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89. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled ; how many were in this army ?-This and the cighteen following questions are usually wrought by a prule called Position, but they are more easily solved oil general priuciples. Thus, $t

12 of the army; therefore, 1000 isia of the whole number of men; and, if 5 twelfths be 1000,- how much is 12 twelfths, or the whole ?

Ans. 2400 men. 90. A farmer being asked how many sheep, he had, answered that he had, them in 5 fields : in the first were 4 of liis flock, in the secondâ, in the third $, in the fourth12, and in the fifth 450; how many had he ?

Ans. 1200. 91. There is a pole, # of which stands in the mud, f in the water, and the rest of it oui of the water; required the part out of the water.

92. If a pole be f in the mud, is in the water, and 6 feet out of the water, what is the length of the pole?

Ans. 90 feet. 93. The amoumt of a z certain school is as follows: 16 of the pupils study grammar, i geography, jo arithinetic, 20. learn to write, and 9 learn to read; what is the number of each ? Ans. 5 in graminar, °30 in geography, 24 in arithmetic, 12 learn to write and 9 learn to read.

94. A man, driving his geese to market, was met by another, who said, "Good morrow, sir, with your hundred geese;" says he, "I have not a hundred; but if I had, in addition to my present number, one half as many as I now have, and 21 geese more, I should have a hun. dred:” how many had he ? 100 - 24 is what part of his present number 1 Ans. he had 65 geese.

95. In an orchard of fruit trees, of them bear apples, & pears, ļ plums, 60 of them peaches, and 40 cherries; how many trees does the orchard contain ?

Ans. 1200. 96. In a certain village, 1 of the houses are painted white, , # red, g yellow, 3 are painted green, and 7 are unpainted how many houses in the village ? 97. Seven eighths of a certain number exceeds four fifths of the same number by 6; required the number. ;- 3=40; consequently, 6 is

40
of the required aumber.

Ans. 80. 93. What number is that, to which if of itself be added, the sum will be 30 ? Ans. 25. 99. What number is that, to which if its and 4 be added, the sum will be 84 ? 81 - 1+it - 3 times, the required number 3

Ans. 48. 100. What number is that, which, being increased by and of itself, and by 22 more, will be made 3 times as much ?. The number, being taken 1, 5, and 3 times, will make ?

101: What number is that, which, being increased by }, }, and f of itself, the sum will be 2314?

Ans. 90. 102. A, B, and C, talking of their ages, B said his age was once and a half the age of A, and C said his age was twice and one lenth the age of both, and that the sum of their ages was 93; what was the age of each ?

Ans. A 12 years, B 18 years, C 63 years old. 103. A schoolmaster being asked how many scholars he had, said, "If I had as many more as I now have, as many, as many, & and I as many, I should then have 435;" what was the number of his pupils ?

Ans. 120. 101. A and B commenced trade with equal sums of money ; A gained a sum equal to 1 of his stock, and B lost $200; then A's

money was double that of B's; what was the stock of 3 each? By the condition of the question, one half of that is, of the stock, is equal to Z of the stock,

3 Ans. $500. lessos 200 conseguently, $200 is of the stock.

105. A man was hired 50 days on 5 these conditions: that, for every day he worked, he should receive $ 75, and, for every day he was idle, he should forfeit $ 25; at the expiration of the time he received $2750 ; how many days did he work, and how many was he idle ?

Had he workel every day, his wages would have been $75 X 50 = $37'50, that is, $10 more than he received; but every day he was idle lessened his wages $75 + $625 = $1; conse quently, he was idle 10 days.

Ans. he wrought 40, and was idle 10 day 3. 106. A and B have the same income; A saves # of his; but B, by spending $30 per annum more than A, at the end of 8 years finds himself $10 in debt; what is their income, and what does each spend per ann.? Ans. their income $200 per ann.; A spends $175 and B $205 per ann.

