with 5 bushels of malt to the barrel when a quarter of malt

costs 50s.?

102. If 10 cannons, which fire 3 rounds in 5 minutes, kill 270 men in 11⁄2 hours, how many cannons which fire 5 rounds in 6 minutes will kill 500 men in 1 hour at the same rate? 103. At what time between 4 and 5 o'clock are the hour and minute hands of a watch together, at right angles, and in opposite directions?

104. A stationer sold quills at 11s. a thousand, by which he cleared of the money, and he afterwards raised them to 13s. 6d. a thousand. What did he gain per cent. by the latter price?

105. Steam requires about 1000° of heat when generated from water, at 212° or 180° above freezing point; this heat not being sensible to the thermometer is latent heat. Then steam may

From this

be considered as water in a high state of rarefaction, containing about 1000° of heat above what its state indicates. it is required to find the temperature of 20 gallons of water at 60°, in which there is 2 gallons of steam at 212°.

Solution:

20 gallons at 60° or 28° of heat

2 gallons at 212° or (1000+180) or 1180 of heat=2360° .. The temperature of the 22 gals.

= 560°

=

= 2920°

2920°

106. To liquify a given quantity of ice requires as much heat as would raise the same weight of water 140° in temperature, or from 32° to 172°. So that if a stone of ice at 32° was mixed with a stone of water at 172o, the result would be 2 stones of water at 32°. Then ice on the point of melting may be considered as water at 172° below 32°, or 140° below freezing point. This is the latent heat of water acquired in liquefac

tion.

From this let us find the temperature of a mixture of 6 lbs of water at 122° with 3 lbs. of ice at 32°.

Solution Since ice on the point of melting may be considered as water 140° below freezing point:

.. 6 lbs. of water at 122° or 90° above freezing point=540°

3 lbs. of ice at 32° or 140° below freezing point = 420°

.. The difference is 120° above 32° which is disseminated

into 9 lbs. of the mixture, .. every lb. will be at 451°.

107. What would be the result of mixing 3 lbs. of water at 100° with 2 lbs. ice at 32°?

108. In 20 lbs. of water at 32° there are floating 2 lbs. of ice, into this 3 lbs. of steam are admitted. Find the temperature of the mixture.

109. A mixture is made of 16 gallons of water at 45°, and of 12 gallons at 62°. Required, the temperature of the liquid.

110. What would be the temperature of a mixture of 24 lbs. of water at 77° with 42 lbs. of ice at 25°?

111. If the pendulum of a clock vibrate the distance of 9 inches in a second of time, how many inches will it vibrate in the course of 7 years 14 days 2 hours 1 min. 56 sec., each year consisting of 365 days 5 hours 48 min. 48 sec.?

112. A boy bought some apples for 6d. ; the, 1, and of what he had amounted to 54. How many could he get for a halfpenny ?

113. Received an order for cloth, at 16s. 6d. per yard. Now, it will take 2 lbs. 2 oz. of wool per yard; the cost of making is 4s. per yard, dressing 2s. per yard, and dying the wool 1s. per lb. How much must I give per lb. for my wool, so as to gain 12 per cent. by this trade?

114. If a cylindrical vessel be 7 feet deep, and will hold 1010 gallons when filled, it is required to know what quantity will run over by putting in the largest heavy cube possible.

115. A room is 32 feet long, 27 feet broad, and 20 feet high. Find the length of the longest pole that can be placed therein.

116. A merchant insured a ship and cargo at the rate of 1 per cent. Now, if .001 of the value of the ship were multiplied by .001 of the value of the cargo, the product would be £1275; and if the cube of .001 of the ship's value were subtracted from the cube of .001 of the cargo's value, the

remainder would be £610750. The sum paid for insurance is required.

117. A city is supplied with water by means of five pipes, and their diameters are, respectively, 4, 4, 5, 6 and 7 inches. The smallest pipe supplies 10 gallons per minute; and the supply of the others is as the squares of their diameters. How many families were supplied on an average, each family consuming 10 gallons of water daily?

118. If 1 lb. Troy of English standard gold, 1 fine, be worth £46. 12s. 6d., what is the value of a coin, weighing 7 dwts. 11 grs., in which 924 parts in 1000 are pure gold?

119. A clock gains 34 min. per day. placed at noon, to point on the evening?

How should its hands be true time at 7 in the

120. A person performs of a piece of work in 13 days; he then receives the assistance of another person, and both together finish it in 6 days. In what time could each do it separately?

