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MISCELLANEOUS QUESTIONS.

square foot ?

Ans. 1

339. 1. What number taken from the square of 48 will leave 16 times 54?

Ana. 1440. 2. What number added to the 31st part of 3813, will make the sum 200 ?

Ang, 77. 3. What will 14 cwt of becf cost, at 5 cents per pound ?

Ans. $78.40. 4. How much in length that is 83 inches wide, will make

Ans. 17** inches. 5. What number is that to which if 4 of f be arlded, the rum will be 1 ?

6. A father dividing his fortune among his sons, gave Aa often as B 3, and C 5 as often as B 6; what was the whole legacy, supposing A's share $5000?

Ans. $11875. 7. A tradesman increased his estate annually by £100 more than 4 part of it, and at the end of 4 years found that his estate amounted to £10342 33. 94.; what had he at first? Ans. £4000

8. A person being asked the time of day, said the time past poon is equal to of the time till midnight; what was the ime ?

Ans. 20 minutes past 5. 9. The hour and minute hand of a clock are together at 19 o'clock; when are they next together? Ans. Il 5 Bin.

10. A young hare starts 40 yards before a greyhound, and is not perceived by him till she has been up 40 seconds ; she scude away at the rate of 10 miles an hour, and the dog ou view niakes after it at the rate of 18. In what time and chio tance will the dog overtake the hare ?

Ans. 60, 28. time, 530 yds. distance. 11. What part of 3d. is part of 20. ?

Ans. . 12. A hare is 50 leaps before a greyhound, and takes 4 leaps w the greyhound 3; but 2 of the greyhound's leeps are as much as 3 of the hare's; how many leaps must the bound cake to catch the hare ?

If 3:1::1:1 the hare's gain.

2:1::1:1 the hound's gains Thep , and ¢ : 1 :: 4:3pe=300, Ana 13. A post iß in the sand, in the water, and 10 feet about the water; what is its length ?

Ana. 24 feet

145

30.

MISCELLANEOUS QUESTIONS.

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14. A nan being asked how many sheep he had, said, if he had as many more, lalf as many more, and 74 sheep, he should have 20; how many had he?

Ane, 5. 15. In an orchard f the trees bear apples, pears, į plums, and 50 of them cherries ; how many trees are there in all ?

Ans. 600. 16. A can do a piece of work alone in 10 days, B can do it in 13; in what time will both together do it? Ans. 545 days.

17. What is the difference between the interest of £350 at 4 per cent. for 8 years, and the discount of the same sum at the same rate, and for the same tinie ?

Ans. £27 345 18. Sound moves at the rate of 1142 feet in a second ; if the time between the lightning and thunder be 20 seconds, what is the distance of the explosion ?

Ans. 4.32+miles. 19. If the earth's diameter be 7911 miles, and that of the moon be 2180, how many moons will be required to make one earth?

Ans. 47.788+ 20. If a cubic foot of iron were drawn into a bar 1 of an inch square, what would be its length, supposing no waste of metal ?

12x12x12_27648in.-2304ft. Ans.

.25X.25 21. A lent B a solid stack of hay, measuring 20 feet every way; some time after B returned a quantity measuring every way 10 feet; what proportion of the hay is yet due ? Ans. s.

22. A general disposing his arny into a square, finds he has 284 soldiers over and above, but increasing each side by one soldier, he wants 25 to fill up the square ; how many soldiers had he?

Ans. 24000. 340. 23. Supposing a pole 75 feet high to stand on a horizon tal plane, at what height must it be cut off, so as that the top of it may fall on a point 55 feet from the bottom, and the end where it was cut off, rest on the stump or upright part?

RULE.-From the square of the length of the pole (i. e. the sum of the hypothe- 75x75mm-55X55–17 $ ft. Ans. nuse and perpendicular), take the square of the base; then divide the remainder 75X2 by twice the length of the pole, and the quotient will be the height at which it must be cut off.

24. Suppose a ship sail from lat. 43° N. between N. and E. till her departure from the meridian be 45 leagues, and the sum of her distance and difference of latitude be 135 leagues; what is the distance sailed, and the latitude come to ? 135x135_45X45 lea. m.

135_60–751. dis.s'd. -60=180—30 of lat. 43° +30=46° come to.) 135X2

Aps.

341. 25. Four men bought a grindstone 6) i..ches in diaineter; how much of its diaineter must cacla grind utf t. lave an equal share of the stone, if one grind his share first, and then another, till the stone is ground away, making no allows ance for the eye?

RULE.—Divide the square of the diameter by the number of men, sube tract the quotient from the square, and extract the square 'rooi of the remainler, which is the length of the cliameter, after the first share is takich off; and by repeating the latter part of the process, all the several shaws may be found. 60X60-42900, the sabtrahend. V3600—900=51.76+ and 450-51.96–8.04, 1st share. 12700-900=4242 and 51.96_-4242-9.54, 2d share. 1800-900-30. aitu 42.42-3031242, 3d share.

and 30, 4th's share. 26. Suppose one of those meteors called fireballs to move parallel to the earth's surface, and 50 niles above it, at the rate of 20 miles per second; in what time will it move round the earth?

The earth's diameter being 7964 miles, the diameter of the orbit will be 7964+50x2=8064, and 8064 X3.1416=25:333.8044, its circumference. Then 25333.8624.-20=1206.693125.21 ('41" 3711 1355" Ans.

27. When first the marriage knot was tied betwixt my wife and me, My age with hers did so agree as nivetecu does with eight and three; But aller'ten and half ten years we man and wife had been, ller age came up is near to mine as two tiines three to nine. 'What were our ages at marriage?

