443. The diameter of the large wheel of a bicycle is 46 inches. How many times will this wheel turn in going a mile? [Ans. to tenths.]

444. The large wheel of John's bicycle is 4 feet in diameter, that of Burt's is 46 inches. In going 2 miles and a half and returning, how many more revolutions are made by Burt's bicycle than by John's? [Ans. to tenths.]

· 445. If a point on the rim of a circular saw whose diameter is 40 inches goes at the rate of 11⁄2 miles per minute, how many revolutions does the saw make a minute? [Ans. to tenths.]

446. How many revolutions would a circular saw whose diameter is 30 inches have to make that the rim might go at the rate of 1 miles a minute?

447. What will it cost to enclose a hectar of land in a circular form with a fence costing $1.25 per meter?

448. At $1.25 per meter for fencing, what will it cost to enclose a square piece of land containing a hectar?

449. Wishing to ascertain the number of cubic inches in an irregular piece of stone, I immersed it in water and found it displaced enough to fill to the depth of 11⁄2 inches a cylindrical dish whose diameter was 6 inches. How many cubic inches in the stone?

450. How many barrels of water, 31 gallons to a barrel, can be contained in a cylindrical tank 8 feet deep and 12 feet in diameter?

451. How many hektoliters in a circular reservoir 6 meters deep, the diameter at the bottom being 60 meters and at the top 70 meters? 452. Estimating the diameter of the earth to be 8000 miles, and its specific gravity to be 5.6, what is its weight in tons?

453. A pipe 4 inches in diameter will drain a certain reservoir in 96 hours. In how many hours would a pipe 16 inches in diameter drain it?

454. If a whale 95 feet long weighs 245 tons, what will a whale similar in form 50 feet long weigh?

455. What must be the height of a tree to contain 125 times as much as a similar tree 30 feet high?

456. Wishing to know the quantity of coal piled 3 meters high in a corner of a coal-bin, I weighed a pile similar in form 4.85 decimeters high, and found it contained 85 pounds. What was the weight of the larger pile?

57. Miscellaneous Examples.

457. What is the par value of stock of which 4 shares, at 72 % discount, sell for $112 ?

458. When the government tax for matches was a cent for every hundred, and $2,000,000 was received per year for the taxes on matches, how many matches were manufactured during the year?

459. From a bushel of fruit and 15 pounds of sugar 25 jars of preserves were made. What was the cost of the preserves per jar, if the cost of the fruit was $1.12 and the sugar was 11 per pound?

460. I sent to my agent a lot of nails which he sold for $963; on this he was allowed a commission of 3%. I directed him to invest the balance in hops, after deducting a commission of 1% for investing. What sum remained to invest?

461. The first instalment of the fund for the Smithsonian Institute was $515169; the residuary legacy was $26210.53. Congress has since added $108620.37, and Mr. Hamilton bequeathed $1000. What is the yearly interest on this fund at 6 %?

462. The Smithsonian Institute also holds certificates and bonds in Virginia worth at par $88125, present value $37000. What per cent has this Virginia stock depreciated ?

463. In my History of England the third chapter begins at the top of the 110th page and ends at the bottom of the 189th. How many pages are there in the chapter?

464. Four per cent per annum paid quarterly is equal to what per cent per annum paid annually, interest at 6 % being allowed on each quarterly interest?

465. A dealer in provisions loses 10 % by giving credit, and pays 21% for having his bills collected. What per cent above cost must he charge for goods, that he may clear 10 %?

466. It is a principle in mechanics that the two arms of a lever are inversely proportional to the pressures at their extremities. What power 6 feet from the fulcrum will balance a weight of 80 pounds 5 feet from the fulcrum? 2 feet from the fulcrum? 15 feet 6 inches?

467. How far from the support of a tilt must a boy weighing 120 pounds be placed to balance another boy weighing 96 pounds and seated 10 feet from the support?

468. What is the compound interest at 6% per annum, payable semiannually, on a note for $1000, dated September 14, 1880, and paid December 2, 1881 ?

469. A water-tank 3 feet in depth and 4 feet square at the base, is supplied by rain from a flat roof 30 feet long and 20 feet wide. What depth of rain must fall to fill the tank?

470. Find the cost of materials and labor for 100 square yards of lath and plaster-work, 3 coats, hard finish, as follows, and make out a bill for the same. Common lime, 4 casks @ $1.00; lump lime, § cask @ $1.35; plaster of Paris, cask @ $1.50; laths, 2000 @ 20 ₫ per hundred; common sand, 7 loads @ 307; white sand, 21⁄2 bu. @ 87 ; nails, 13 lbs. @ 57; hair, 4 bu. @ 15; mason's labor, 3 days @ $2.50; laborer, 3 days @ $1.25; cartage, $2.00.

471. A speculator had 10 rectangular lots of land, situated side by side and having their fronts in the same straight line. Each lot was 66 ft. wide in front and 132 ft. deep. What was the cost of fencing these lots at $20 a rod for the front remainder?

fences, and $10 a rod for the

472. Suppose coal to be worth $6 a ton, and the net cost of manufacturing coal-gas to be 15 % of the price of the coal. If a ton of coal yields 12000 cubic feet of gas, what is the cost of gas per thousand feet?

