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serving to himself 1 of 1 per cent. on the sale of the bill, and 2 per cent. commission on the investment ?

110. The greatest term in a series of continual proportionals is 10, the ratio 13, and the number of terms 12. What is the sum of the series ?

111. What is the area of a circle, the diameter of which is 200 feet?

112. What sum of money must be put on interest, at the rate of 6 per cent. a year, to gain $ 27.83 in 11

months ?

113. A person found two sums of money; I of the first added to ļof the second was $ 120. The two sums together were $ 400. What was each sum?

114. What number is that, whose cube root is equal to the square root of 361?

115. If a family of 9 persons spend $ 305. in 4 months, how many dollars would maintain them 8 months, if 5 persons more were added to the family?

116. Bought 5 hhds. of wine at 1 dollar per gallon, cash; having kept it 3 months and 23 days, I sold it at $1.20 per gallon, on a credit of 5 months; 16 gallons having leaked out while in my possession. What was my cash gain ?

117. A grocer having sugars at $12, $10, and $ 8 per cwt. would make a mixture of 30 cwt. worth $ 9 per cwt. What quantity of each must he take ?

118. What sum of money on interest at 6 per cent. a year, will amount to $1295.19, in 13 months 6 days ?

119. How much must be paid for the transportation of 7261. lb. 60 miles, at the rate of $ 10 for the transportation of 2000 lb. 47 miles ?

120. A farmer sold 17 bushels of rye, and 13 bushels of wheat for $31.55. The wheat, at 35 cents a bushel more than the rye. What was each per bushel ?

121. A man bought apples at 5 cents a dozen, half of which he exchanged for pears, at the rate of 8 apples for 5 pears; he then sold all his apples and pears at a cent apiece, and thus gained 19 cents. How many apples did he buy, and how much did they cost ?

122. The sides of two square pieces of ground are as 3 10 5, and the sum of their superficial contents is 30600
square feet. . What is the length of a side of each piece?

123. If 96 boards, 15 feet 6 inches long and 14 inches

wide, will floor a place, how many will it take if the boards

are only 11 feet 4 inches long and 9 inches wide ?

124. A certain club spent at a supper, 43 dollars 56

cents, and the expense of each was as many cents as there
were persons in the company. What did each pay?

125. If 20 feet of iron railing weigh 1000 lb. when the

bars are 14 inch square, what will 50 feet come to, at 93

cents per lb. when the bars are of an inch square ?

126. A stationer sold quills at $1.83į per thousand,

and gained 1 of the first cost; but quills growing scarce,

he raised the price to $2.04 per thousand. What did

he gain per cent. by the last sale ?

127. A merchant purchased goods to the amount of

3472 dollars, which he sold at a loss of 12 i per cent.

and invested the proceeds of the sale in other goods, which

he sold at a profit of 13 per cent. Did he gain or lose

by these transactions, and how much?

128. A house completely finished, has cost the owner

$ 12894; it is 4 stories high, and the ground floor is

divided into two shops, one of which is let at $ 225, the

other at $ 200 a year; the three upper stories are let for

$ 450 a year; the annual expense for repairs is $ 36.89.

What per cent. does the house pay?

129. A merchant in Boston received from New Orleans

a bill at 30 days sight; he allowed 1 per cent. discount
for present payment, and received $ 2530.44. What sum

was the bill drawn for; and what was the discount ?

130. A merchant sold a parcel of coffee at 15 cents

per lb. and lost 10 per cent.; soon after he sold another

parcel, to the amount of $ 525. and gained 40 per cent.

How many pouds were there in the last parcel; and at

what price per lb. was it sold ?

131. G received from H 760lb. of rough tallow to try

out, at 60 cents per 100lb. clear, and was to take his pay
in rough tallow at 8 cents per lb.; G returned 615 lb. clear,
and H paid him the balance due to him in rough tallow.
Allowing 19 per cent. for waste, what was the balance
due to G?