107. A man, lying at the point of death, left to his 3 sons his property ; to Awanting $20, to B 4, and to the rest, which was $10 less than the share of À ; what was each one's share

Ans. $30, $50, and $70. 103. There is a fish, whose head is 4 feet long; his tail is as long as his head and the length of his body, and his body as long as his head and tail: what is the length of the fish - The pupil will perceive that the length of the body is one half the length of the fish. Ans. 32 feet.

109. A can do a certain piece of work in 4 days, and B can do the same work in 3 days; in what time would both, working together, perform it?

Ans. 15 days. 110. Three persons can perform a certain piece of work in the following manner : 7A and B can do it in 4 days, B aud C in 6 days, and A and C in 5 days; in what time can they all do it together ?

days. 111. A and B can do a piece of work in 5 days ; A can do it in 7 days; in how can B do it?

Ans. 17 days. 112. A man died, leaving $1000 to be divided between his two sons, one 14, and the other 18 years of age, in such proportion that the share of each, being put to interest at 6 per cent, should amount to the same sumn when they should arrive at the age of 21; what did each receive?

Ans. the elder, $546-153+; the younger, $453-846 + 113. A house being let upon a lease of 5 years, at $60 per annum, and the rent being in ar. rear for the whole time, what is the sum due at the end of the term, simple interest being allowed at 6 per cent.?

Ans. $335. 114. If 3 dozen pair of gloves be egnal in value to 40 yards of calico, and 100 yards of calico to three pieces ut satinet of 30 yarıls each, and the satinet be worth 50 cents per yard, how many pair of gloves can be bought for $4 ?

Ans 8 pair 115 A, B, and C, would divide $100 between them, so as that B may have $3 more than A, sud C $4 more thau B; how much must each man have ? Ans. A $30, B $33, and C $37

=48

i

116. A man has pint bottles, and half pint bottles; how much wine will it take to fill 1 of each sort? - how much to fill 2 of each sort? how much to fill 6 of each sort?

117. A man would draw off 30 gallons of wine into 1 pint and 2 pint bottles, of each an equal number; how many bottles will it take of each kind to contain the 30 gallons? Ans. 80 of each.

118. A merchant has canisters, some holding 5 pounds, some 7 pounds, and some 12 pounds how many, of each an equal number, can be filled out of 12 cwt. 3 qrs. 12 lbs. of tea ? Ans, 60.

119. If 18 grains of silver make a thimble, and 12 pwts. make a tea spoon, how many, of sach an equal number, can be made from 15 oz. 6 pwts. of silver ?

Ans. 24 of each. 120. Let 60 cents be divided among three boys, in such a manner that as often as the first has 3 cents, the second shall have 5 cents, and the third 7 cents; how many cents will each receive?

Ans. 12, 20, and 28 cents. 121. A gentleman, having 50 shillings to pay among his laborers for a day's work, would give to every boy 6'd., to every woman 8 d., and to every man 16 d.; the number of boys, women, and men, was the same; I demand the number of each.

Ans. 20. 122. A gentleman had 71. 17 s. 6 d. to pay among his laborers : to every boy he gave 6 d., to every woman 8 d., and to every man 16 d.; and there were for every boy 3 women, and for every woman 2 men; I demand the number of each. Ans. 15 boys, 45 women, and 90 men.

123. A farmer bought a sheep, a cow, and a yoke of oxen, for $8250; he gave for the cow 8 times as much as for the sheep, and for the oxen 3 times as much as for the cow; how much did he give for each?

Ans. for the sheep:15$2:50, the cow $20, and the oxen $60. 124. There was a farm, of which a owned f, and B was each one's share of the money?

21; the farm was sold for $1764 ; what

Ans. A's $504, and B's $1260. 11

125. Four men traded together on a capital of $3000, of whichA put in A, B,C1and D iz; at the end of 3 years they had gained $2364 ; what was each one's share of the

pain? 126. Three merchants accompanied ; A furnished 2 of the capital, B &, and the rest; they gain $1250; what part of the capital did C furnish, Sand what is each one's share of the gain?