121. If 3 miles 4 furlongs 93 yards be run in 6 min. 4 sec., how much is that short of a mile a minute?

122. Find the edge of a cubical block of coal, weighing 2000 tons. (See table of sp. gr.)

123. How much per cent. is 14s. 6d. gain on £4. 5s. ?

124. The difference between the year in the Julian calendar and the true year is .007736 days, which the Gregorian calendar corrects, by omitting 3 days in 400 years. Find how much the error would have accumulated under the Julian calendar, from A.D. to A.D. 1854.

125. The external and internal diameters of an iron shell are 8.36 and 6.45 inches. Required, the weight of the shell, and the quantity of gunpowder it will contain?

126. A cubical box, 1 foot in height, is filled with water; and 8 equal spheres, foot in diameter, are placed in it. What volume of water remains ?

127 A scale of German inches is placed by the side of a scale of English inches, so that the first division of the two scales coincide. Find the divisions of the English scale which coin

287

cides nearest with the German scale. (The length of each scale is 10 feet, and 100 German inches are the same as 106.577 English inches.)

128. If a person invest in the 3 per cent., at 924, including the broker's commission. What interest will he get per

cent.?

129. How many ounces of tea, at 3d., 4d., 5d., and 8d., are required to make a mixture at 6d. ?

130. If 24 pioneers, in 2 days of 12 hours long, can dig a trench 139.75 yards long, 44 wide, and 24 deep, what length of trench will 90 pioneers, in, 4 days of 93 hours long, dig, the trench being 43 yards wide and 3 deep?

131. Express 2 Sparsh piastres in French money, exchange being at the rate of 25 francs per £1 sterling, and £3. 7s. 6d. for 20 piastr

es.

132. A caw mow 2 acres of grass in 43 days, B 21 acres in 3 days they mow together a field of 10 acres.

12

wil

In what time

they do it, and how many acres will each mow?

63. The water in a river, 16 feet deep and 144 yards wide, flows at the rate of 34 miles per hour. Find how many cubic feet of water run into the sea per minute; also the number of tons, supposing a cubic foot of water to weigh 1000 ounces?

134. Through a piece of wood, 2 feet 4 inches in length, a hole is made, the section of which is a square of 8 inches on a side, and the largest possible cylinder is inserted in the hole. Find the space left vacant.

135. If a gallon of water were resolved into the oxygen and hydrogen of which it is composed, it is required to determine the volume into what it would thus be expanded, water being 741 times heavier than an equal volume of oxygen, and 9699 times heavier than an equal bulk of hydrogen.

136. A person mixes 11 lbs. of tea with 5 lbs. of an inferior quality, and he gains 16 per cent. by selling the mixture at 7s. 3d. per lb. Find the prime cost, when a pound of the one costs ls. more than a pound of the other.

137. Find the converging fractions approaching to

5 h. 48 m. 48 s.

24 hrs.

138. At what rate per cent. per annum must £1200 be lent for 2 years, to amount to £1348.32 ?

139. How must goods bought at 8s. 4d. a yard, be sold to realize 15 per cent., allowing 5 per cent. on the cost for expenses? 140. A train moves the first minute at the rate of 6 miles an hour, each minute its speed increases by of 8 miles. At what rate per hour will it travel in 10 minutes?

141. £62 10s. is paid, the first payment being £1 11s. 3d., the others increasing three-fold, find the number of payments.

142. Exchange between Russia and England is 6.28 rubles, per £1, and between Russia and America, 6.28 rubles for 4.55 dollars; also between America and England 4.85 dollars, per £1. Find the gain on transmitting 6000 rubles through England to America?

143. The Britannia tubular bridge consists of two rectangular tubes of iron, each 1513 feet in length, 26 feet in average depth, and 14 feet 8 inches in width, the internal depth and width being respectively reduced by construction to 22 and 14 feet. Find the volume of air in the tube, and also the contents of the construction itself?

144. The length of Jupiter's orbit is found to be 3104000000 miles, which is described in 4332.62 days. The length of the earth's orbit is 596900000 miles, which the earth describes in 365.26 days. What is the difference of the uniform rate of speed per hour of the two planets.

145. It is supposed that one man consumes 25 cubic feet of oxygen in 24 hours; and supposing he takes 21 respirations in a minute, how much does he consume at each respiration? 146. An omnibus conductor was convicted of defrauding his master, who stated that if he were thus defrauded, of only 3d. for every journey made by each of the omnibusses of which he was the proprietor, he should lose £2901. 15s. per annum. Supposing each omnibus took 6 journeys daily, how many omnibusses had the master?