2. What is an increasing Series? Decreasing Series? Art. 325.

3. Define the terms, means and extremes of a Progression. Art. 326.

4. How many parts are there in every Geometrical Progression? Art. 326.

5. How many must be known before the rest can be found? Art. 326.

do

6. Knowing the first term, the ratio, the number of terms, how you find the last term? Art. 327.

7. The first term of a decreasing geometrical series is 729, the ratio; what is the 10 term? Art. 327. Ex.-3.

8. Knowing the two extremes and the ratio, how do you find the sum of the terms? Art. 328.

9. A merchant engaging in business trebled his capital once in 4 years; if he commenced with $2000, what will his capital amount to at the end of the 12th year? Art. 327. Ex. 6.

10. A laborer agreed to thresh 64 days for a farmer, on the condition that he should give him 1 grain of wheat for the first day's labor, 2 grains for the second, and double each succeeding day; what number of bushels would he receive, supposing a pint to contain 7,680 grains, and what number of ships, each carrying 1000 tons burden, might be loaded, allowing 40 bushels to a ton? Art. 328. Ex. 5.

ANALYSIS.

1. Define Analysis and tell wherein it differs from the "Rule of Three."

2. By analysis find the cost of 12 lbs. of tea at 6s. and 8d. a pound, Pennsylvania currency. Page 329. Ex. 7.

3. A general arranging his army in the form of a square, finds that he has 44 remaining; but by increasing each side by another man, he wants 49 to fill up the square; how many men had he? Page 348.

Ex. 103.

4. If a ball 2 inches in diameter weighs 5 pounds, what will be the diameter of another ball of the same material that weighs 78,125 pounds? Page 350. Ex. 120.

MENSURATION.

1. Define Mensuration. Surface Square. Art. 329, 330. 2. What is a triangle? Base of a triangle? Altitude? 3. Which side is the hypothenuse of a right-angled triangle? Art. 331.

4. What is the area of a triangle equal to? What is a rectangle?

5. Define a Parallelogram. Trapezoid. Art. 335.

6. How do you find the area of a Parallelogram? Square? Rectangle, or Trapezoid? Art, 336.

7. What is the area of a trapezoid whose parallel sides are 15 chains and 245 chains, and the perpendicular height 30.80 chains? Art. 337. Ex. 5.

8. Define a Circle. Radius. Center. Art. 337.

9. How do you find the diameter when the circumference is known? Art. 338.

10. What is the area of a circle whose diameter is 5? Art. 339. Ex. 2.

11. How do you find the surface of a sphere? Contents of a sphere? Art. 343.

12. Required the area and contents of the earth, its mean diameter being 7918.7 miles. Art. 343. Ex. 5.

13. How do you find the convex surface of a Prism? Its contents? Art. 346.

14. What is a cylinder? How do you find its convex surface? Art. 348.

15. What are the contents of a cylinder the diameter of whose base is 25 feet, and altitude 15? Art. 349. Ex. 5.

16. Define a pyramid. How do you find the contents of a pyramid? Art. 351.

17. A Pyramid with a square base, of which each side is 15, has an altitude of 24; what are its contents? Art. 351. Ex. 7. How do you find the contents of a cone?

18. Define a cone.

Art. 353.

19. What are the contents of a cone whose altitude is 27 feet, and the diameter of the base 20 feet? Art. 353. Ex. 4.

GAUGING.

1. What is a cask gauging? How many varieties of casks are there?

2. Give the rule for finding the mean diameter.

Art. 356.

3. How do you find the contents in cubic inches? Art. 357. 4. How many wine gallons in a cask of which the head diameter is 24 inches, bung diameter 36 inches, and length 3 feet 6 inches, the cask being of the second variety? Art. 357. Ex. 4.

MECHANICAL POWERS.