Ans. C furnished , of the capital, and A's share of the gain was $500, B's $468-75, and C's $281625.

40 127. A. B, and C traded in company ; -A put in $500, B $350, and C 120 yards of cloth; they gained $332-50, of which C's share was $120; what was the value of C's cloth per yard, and what was A and B's shares of the gain?

Note. C's gain being $120, is me of the whole gain ; hence the gain of A and B is readily found; also the price at which C's cloth was valued per yard.

Ans. C's cloth, per yard, $4; A's share of the gain $125; B's do. $87-50. 128. Three gardeners, A, B, and 'C, having bought a piece of ground, find the profits of it amount to 120 l. per annum. Now the sum of money which they laid down was in such proportion, that as often as A paid 51., B paid 7 l., and as often as B paid 4 h, C paid 61. I demand how much each man must have per annum of the gain. Note. By the question, so often as À paid 5 l., C paid &. of 71,

Ans. A 26 1.413 s. 4 d., B 37 1. 6 s. 8 d., C 56 l. 129. A gentleman divided his fortune among his sons, giving A 9 l. as often as B 5 l., and C 8 l. as often as B 72.; C's dividend was 15373; to what did the whole estate amount?

Ans. 11583 1. 8 s. 10 d. 130. A and B undertake a piece of work for $54, on which A employed 3 hands 5 days, and B employed 7 hands 3 days : what part of the work was done by A, what part by B, and what was each one's share of the money? Ans. A 5 and B 1 ; A's money $2250, B's $31.50.

131, A and B trade in company for 1 year only ;12 on the 12 first of January sA put in $1200, but B could not put any money into the stock until the first of April; what did ke then put in to have an equal share with A'at the end of the year?

Ans. $1600. 132. A, B, C, and D, spent 35 s. at a reckoning, and, being a little dipped, agreed that A should pay , B , C$, and D *; what did each

pay in this proportion ?

Ans. A 13 s. 4 d., B 10 s., C6 s. 8 d., and D 5s. 133. There are 3 horses, belonging to 3 men, ernployed to draw a load of plaster from Boston to Windsor, for 13$ 26-45; A and B's horses together are supposed to do # of the work, A and _9, Band C's

20; they are to be paid proportionally; whai is each one's share of the money? 10'

10 A's $11'50 (=

23 Ans.

5 B's $ 575

23 C's $ 9-20 (-23) Proof,

$26-45. 134. A person, who was possessed off of a vessel, sold f of his share for 375 l. ; what was the vessel worth?

Ans. 1500 1. 135. A gay fellow soon got the better of of his fortune; he then gave 1500 l. for a conmission, and his profusion continued till he had' but 450 1. left, which he found to be just of his money after he had purchased his commission ; what was his fortune at first ? Ans. 3780 1.

136 A younger brother received 1560 1; which was just 12 of his elder brother's fortune, and 57 times the elder what was the value of his estate ?

Ans. 19165 l. 14 s. 3- d.

5 137. A gentleman left his son a fortune, 1. of which he spent in 3 months ; f or of Wihere. mainder lasted him nine months longer, when he had only 537 l. left; what was the sum bequeathed him by his father ?

Ans. 2082 1. 18 s. If1 d. 138. A cannon ball, at the first discharge, flies about a mile in eight seconds; at this rate how long would a bull be in passing from the earth to the sun, it being 95173000 miles dis ant?

Ans. 24 years, 46 days, 7 ouro, 33 minutes, 20 seconds

1623 of a grain

139. A general, disposing his army into a square battalion, found he had 231 over and above, but increasing each side with one soldier, he wanted 44 to fill up the square; of how many men did his army consist ?

Ans. 19000. 140. A and B cleared, by an adventure at sea, 45 guineas, which was 35 l. per cent. upon the money advanced, and with which they agreed to purchase a genteel horse and carriage, whereof they were to have the use in proportion to the sums adventured, which was found to be 11 to A as often as 8 to B; what money did each adventure ?