132. A merchant received on consignment 3 lots of hops, viz. 810lb. from Allen; 720lb. from Bond; and 1872 lb. from Cook. On inspection, Bond's hops were found to be 12 per cent. better than Allen's; and Cook's 25 per cent. better than Bond's. A sale of the 3 lots together was effected at 10 cents per lb. What was the just share of the amount for each ?

133. A and B hired a coach in Boston to go 50 miles, for $25. with liberty to take in two more when they pleased. After riding 15 miles they took in C, who wished to go the remainder of the journey out, and return with them to Boston. On their return, at the distance of 25 miles from Boston, they admitted D for the remainder of the journey. You are required to settle the coach hire equitably between them.

134. Suppose a rope 7.1365 rods long, to have one end attached to a horse's head, and the other end fastened to a stake, in the centre of a field; how much land will the horse be allowed to graze upon ? · 135. A cistern is to be constructed, in the form of a cylinder, to hold 850 gallons. If the diameter of the end be made 6 feet, what must be the length of the side ?

136. Suppose the propelling wheels of a locomotive engine to be 3 feet 4 inches in diameter, and to make 396 revolutions in a minute; what distance will the engine move forward in one hour ?

137. If 12 oxen eat up 3 acres of grass in 4 weeks, and 21 oxen eat up 10 acres in 9 weeks, how many oxen will eat up 24 acres in 18 weeks; the grass being at first equal on every acre, and growing uniformly ?

THE END.

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INDEX

Definitions of Quantity, Numbers, and Arithmetic ..............

Notation and Numeration .......

.............

Addition .........................

Subtraction .........................

........................

Multiplication ... . . . . . . . . . . . . . ...

Division .......

.............

Properties of Numbers ..............

.........

Problems ..........

Compound Numbers ..........

Fractions ............

................

Decimal Fractions ............

Infinite Decimals ........

Relations of Numbers

Percentage .............

Commission

Stocks .............

Insurance .........................

Interest ...............

..........

Partial Payments ........

Compound Interest

.............

Discount ....................

...........

Banking .........

112
Equation of Payments ...........

.............

114
Profit and Loss .................
Partnership ..........................................................

117
Bankruptcy ..................
Assessment of Taxes ............
General Average

........................

124
Custom-House Business.............
Ratio ..........
Proportion ........

..............

132
Compound Proportion ......... ........

..............
Conjoined Proportion ..............

............. 145
Duodecimals

...........

148
Involution ..........

......................... 153
Evolution .......

............ 157
Extraction of the Square Root ........

.......... 160

........

............

110

...................................................

..........

...........

116

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II MICUlal....................................................

203

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Extraction of the Cube Root ...........
Roots of All Powers
Equidifferent Series ................................. ................
Continual Proportionals ..........................................
Compound Interest by Series ..
Compound Discount ............. ...............................
Annuities .............................................................
Alligation Medial ....................
Alligation Alternate .............................................
Pernjutations ........................................................

210
Combinations ...............

............. 213
Exchange ................

................... 216
Great Britain .......... 220 Trieste .................. 232
France .................. 221 Rome .................... 233
Hamburgh .............. 222 Malta .................
Amsterdam & Antwerp 223 Smyrna ............
Portugal

224 Calcutta
Spain

......... 225 Bombay
Sweden .......

226 Madras .........
Russia .................. 227 Canton ..............
Prussja .................. 228 Japan ..............
Denmark

228 Sumatra ..........
Naples ................. 229 Acheen ............
Sicily .................... 229

229 Java ...................
Leghorn ................ 230 Manilla ..................
Genoa .................... 231 Colombo ................

Venice .................. 231 Mauritius ................ 240
Arbitration of Exchange ...............

...........

240
Compound Arbitration ............................................ 243
Foreign Coins ..........................

245
Foreign Weights and Measures

250
Mensuration

......... ................... 257
Gauging of Casks ...........
Tonnage of Vessels............ ................................. 264
Mechanical Powers ................................................ 266
Miscellaneous Questions .........

275

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.........

Teasures ........

263

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