11. The amount of water that flows over Niagara Falls averages 264,000 cu. ft. a second. Find the average number of gallons carried over the falls in a second.

12. The diagonal of a square is 20 ft. Find to two decimal places the length of one side.

13. If in. on a map represents an actual distance of 35 mi., what distance on the map represents 28.4 mi. ?

14. How many loads of gravel averaging 1 cu. yd. will be required to grade 2 mi. of road, the gravel to be laid 14 ft. wide and 6 in. deep?

15. If a dealer pays $9737.50 for some wool, including the purchasing agent's commission of 21%, how much is the amount of the commission?

16. The sugar contained in the sugar beet is 61% of the weight of the beet. How many pounds of beets will be required to produce 122 lb. of sugar?

17. How many boards 12 ft. long will be required to build a straight fence 4 boards high about a rectangular field 40 rd. wide containing 20 acres?

18. Find the circumference of a circle whose diameter is 22.6 in., using 3.1416 as the ratio of circumference to diameter; also using 34; also using the ratio 355:113.

19. If 15 burners, each consuming 6 cu. ft. of gas per hour, are used on an average 4 hr. per day for 365 days, what will be the gas bill at 80 per thousand?

20. Flint glass contains by weight 72% sand, 14% soda, 12% lime, and 2% alumina. Find the number of pounds of each of these substances in 150 lb. of flint glass.

21. A bell weighing 1250 lb. is composed of 77% copper, 21% tin, and the rest zinc. How many pounds of each metal does the bell contain?

22. Bronze contains 9 parts of copper by weight to 2 parts of tin. How many pounds of tin in a bronze statue that weighs 2662 lb.?

23. The time from one new moon to the next is 29 da. 12 hr. 44 min. 3 sec. Express this in days and the decimal fraction of a day.

24. Find the difference in the number of acres in two fields, one of which contains 75 sq. rd., and the other of which is 75 rd. square.

25. Find to the nearest pound the weight of the air in a schoolroom 30' x 16' x 12', if water is 770 times as heavy as air and weighs 1000 oz. per cubic foot.

26. If a certain gun metal is composed of 84% copper and the rest tin, how many pounds of tin will be needed with 58.8 lb. of copper to make the gun metal?

27. A man, computing the cost of 54 articles, multiplied by mistake the cost of each by 45 instead of 54, and obtained $121.50. What was the cost of the 54 articles?

28. A company with a capital of $350,000 earned net $28,250 last year. It paid a 7% dividend and carried the balance to surplus. How much did it carry to surplus?

29. A gardener finds that a bin 8 ft. long, 3 ft. 6 in. wide, and 5 ft. deep holds 112 bu. How many bushels in a bin that is 25% longer, 25% narrower, and has the same depth?

30. Find the cost of a stair carpet at $1.35 a yard for a straight flight of 19 steps 10 in. wide and 8 in. rise, allowing 15 in. extra for the bottom of the stairs and the same for the top.

31. Water is flowing into a rectangular tank whose base is 6 ft. 8 in. long and 4 ft. 6 in. wide, at the rate of 2 cu. ft. in 3 min. How long will it take the water to fill it to a depth of 6 ft.?

32. Find the cost of 325 boards 16 ft. long, 4 in. wide, and in. thick at $27 per M.

33. Find the number of dry quarts a cylindrical measure 161⁄2 in. in diameter and 1 ft. high will hold.

34. At what rate will $1250 yield $112.50 interest in 2 yr.? at what rate will it yield $206.25 interest in 3 yr.?

35. What fraction of the year 1912 is the time from January 20 to March 15, including both of these days?

36. On seven successive days at noon the thermometer indicated 66°, 72°, 61°, 68°, 73°, 62°, 65°. What was the average for the week?

37. On seven successive days the barometer indicated 29.22 in., 29.18 in., 29.65 in., 30.02 in., 30.12 in., 30.18 in., and 30.21 in. What was the average for the week?

38. A cubic inch of iron weighs 43 oz. Find the weight in pounds of an iron bar 1 in. square at the end and 1 yd. long; 1 in. square at the end and 15 ft. long.

39. The driving wheels of a locomotive are 6 ft. 8 in. in diameter. How many revolutions a minute does each wheel make when the locomotive is traveling 48 mi. an hour?

40. When water is heated from 32° to 212° it expands in volume. If a cubic foot of water at the freezing point weighs 624 lb., what does a cubic foot of boiling water weigh?

41. A man bought a bill of goods in Paris to the value of 2600 fr. He paid 40% ad valorem duty and $17.65 freight, and sent a draft for the purchase price when exchange was 19.4. What was the total cost?

42. A pole is broken by the wind 12 ft. above the ground. The two parts hang together, but the upper part is bent over and touches the ground 12 ft. from the base. How long was the pole originally? (Two decimals.)

cu. yd. of sand to make bricks are allowed per

43. If it takes 1 bbl. of lime and mortar for 1000 bricks, and if 22 cubic foot of wall, how much lime and how much sand are needed for a wall 28' x 6' x 1'6"?

44. The diagonal of one face of a cube is √450 in. Find the number of square inches in the entire surface of the cube and the number of cubic inches in the volume.

45. If a horse is tethered by a 40-foot rope, the length of the largest circumference he can walk around is how many times what it would be if he were tethered by a 20-foot rope?

46. In Ex. 45 the horse can graze over how many times as much ground in the first case as in the second?

47. One man can do a piece of work in 8 days and another man can do it in 10 days. How many days will it take the two together to do the work?

48. If X can build a wall in 18 days, Y in 15 days, and Z in 12 days, how many days will it take all three working together to build the wall?

49. If X, Y, and Z working together can dig a ditch in 24 hr., and X and Z working together can dig it in 32 hr., how many hours will it take Y alone to dig the ditch?

50. A water tank can be filled by three pipes, running separately, in 4 hours, 5 hours, and 6 hours respectively. In how many hours will the empty tank be filled by all three running together?

51. If the eye is 8 in. above the surface of a lake it can see about 1 mi.; if it is 22 × 8 in. above the surface, 2 mi.; if it is 32 × 8 in. above the surface, 3 mi.; and so on, the height being approximately 8 in. multiplied by the square of the distance in miles. About how far can a man see in one direction, if his eye is 36 ft. above the surface of the sea? (Two decimals.)

APPENDIX

186. Subjects Treated. In this Appendix are included certain subjects now generally omitted from courses in arithmetic, but still demanded by schools that have not diminished the time formerly assigned to this study. There are also included several tables that will prove helpful to the student and teacher, and will be of value for reference after the school course is completed. Local conditions should determine what portion of this material should be used. It may all be omitted if desired, or such selections may be made as seem best.

Arithmetical and Geometric Progressions, for example, are best treated in algebra, but for pupils who take no algebra the subject has considerable interest and offers opportunity for exercise in computation. Compound Interest, used chiefly in computing the growth of funds the interest on which is reinvested when due, follows naturally from the study of Geometric Progression, and affords practice in the use of tables. Repeating Decimals, while of little practical value, are interesting applications of progressions, and are frequently met in official examinations. The Proof by Casting out Nines is so important that teachers are advised always to use it with their classes. A large amount of extra drill work has also been provided, from which teachers may select problems as needed. A few problems of a recreative nature have been added that can hardly fail to appeal to many pupils.