Ans. A 101 l. 4 s. 24, d., B 75 1. 155. 9

1

15 141. Tubes may be made of gold, weighing not more than at the rate of per foot; what would be the weight of such a tube, which would extend across the Atlantic

. 142. A military officer drew up his soldiers in rank and file, having the number in rank13 and file equal; on being reinforced with three times his first number of men, he placed them all in the same form, and then the number in rank and file was just double what it was at first; he was again reinforced with three times his whole number of men, and, after placing them all in the same forın as at first, his number in rank and file was 40 men each; how many men had he at first?

Ans. 100 men. 143. Supposing a man to stand 80 feet froin a steeple, and that a line reaching from the belo fry to the man is just 100 feet in length; the top of the spire is 3 times as high above the ground as the steeple is; what is the height of the spire; and the length of a line reaching from the top of the spire to the man? See 1 109.

Ans. to last, 197 feet, nearly. 144. I'wo ships sail from the same port; one sails directly east, at the rate of 10 miles aa hour, and the other directly south, at the rate of 74 miles an hour; how many iniles apart will they be at the end of 1 hour ? 2 hours ? —-21 hours ? — 3 days ? Ans. to last, 900 miles.

145. There is a square field, each side of which is 50 rods; what is the distance between opposite corners ?

Ans. 70-71 + rods 146. What is the area of a square field, of which the opposite corners are 70 71 rods apart? and what is the length of each side?

Ans, to the last, 50 rods, nearly. 147. There is an oblong field, 20 rods wide, and the distance of the opposite corners is 33 rods: what is the length of the field ? —its area ?

Ans. Length, 26% rods; area, 3 acres, 1 rood, 13 rods. 148. There is a room 18 feet square ; how many yards of carpeting, 1 yard wide, will be required to cover the floor of it?

192 = 321 ft. = 36 yards, Ans. 149. If the floor of a square room contuin 36 square yards, how many feet does it measure on each side ?

Ans. 18 feet When one side of a square is given, how do you find its area, or superficial contents ? When the area, or superficial contents of a square is given, how do you find one side? 150. If an oblong piece of ground be 80 rods long and 20 rods wide, what is its area ? D

'C

Note. A Parallelogram, or Oblong, has its op. posite sides equal and parallel, but the adjacent sides unequal. Thus, A B C D is a parallelogram, and also EFCD, and it is easy to see that the contents

of both are equal. Ans. 1600 rods, = 10 acres. E A

151. What is the length of an oblong, or parallelogram, whose area is 10 acres, and whose breadth is 20 rods ?

Ans. 80 rods. 152. If the area be 10 acres, and the length 80 rods, what is the other side ? When the length and breadth are given, how do yon find the area of an oblong or parallelogram ? When the area and one side are given, how do you find the other side ?

153. If a board be 18 inches wide at one end, and 10 inches wide at the other, what is the mean or average width of the board ?

Ans. 14 inches. When the greatest and least width are given, how do you find the mean width ?

154. How many square feet in a board 16 feet long, 168 feet wide at one end, and 1'3 at the other ?

Mean width, 1313 = 1:55; and 1455 x 16 = 24'8 feet, Ans. 155. What is the number of square feet in a board 20 feet long, 2 feet wide at one end, and running to a point at the other í

Ans. 20 feet. How do you find the contents of a straight edged board, when one end is wider than the other? If the length be in feet, and the breadth in feet, in what denomination will the product be ? If the length be feet, and the breadth inches, what parts of a foot will be the product ?

156. There is an oblong field, 40 rods long and 20 rods wide ; if a straight line bedrawn from one corner to the opposite corner, it will be divided into two eqnal right-angled triangles ; what is the area of each ?

Ans. 400 square rods, = 2 acres, 2 roods 157. What is the area of a triangle, of which the base is 30 rods, and the perpendicular 10 rods?

Ans. 150 rods. 153. If the area be 150 rods, and the base 30 rods, what is the perpendicular ? Ans. 10 rods. 159. If the perpendicular be 10 rods, and the area 150 rods, whai is the base ? Ans. 30 rods,

When the legs (the base and perpendicular) of a right-angled triangle are given, how do vou find the area? When the area and one of the legs are given, how do you find the other leg?