473. North Eastland, near Spitzbergen, is said to be covered with a glacier from 2000 to 3000 feet deep. At the average depth of 2500 feet, what pressure is exerted by the iceberg upon a square foot of earth beneath, if the ice is 0.9 as heavy as water?

474. Wishing to get $400 from a bank on 3 months, the cashier added the discount for 3 mo. 3 d. to the $400 and directed me to draw my note for the amount. When this note was discounted, how much did the proceeds fall short of $ 400 ?

475. A collector received $5.87 as his commission at 5 % on the amount of his collections for 1 day. If the debtors were allowed 10 % discount from the face of their bills, what was the total due on the bills collected?

476. If Mr. Cook gets $25 a month for rent of a house worth $6000, and on which he pays $70 a year for taxes, how much does he lose a year, money being worth 6 %?

At what price can Mr. Cook afford to sell the house?

477. A party of emigrants bought a township of government land at $1.25 an acre. Reserving 150 acres for public purposes and setting aside 200 acres which were worthless, they divided half of the remainder into farms which sold at $4 an acre, and the other half into farms which sold at $5 an acre. After selling all the farms, and paying the first cost of the township, how much money was left?

478. A person buys coffee at $29 per hundred pounds, and chicory at $11.75, and mixes them in the proportion of 2 of chicory to 5 of coffee. He sells the mixture at 38 a pound. What is his gain per cent?

479. In Lombardy 60,000,000 cubic yards of water are daily distributed over 1,375,000 acres of land. If this water were equally distributed over the surface, what would be its depth in inches?

480. If a body moving at the rate of 40 miles per hour could go from the sun to Jupiter, whose mean distance is 475,692,000 miles, how many years of 365 days each would it require to make the passage?

481. How many years would it take the body mentioned above to go from the sun to Neptune 27,270,308,000 miles further from the sun than Jupiter is?

482. On a note for $400 having three years to run find the difference between bankers' discount and true discount, at 6 % ?

483. The rate of discount at the bank being 5%, what would be the total proceeds on the 14th of June, 1880, of the following notes:

$500, given for 6 mo., dated May 17, 1880.

$750, given for 3 mo., dated May 23, 1880.

$254, given for 4 mo., dated May 31, 1880.

$435, given for 2 mo., dated June 6, 1880.

484. The largest known diamond in the world in its original state weighed 900 carats of 31 Troy grains each; what was its weight in Troy units?

485. The Kohinoor, now owned by Queen Victoria, once weighed 186 carats, but lost in cutting 82 carats. What is its present weight in Troy units? What per cent was lost in cutting?

486. Among the crown jewels of Russia is a diamond that weighs 194 carats, which was bought for $450000 and an annuity of $ 20000. What is the yearly expense of the jewel to Russia if money is worth 4 % per annum?

487. In the temple at Baalbec is a stone 66 feet long 12 feet wide and 12 feet thick. If its specific gravity is 2.6, what is its weight?

488. What is gained by selling a hundred powder-kegs at 16 apiece, the cost per hundred being $1.87 for making and $1.75 for hooping, eight hoops at $0.045 per hundred being required for each keg, and the value of the other stock being 8 per keg?

489. The rate of a clock is 0.000375 fast.

it gain in one week?

How much time does

490. What is the average date for making the following payments: $100, due May 28, 1879; $250, due July 3, 1879; $150, due August 31, 1879; $200, due September 26, 1879; $400, due November 30, 1879.

491. Which is the more valuable, and how much more, $1200 paid to-day or $1500 paid four years hence, the use of money being worth 6% a year?

492. A man agreed to pay $800 with interest at 6% annually. Suppose the payment of interest was deferred at the end of the first and second years, and that simple interest was allowed upon the deferred payments, what would be due at the end of the third year?

493. Mr. Lamb offered to sell his house for $4500, but, finding no customer, he was obliged to keep it five years; he then sold it for $8000. If he received $200 per year for rent more than he paid for taxes and repairs on the house, money being worth 6 % a year, how much did he gain by keeping the property? What per cent on the $4500?

494. Pure iron weighs 7.79 times as much as an equal bulk of water. A cubic foot of water weighs 1000 oz. Av. How many cubic inches in a cube of iron weighing 1 lb. Av.?

495. Find the diameter of a cast-iron ball weighing 9 lbs., supposing that the iron weighs 7.2 times as much as an equal bulk of water.

496. Intensity of light from a given object varies inversely as the squares of the distances. If your book is 27 inches from the light and mine is 6 feet 9 inches, how many times as great is the light on your book as on mine?

497. There is a cypress-tree in Lombardy said to have been quite a large tree 42 years B. C. Suppose it to have been planted 87 years B. C., what is its age in 1880 A. D.?

498. This tree is 121 feet high. What must be the length of a cord that will reach from the top to the ground 50 feet in a horizontal line from the base?