Aus. 57 and 33. 28. A 'body weighing 30 lb. is impelled by such a force as to pend it 20 rods in a second; with wlint velocity would a body weighing 12 lb. move, if it were impelled by the same force ?

Ans. 50 rods. 20. In a thunder storm I observed by my cloch that it was 6 seconds between the lightning and thunder; at what distance was the explosion ?

Ans. 6852 ft.=11

miles 30. There is a square pyramid, each side of whose base is 30 inches, and whose perpendicular height is 120 inches, to be divided into three equal parts by sections parallel to its buse; what will be the perpendicular height of each part?

30X30X 40=36000, the solidity in inches. Now } of this is 24000, and dis 12000. Therefore, as 36000 : 120X120x120

S 24000 : 1152000?

12000 : 576000) Then, „31152000=104.8. Also, 3576000–83.2. Then 120–104.8=152, length of the thickeest part, and 104.8–83.221.6, length of the middle part; consequently, 83.2 is the length of the top part.

41.

MISCELLANEOUS QUESTIONS.

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31. I have a square stick of timber 18. inches by 14, but one with a third part of the timber in it, provided it be 8 inches deep, will serve ; low wide will it be? Ans. 104 inches.

32. There are 4 spheres, each 4 inches in diameter, lying so as to touch each other, in the form of a square, and on the middle of this square is put a fifth ball of the same diameter; what is the distance between the two horizontal planes passe ing through the centres of the balls ?

742+42 : 2-2.828+ inches, Ans. 33. There are 2 balls, each 4 inches in diameter, which touch each other, and another hall of the same diameter is so placed between them that their centres are in the same vertical plane; what is the distance between the horizontal planes which pass through their centres?

42_22=3.46+-in. Ans. 34. A military officer drew up his soldiers in rank and file, having the number in rank 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 number of men, and after placing the whole in the samc form as at first, his number in rank and file was 40 men each; how many men had he at first ?

Ans. 100. 35. If a weight of 1440 lb. be placed 1 foot from the prop, at what distance from the prop must a power of 160 lb. be applied to balance it?

Ans. 9 feet. 36. Three men wishing to carry a stick of timber, which is of uniform size and density, and 30 feet long; if one man takes hold aj vne tad of tho stick, how far from the other end must. the other two take hold together, that each may pear an equal portion?

Ans. 71 feet. The centre of gravity being in the middle of the stick, we piay regard ils weight as all accumulated in that point, and the stick itself as a lever supporting it; and then the parts borne will be inversely as the distances from the middle, and the reverse, i. e. the man at the Blied being 15 feet from the middle, the 2 must be of 15, or 7.5 feet from the middle, and 157.5=7.5=the distance from the end.

Where ought the 2 men to take hold in order to carry of the stick?

"The one being 15 feet from the middle, the trno, in order to carry 3 simes as much, must be 1-3d of 15-5 feet from the middle, and 15 10 tt., the distance from the end.

37. Suppose a pole 100 feet high, to be 24 inches in diame, ter at the ground, and 4 in. do, at the top, and a vine 1} inch in diameter at the ground to run up this pcle, winding round every 3 and gradually diminishing so as to come to a point at the top of the parede, whet is the length of the vine ?

Ans. 162 feet, 11.971 inches,

PRACTICAL RULES AND TABLES

Measures.

1

32

1

10

312. MEASURES OF CAPACITY. The English Winchester bushel, containing 2150.4 cubic inches, or 77.6274 lb. avoirdupois, of pure water, at its maximum density, is established, at the custom-houses in the United States, as the standard of dry measure; and the wine gallon of 2:31 cubic inches, or 8.339 lb. of water, as above, is established as the standard of liquid measure. The above are also the measures established by law in Vermont and some other states, But in New York, according to their revised laws, the legal bushel contains 2211.84 cubic inches, and the liquid gallon 221.18 cubic inches.

In measuring coal, lime, ashes, and some other articles, it is customary to use a larger measure. In Vermont the bushel for these articles is established by law at 38 quarts, of which the cominon bushel holds 32, but in most places the bushel for coal, &c. contains 40 quarts.

bush.jqts. cubic inches. cubic feet. Winchester measure,

2150.4 1.2445 Verinont coal, &c. measure,

30 553.6 1.47777 Common coal, &c. measure,

2683. 1.5555 1 cubic foot-0.80356 bush. Winchester measure. 1 cubic fant-067669 bush. Vermont coal, &c, measure. 1 cubic fuot=0.64285 bush. com. coal, &c, measure. 343. To find how many bushels any bin, box, or coal-house will contain.

RULE.--Find the content in feet, and multiply, it by the decimal of a bushel standing against 1 cul-ic foot in the above table.

EXAMPLES. 1. The dimensions of a coal-box were length 12.5 ft., height 3.4 ft., width at the top 3.94 it., width at the bottom 2.7 ft.; how many bushels of each of the above measures will it hold ? 3.94+2.756.61, and 6.64---2-3.32, and 3.32X3.4 X 12.5–141.1 cubic feet. Then 141.1 X0.8 =112.88 bush. Win.

141.1 X 0.677= 95.52 bush. Vt. coal meas.

141.1 X 0.04 = 90.30 bush. coin. coal meas. 2. If a coal-house be 50 feet long, 40 feet widr, and 20 feet high, how many bushels will it hold? FOX 40x20=40000 cn. ft., and 40000X0.07669=27067 b. Vt. m. 50X40X20-40000 cu. ft., and 40000X0.61283-25714 b. c. m.

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