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serving to himself 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 1}, 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 118 months ?

113. A person found two sums of money; } 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 to 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 1000lb. when the bars are 14 inch square, what will 50 feet come to, at 9 cents per lb. when the bars are s of an inch square ?

126. A stationer sold quills at $ 1.83} per thousand, and gained 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 ) 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 $35.89. 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 pounds were there in the last parcel; and at what price per Ib. was it sold ?

131. G received from H 760lb. of rough tallow to try out, at 60 cents per 100 lb. clear, and was to take his

ray in rough tallow at 8 cents per lb.; G returned 615lb. clear, and I paid him the balance due to him in rough tallow. Allowing 18 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 124 per cent. better than Alien'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 71.365 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 ena 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 390 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

287

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
Cominission
Stocks ....
Insurance
Interest
Partial Payments
Compound Interest
Discount
Banking
Equation of Payments
Profit and Loss
Partnership
Bankruptcy
Assessment of Taxes
General Average
Custom-House Business.
Ratio
Proportion
Compound Proportion
Conjoined Proportion
Duodecimals
Involution
Evolution
Extraction if the Square Root ....

5
6
9
10
11
14
18
20
25
36
51
67
74
86
90
91
92
93
102
107
110
112
114
116
117
121
122
124
127
131
132
140
145
148
15**
151
361

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Extraction of the Cube Root
Roots of All Powers ....
Equidifferent Series
Continual Proportionais
Compound Interest by Series
Compound Discount
Annuities
Alligation Medial
Alligation Alternate
Permutation's
Combinations
Exchange
Great Britain

220 Trieste
France

221 Rome
Hamburgh

-222 Malta
Amsterdam & Antwerp 223. Smyrna
Portugal

224 Calcutta
Spain

225 Bombay
Sweden

226 Madras
Russia

227 Canton
Prussia

228 Japan
Denmark

228 Sumatra
Naples

229 Acheen
Sicily

229 Java
Leghorn

230 Manilla
Genoa

231 Colombo
Venice

231 Mauritius .......
Arbitration of Exchange
Compound Arbitration
Foreign Coins
Foreign Weights and Measures
Mensuration
Gauging of Casks
Tonnage of Vessels...
Mechanical Powers
Miscellaneous Questions

174.
182

184
..... 188

194
195
196
201
203
210
213

21€
232
233
233
234
235
236
236
237
237
238
238
239
239

239
..... 240

240
243
245
250
257
263
264
266
275

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