Note. Any triangle may be divided into two right-angled triangles, by drawing a perpendicular from one corner to the opposite side, as may be seen by the annexed figure. C

Here A B C is a triangle, divided into two right-angled triangles, AdC, and d BC; therefore, the whole base, AB, multiplied by one half the perpendicular ac, will give the area of the whole. If A B = 60 feet, and dC= 16 feet, what is the area ?

Ans. 480 feel

160. There is a triangle, each side of which is 10 feet; what is the length of a perpendicular from one angle to its opposite side ? and what is the area of the triangle?

Note. It is plain, the perpendicular will divide the opposite side into two equal parts. See 1 109.

Ans. Perpendicular, 8-66 + feet; area, 43-3 + feet. 161. What is the solid contents of a cube measuring 6 feet on each side 1 Ans. 216 feet. When one side of a cube is given, how do you find its solid contents ? When the solid contents of a cube are given, how do you find one side of it?

162. How many cubic inches in a brick which is 8 inches long, 4 inches wide, and 2 inches thick ? in 2 bricks? in 10 bricks?

Ans to last, 640 cubic inched. 163. How many bricks in a cubic foot ? -in 40 cubic feet? - in 1000 cubic feet ?

Ans. to last, 27000. 164. How many bricks will it take to build a wall 40 feet in length, 12 feet high, and 2 feet thick ?

Ans. 25920. 165. If a wall be 150 bricks, -- 100 feet, in length, and 4 bricks, - 16 inches, in thickness, how many bricks will lay 1 course? - 2 courses 1 — 10 courses? If the wall be 48 cour. Bes, = 8 ft. high, how many bricks will build it? 150 X 4600, and 600 X 48 = 28800, Ans.

166. The river Po is 1000 feet broad, and 10 feet deep, and it runs at the rate of 4 miles ar hour; in what time will it discharge a cubic mile of water (reckoning 5000 feet to the mile) into the sea ?

Ans. 26 days, 1 hour. 167. If the country which supplies the river Po with water be 380 miles long and 120 broad, and the whole land upon the surface of the earth be 62,700,000 square miles, and if the quantity of water discharged by the rivers into the sea be everywhere proportional to the exteni of land by which the rivers are supplied; how many times greater than the Po will the whole amount of the rivers be ?

Ans. 1375 times. 168. Upon the same supposition, what quantity of water, altogether, will be discharged by all the rivers into the sea in a year, or 365 days?

Ans. 19272 cubic miles 169. If the proportion of the sea on the surface of the earth to that of land be as 104 10 5, and the mean depth of the sea be a quarter of a mile ; how many years would it take, if the ocean were empty, to fill it by the rivers running at the present rate? Ans. 1708 years, 17 days, 12 h.

170. If a cubic foot of water weigh 1000 oz. avoirdupois, and the weight of mercury be 134 times greater than of water, and the height of the mercury in the barometer (the weight of which is equal to the weighi of a column of air on the saine base, extending to the top of the atmosphere) be 30 inches, what will be the weight of the air upon a square foot ? --- a square mile ? and what will be the whole weight of the atmosphere, supposing the size of the earth as in questious 166 and 168?

Ans. 2109 375 lbs. weight on a square foot.

52734375000 ihs. weight on a square ruile.

10249980468750000000 lbs. weight of the whole atmosphere. 171. If a circle be 14 feet in diameter, what is its circumference ?

Note. It is found by calculation that the circumference of a circle measures about 3 times as much as its diameter, or, more acenrately, in decimals, 3:14159 times. Ans. 14 dieet.

172. If a wheel measure 4 ft. across from side to side, how many ft. around it? Ans. 124 feet. 173. If the diameter of a circnlar pond be 117 feet, what is its circumference ? Ans. 462 ft. 174. What is the diameter of a circle whose circumference is 462 feet ? Ans. 147 feet.

