncing the name of the group; thus, "Two hundred seventy-nine thousandths, thirty-six millionths, two hundred five billionths."

The expression 0.36038 would be read, "Three hundred sixty thousandths, thirty-eight hundred thousandths."

5. Contractions in Multiplication (Art. 83).

To multiply by 9, 99, 999, etc.

Since 9 times a number is the same as 10 times the number less once the number, and 99 times a number is 100 times the number less once the number, and so on,

To multiply by any number whose terms are all 9's: Annex as many zeros to the expression for the multiplicand as there are 9's in that

CONTRACTIONS IN MULTIPLICATION.

301

of the multiplier, and from the number thus expressed subtract the mub tiplicand; thus, 27 × 99 =

= 2700-27=2673.

NOTE. In Example 6, multiply by 1000, and subtract twice the multiplicand.

(7.) 356 × 9995 = ?

(8.) 54932 × 999997 = ?

6. To multiply by a composite number.

Separate the multiplier into convenient factors, multiply the multiplicand by one of the factors, and that product by another factor, and so on, till all the factors have been used; the last product is the answer : thus, 41 × 25 = 41 × 5 × 5.

Examples for the Slate.

9. Multiply 368 by 72; by 36. 10. Multiply 4079 by 81; by 48. 11. Multiply 2145 by 108; by 144.

12. Multiply 50411 by 55; by 150.

7. To multiply by aliquot parts of 10, 100, 1000, etc.

Multiply by 10, 100, 1000, etc., as the case may require, and then find the required part; thus,

To multiply by 25, multiply by 100 and divide by 4.

By 125, multiply by 1000 and divide by 8.

By 33, multiply by 100 and divide by 3.

By 16, multiply by 100 and divide by 6.

By 12, multiply by 100 and divide by 8. (See Arts. 258 to 261.)

8. To multiply when the number of tens is the same in the multiplicand and multiplier, and the sum of the units is ten.

23

27 Multiply the number of tens by the number of tens plus one; write the product as hundreds; at the right express the product of the units by the units.

621