PROBLEMS.

1. St. Paul is in longitude 93° 5' W. Find the difference between the local and the standard time of St. Paul.

Process.

93° 5'

90°

15) 3° 5'

12 min. 20 sec.

Explanation.

St. Paul is within 7° 30′ of 90°, and is within the central time-belt. Its distance from the 90th meridian is 3° 5′, which, divided by 15, gives 12 min. 20 sec., the difference of time required.

2. Boston is in longitude 71° 3' 30". Find the difference between the local and the standard time of Boston.

3. Pittsburg is within 7° 30′ from Philadelphia, which lies close to the middle meridian of the eastern belt. When it is noon at Philadelphia, what is the standard time at Pittsburg? 4. Galveston is in longitude 94° 50′ W. When it is noon there by local time, what hour is it by standard time?

5. St. Louis is in longitude 90° 15′ 15′′ W. When it is noon there by standard time, what is the local time?

MISCELLANEOUS PROBLEMS.

1. If one doz. pints of oil cost $4.00, what is the cost of one qt.?

2. A gentleman in travelling found at a certain railroad station that his watch was 1 hr. and 25 min. slow. What direction was he travelling? How far had he travelled?

3. A note dated June 12, 1896, was paid Jan. 5, 1897. How long did the note run?

4. How many steps yd. long will a man take in walking 1 mi. and 580 yd.?

5. If 10 grain bins contain 254 bu. 3 pk. 7 qt. 1 pt., what does 1 bin contain?

6. Since noon the sun has seemed to pass through 10° 43' 35". What is the time of day?

7. If a cu. ft. of water weighs 1000 oz., how many 1b. avoirdupois does a cu. yd. of water weigh?

8. When it is 1 hr. 37 min. 12 sec. P.M. at Bangor (68° 47′ W.), what is the time at St. Paul (93° 5' W.)?

9. A crib measuring 16 ft. × 6 ft. 9 in. × 7 ft. is full of corn in the ear. How many bu. of shelled corn will there be? 10. In 556,688 ft. how many miles?

11. How many gal. of air in a room 16 ft. long, 11 ft. wide, and 10 ft. high?

12. How many bu. of shelled corn will fill a vat that holds 6000 gal. of water?

13. A block of marble 4 ft. long and 2 ft. wide contains 12 cu. ft. How thick is the block?

14. How many bu. in 6 tons of oats?

15. How much is gained on 65 doz. eggs bought at $.15 a doz. and sold at the rate of 13 doz. for $.25?

16. What is the cost of 4 tons and 468 pounds of hay at $12 a ton?

17. A firkin of butter weighed 61 lb. 12 oz. How much did the vessel itself weigh?

18. If a man can do a piece of work in 22 hr. 30 min. 25 sec., what part of it can he do in 13 hr. 11 min. 15 sec.?

19. Divide 3 gal. 2 qt. 2.03 pt. by 18, and reduce the result to the decimal of a barrel.

20. What decimal of a lb. avoirdupois is a lb. troy? 21. How many bu. of potatoes in 2240 lb?

22. The longitude of New York is 74° 0' 3" W.; of London, 0° 5' 48" W. Find the difference of time between the two cities. Which has the earlier time?

23. If a bicycle wheel 7 ft. 4 in. in circumference makes 3 revolutions in a second, at what rate per hour is the rider going? 24. How many francs equal $1.00?

25. Reduce £3 8s. 4d. to dollars, U. S. currency.

26. The annual cost of Spanish royalty is 9,500,000 pesetas. Reduce to U. S. money. (Peseta = $.193.)

27. Latitude is distance north or south from the Equator. If a man travels due north from the Equator 2500 mi., what latitude does he reach? (1° = 691 mile.)

28. 3780 gal. of water will fill how many barrels ?

29. If hyoscine hydrobromate is worth $12.50 a grain, what will be the cost of 12 tablets of the drug, each containing .01 of a grain?

30. A owns

of a farm, and B owns the remainder.

of

the difference between their shares is 16 A. 80 sq. rd. Find the share of each in acres.

1. Define:

REVIEW.

1. Denominate Number.
2. Compound Denomi-
nate Number.

3. Money.

4. U. S. Money.
5. Sterling Money.
6. Reduction.

7. Reduction Descending.
8. Reduction Ascending.
9. Extension.
10. Linear Measures.
11. Surface Measures.

12. Measures of Volume.

13. Measures of Capacity.
14. Angle.

15. Rectangle.

16. Square.
17. Area.

18. Solid.

19. Rectangular Solid,
20. Cube.
21. Volume.

22. Solid Contents.
23. Board Measure.
24. Weight.
25. Troy Weight.
26. Apothecaries' Weight.
27. Circular Measure.
28. Circle.

29. Circumference.
30. Arc.

31. Quadrant.
32. Degree.

33. Fractional Relation.

34. Uniform Scale.

35. Varying Scale.

36. Longitude.

37. Standard Time.

PART II.

PERCENTAGE.

INDUCTIVE STEPS.

1. A man earned $5 and spent $1.00. What fractional part of the $5 did he spend? What part of $10 would he have spent? What part of $50? What part of 100?

2. $20 out of $100 means 20 per hundred, or 20 per cent. 3. What is the meaning of 10 per cent? Of 25 per cent.? Of 50 per cent.? Of 75 per cent.? Of 100 per cent.?

4. Having taken 100 per cent. of a sum of money, how much is left?

5. How much is 1 per cent. of $100? Of $200? Of $1000? 6. What is 5 per cent. of $200? Of 100 acres? Of 500 men?

7. What is 6 per cent. of $600? Of 900 sheep? Of 1200 yards?

DEFINITIONS.

1. Percentage means computation by the hundred, and has 100 for its unit. One per cent. of any number is of it; 5 per cent. is 10 of it.

Per cent. is a contraction of the Latin per centum, by the hundred. 2. The result of computation is also called Percentage.

3. The Symbol for per cent. is %. Per cent., however, may be expressed in five different ways: 6 per cent. = 6% = .06 The best way in any given case is the one

that affords the shortest solution.

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