175. If the distance through the centre of the earth, from side to side, be 7911 miles, how many miles around it?

7911 X 314159 - 24853 square miles, nearly, Ans. 176. What is the area or contents of a circle whose diameter is 7 ft. and its circumference 22 ft. Note. The area of a circle may be found by multiplying the diaineter into the circumference.

Ans. 39f square feet. 177. What is the area of a circle whose circumference is 176 rods? 178.Ifa circle is drawn within

a square containing 1 square rod, what is the area of that circle? Note.' The diameter of the circle being 1 rod, the circumference will be 3-11159.

Ans. "7654 of a square rod, nearly. Hence, if we square the diameter of any circle, and multiply the square by '7854, the pro. duct will be the area of the circle. 179. What is the area of a circle whose diameter is 10 rods ?

102 X 7851 78'54, Ans. 78454 rods, 180. How many square inches of leather will cover a ball 34 inches in diameter ?

Note. The area of a globe or ball is 4 times as much as the area of a circle of the same diameter, and may be found, therefore, by multiplying the whole circumference into the whole diameter.

Ans. 334 square inches. 181. What is the number of square miles on the surface of the earth, supposing its diameter 7911 miles ?

7911 X 24853 – 196,612,083, Ans. 182. How many solid inches in a hall 7 inches in diameter?

Note. The solid contents of a globe are found by multiplying its area by part of its diameter.

Ans. 1792 solid inches. 183. What is the number of cubic miles in the earth, supposing its diameter as above ?

Ans. 259,233,031,435 miles 184. What is the capacity, in cubic inches, of a hollow globe 20 inches in diameter, and how much wine will it contain, 1 gallon being 231 cubic inches?

Ans. 41888 + cubic inches, and 18:13 + gallons. 185. There is a round log, all the way of a bigness; the areas of the circular ends of it are each 3 square feet; how many solid feet does 1 foot in length of this log contain ? - 2 feet in length? - 3 feet? 10 feet? A solid of this form is called a Cylinder.-How do you find the solid content of a cylinder, when the area of one end, and the length, are given?

186. What is the solid content of a round stick 20 feet long and 7 inches through, that is, the ends being 7 inches in diameter? Find the area of one end, as before taught, and multiply it by the length. Ans.54317+.cubic ft. If you multiply square inches by inches in length, what parts of a foot will the product be ?

if square Inches by feet in length, what part 2

The point

187. A bushel measure is 1845 inches in diameter, and 8 inches deep; how many cubic inches does it contain ?

Ans. 2150ʻ! + It is plain, from the above, that the solid content of all bodies which are of uniform bigness throughout, whatever may be the form of the ends, is found by multiplying the area of one end into its height or lingth. Solids which decrease gradually from the base till they come to a point, are generally called Pyramids. If the base be a square, it is called a square pyramid; If a triangle, a triangular pyramid; if a circle, a circular pyramid, or a cone. at the top of a pyramid is called the vertex, and a line, drawn from the vertex perpendicular to the bnse, is called the perpendicular height of the pyramid. The solid content of any pyramid may be found by multiplying the area of the base by of the perpendicular neighi.

188. What is the solid content of a pyramid whose base is 4 feet square, and the perpendi. cular height 9 feet?

423

Ans. 48 feet. 189. There is a cone, whose height is 27 feet, and whose base is 7 feet in diameter ; what is its content?

Ans, 3464 feet. 190. There is a cask, whose head diameter is 25 inches, bung diameter 31 inches, and whose length is 36 inches; how many wine gallons does it coniain? how many beer gallons ?

Note. The mean diameter of the cask may be found by adding 2 thirds, or, if the staves be but little curving, 6 tenths, of the difference between the head and bung diameters, to the head diaineter. The cask will then be reduced to a cylinder. Now, if the square of the meau dia. meter be multiplied by '7854, (ex. 177,) the product will be the area of one end, and that, mul. siplied by the length, in inches, will

give the solid content, in cubic inches (ex. 185,) which divided by 231, (note to table, wine meas.) will give the content in wine gallons, and, divided by 282, (iote to table, beer meas.) will give the content in ale or beer gallons.