1. How many simple machines are there? Art. 358.

2. Name and describe each. Describe each variety of levers. Art. 361.

3. When is an equilibrium produced in all the levers?

4. What is the proportion between the weight and power? Art. 362.

5. In a lever of the third, the distance from the fulcrum to the weight is 12 feet, and to the power 8 feet; what power will be necessary to sustain a weight of 100 lbs.? Art. 362. Ex. 8.

PULLEY.

1. Define a pulley. How many kinds are there? Art. 365. 2. Does a fixed or movable pulley give any increase of power? Art. 366.

3. What advantage will be gained by several movable pulleys? Art. 367.

4. In two movable pulleys with 4 cords, what power will support a weight of 100 lbs.? Art. 368. Ex. 3.

5. Define an inclined Plane. Wedge. What used for. Art. 381.

6. Define a Screw. Nut. What is the power of a screw? Art. 381.

7. If a power of 300 lbs. applied at the end of a lever 15 feet long will sustain a weight of 282,744 lbs., what is the distance between the threads of the screw? Art. 381. Ex. 4.

UNIFORM MOTION.

1. Define uniform motion. Velocity of a moving body. Art. 383.

2. To what is the space passed over in a unit of time equal? Art. 384.

3. To what is the space passed over in uniform motion equal?

LAWS OF FALLING BODIES.

1. How does the velocity of a falling body change? Art. 386. 2. State and explain the four principles involved in falling bodies. Art. 386.

3. How far will a body ascend when projected upwards? Art. 387.

4. Are the above laws perfectly or only approximately true? Art. 388.

5. A stone is dropped from the top of a bridge and strikes the water in 2.5 seconds; what is the height of the bridge? Art. 388.

Ex. 9.

6. A rocket is projected vertically upwards with a velocity of 386 feet; after what time will it begin to fall, and to what height will it rise? Art. 388. Ex. 15.

SPECIFIC GRAVITY.

1. Define specific gravity. What is the standard for measuring the specific gravity of a body? Art. 389.

2. How do you find the specific gravity of a body? Art. 389. 3. A piece of copper weighs 93 grains in air, and 82 grains in water; what is its specific gravity? Art. 389. Ex. 1.

4. What weight of mercury will a conical vase contain of which the radius of the base is 9 inches, and the altitude 34 inches, the specific gravity of the mercury being 13.596? Art. 389. Ex.

15.

5. To what is the volume of a vapor or gas proportional?

Art. 390.

6. To what is its density proportional?

7. Eight quarts of hydrogen gas are contained in a vessel and submitted to a pressure of 22 lbs.; how many quarts of gas will

there be if the pressure is changed 9 pounds? Art. 390. Ex.

6.

APPENDIX.

NOTE. The design and limit of this work require that the questions on this part of Arithmetic be comprehensive.

1. Name and tell how many kinds of units there are in Aritnmetic. Art. 991.

2. Describe an abstract unit, and each unit in its order. Art. 392.

3. Describe the unit of currency. Length. Weight. Surface.

Time.

4. Repeat accurately the tables of the various units in their order: First, U. S. money. Art. 404. 2d, English money. Art. 406.

5. 5th, Table of Linear Measure. Art. 407 6. Cloth Measure. Art. 410.

7. Square Measure. Art. 411.

412.

8. Cubic Measure. Art. 413. Beer Measure.

Surveyor's Measure. Art.

Wine Measure. Art. 414.

9. Dry Measure. Art. 416. Avoirdupois Weight. Art. 417. Troy Weight.

10. Apothecaries' Weight. Art. 419. Measure of Time. Circular Measure.*

11. Miscellaneous Table. Books and Paper. Art. 422.

REMARK.-Many additional questions might be proposed in this branch. But the candidate who answers accurately the foregoing questions, assigning reasons for his views, need not fear an Examination before any Board of Examiners in this branch.

Solve the following:

For value received, seven years from date, I promise to pay the Kenosha and Mississippi Cotton Growing Association $7897.86, in seven equal annual payments, at seven per cent. compound interest. What sum must be paid each year?

KENOSHA, Wis., Jan. 23, 1864.

I. S.