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ON THE STEAM ENGINE.

Steam at the temperature of 212° is 1800 times its bulk in water; or, one cubic foot of steam, when its elasticity is equal to thirty inches of mercury, contains one cubic inch of water. Therefore, when an engine in good order, is performing its regular work, the effective pressure may be taken at eight pounds on each square inch of the surface of the piston.

CASE I.

To calculate the power of an Engine.

It has been demonstrated in the Franklin Institute, of Philadelphia, that a horse can draw 200 lbs. at the rate of 21⁄2 miles an hour, or 220 feet in a minute with a continuance drawing over a pully, that is, 200 × 220 = 44000 lbs. at 1 foot per minute, or 1 lb. at 44000 feet per minute.

RULE 1.- Multiply the area of the cylinder by the effective pressure, say 8 lbs., the product is the weight the engine can raise. Multiply this weight by the number of feet the piston travels in one minute, the product will give the momentum, divide this momentum by a horse power, and the quotient will be the number of horse power in the engine.

2. The velocity of an engine being 220 feet per minute, 25 inches of the area of the cylinder is equal to one .horse power.

TABLE FIRST.

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1. What is the power of an engine, the cylinder being 42 inches diameter and stroke 5 feet?

422 × .7854 × 8 × 210

44000

74.44 horse power.

2. What size of cylinder will a 60 horse power engine require when the stroke is 6 feet?

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Examples calculated by Rule Second.

1. What diameter is the cylinder of a 40 horse engine, common pressure?

✓ 40 × 25

.7854

=

35.7 say 35 inches diameter.

CASE II.

To find the power to lift a weight at any velocity. RULE.-Multiply the weight in pounds, by the velo

city in feet, and divide by the horse power, the quotient

will be the number of horse power.

TABLE SECOND.

When the effective pressure | The area equal to one

on each inch of piston is

53 pounds.

horse power will be

3.70 inches.

48

66

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1. What diameter is the cylinder of a 40 horse engine, effective pressure 33 lbs. on the square inch?

✔ 40 × 6.06

= say 17 inches diameter.

2. The cylinder of an engine is 40 inches diameter, and the effective pressure is 20 lbs. on the square inch, what is the power of the engine?

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When the sum and difference of any two numbers are given, to find the numbers.

RULE. To half the sum add half the difference, for the greater number. From half the sum, take half the difference for the lesser number.

THEOREM 2.

The product of the sum and difference of 'bers is equal to the difference of their

THEOREM 3.

any two num

squares.

If the difference of the squares of two numbers be divided by their difference, the quotient will be the sum; and if by the sum of the numbers, the quotient will be the difference.

THEOREM 4.

If a number be divided into any two parts, the square of the number is equal to the sum of the squares of the two parts, and twice the product of those parts.

THEOREM 5.

If the difference of the cubes of any two numbers be divided by their difference, the quotient arising will be equal to the sum of the squares of the two numbers together with their product.

THEOREM 6.

When the sum and product of two numbers are given to find the numbers

*These Theorems should be committed to memory.

RULE-Square the sum of the numbers, and from that square, subtract 4 times the product, the square root of that difference will give the difference of the numbers, then agreeably to Theorem 1, by having the sum and difference we can easily find the numbers.

THEOREM 7.

The sum, and sum of the squares of two numbers being given to find the numbers.

RULE.-Subtract the sum of the squares of the numbers, from the square of their sum, and half the remainder will be their product. When the sum and product are given, we can find the numbers agreeably to Theorem 6.

QUESTIONS FOR EXERCISE.
1. A wealthy man two daughters had,
And both were very fair,

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A. A bullet is dropped from the top of a building, and found to reach the ground in 2 seconds. Required its height? Ans. 2 x 4 = 8 and 8 x8 = 64 feet. B. Admitting I let fall a bullet from the top of a building, and found it reached the ground in 1 seconds. Required its height?

2. If a roll of butter weighs in one being changed into the other weighs 4 true weight of the butter?

Ans. 36 ft. scale 24 lbs., and lbs.; what is the

Ans. 3 lbs.

3. A farmer hired two men, Reuben and Richard, for $30, (being the wages of both for 1 month,) to Reuben he gave $4 per month more than to Richard. How much

did each get per month?

Ans. Reuben got $17 and Richard $13.

4. There is a certain number which being divided by 11, the quotient resulting multiplied by 5, that product divided by 4, from the quotient subtract 75, to the remainder add 40, and half the sum shall make 45. Required the number? Ans. 1100. 5. What is the discount of $400 for 2 years, 8 months, 24 days, at 6 per cent. per annum? Ans. $56.36. 6. What is the interest of $400 for 2 years, 8 months, 24 days, at 6 per cent.? Ans. $65.60.

7. A merchant in Baltimore received from New Orleans a bill at 30 days sight; he allowed 1 per cent. discount for present payment, and received $2530.44; what sum was the bill drawn for; and what was the discount? Ans $2555.74+ disct. $25.30.

8. Bunker Hill monument is 30 feet square at its base, and is to be 15 feet square at its top, its height is to be 220, from the bottom to the top through its centre, is a cylindrical avenue 15 feet in diameter at the bottom, and about 11 feet at the top. How many cubic feet will there be in the monument? Ans. 86068.518+ ft. that if to the first you

9. Divide 40 into 4 such parts, add 4, from the second subtract 4, multiply the third by 4, and divide the fourth by 4; the sum, difference, product and quotient will be equal? Ans. 1, 5, and 18. 10. Find two numbers in a given ratio as 6 to 9, so that their sum and product may be equal? 2 and 1.

52

11. Two drovers, A and B, (from the state of Ohio) stopped at the "Three Tun Tavern," in the city of Baltimore, each having a drove of cattle; A had 21 head, in his drove, and B 19; they agreed to join both together, and sell them for $27 per head; and, that A should receive

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