In this process, we see that the square of the mean diameter will be multiplied by '7854, and divided, for wine gallons, by 231. Hence we may contract the operation by only multiplying by their quotient, ('2914 = '0034 ;) that is, by '0034, (or by 34, pointing off 4 figures from the product for decimals.) For the same reason we may, for beer gallons, multiply by (*28924

0028, nearly,) "0028, &c.

Hence this concise RULE, for gauging or measuring casks,Multiply the square of the mean diameter by the length ; multiply this product by 31 for wine, or bry 28 for beer, and pointing off 4 decimals, the product will be the content in gallons and decimals of a gallon.

In the above example, the bung diameter, 31 in. - 25 in. the head diameter - 6 in differ. ence, and of 6 - 4 inches ; 25 in. + 4 in. - 29 in. mean diameter, Then 2 92 811, and 841 X 36 in. - 30276.

Then,

30276 X 34 - 1029331. Ans. 102.9384 wine gallons.

30276 X 28 = 847728. Ans. 81*7728 beer gallons. 191. How many wine gallons in a cask whose bung diameter is 36 inches, head diameter 27 inches, and length 45 inches.

Ans. 166-617. 192. There is a lever 10 feet long, and the fulcrum, or prop, on which it turns, is 2 feet from one cnd; how many pounds weight, at the end 2 feet from the prop, will be balanced by a power of 42 pounds at the other end, 8 feet from the prop?

Note. In turning around the prop, the end of the lever 8 feet from the prop will evidently pass over a space of 8 inches, while the end 2 feet from the prop passes over a space of 2 inches. Now, it is a fundamental principle in mechanics, that the weight and power will exactly bal ance each other, when they are inversely as the spaces they pass over. Hence, in this exam ple, 2 pounds, 8 feet from the prop, will balance 8 pounds 2 feet from the prop; therefore, if we divide the distance of the power from the prop by the distance of the weight from the prop, the quotient will always express the ratio of the weight to the power : = 4, that is, the weighi will be 4 times as much as the power. 42 X 4 = 168.

Ans, 163 lbs. 193. Supposing the lever as above, what power would it require to raise 1000 pounds ?

Ans. 1000 = 250 pounds. 194, If the weight to be raised be 5 times as much as the power to be applied, and the distance of the weight from the prop be 4 feet, how far from the prop must the power be applied ?

Ans. 20 feet. 195. If the greater distance be 40 feet, and the less of a foot, and the power 175 pounds, what is the weight 1

Ans. 14000 pounds. 196. Two men carry a kettle, weighing 200 pounds; the kettle is suspended on a pole, the bale being 2 feet 6 inches from the hands of one, and 3 feet 4 inches from the hunds of the other; how many pounds does each bear ?

Ans. 1142 pounds; 855 pounds. 197. There is a windlass, the wheel of which is 60 inches in diameter, and the axis around which the rope coils is 6 inches in diameter; how many pounds on the axle will be balanced by 240 pounds at the wheel ?

The spaces passed over are evidently as the diameters, or the circumferences; there fore, 60 = 10, ratio.

Ans. 2100 pounds. 199. If the diameter of the wheel he 60 inches, what must be the diameter of the axle, UNE the ratio of the weight to the power may be 10 to 1?

Ans. 6 inches. Note. This calculation is on the supposition that there is no friction, for which it is usual to add to the power which is to work the machine.

199. There is a screw, whose threails are 1 inch asınder, which is turned hy a lever 5 feet, = 60 inches, long; what is the ratio of the weight to the power?

Noie. The power applied to the end of the lever will describe the circunference of a circle 60X? = 120 inches in diameter, while the weight is raised l'inch; therefore, the ratio will be found by dividing the circumference of a circle, whose diameter is twice the length of the lever, by the distance between two threas of the crew.

Note.

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