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trial divisor is contained in the remainder and place this figure as the second figure in the answer; also add this number to the trial divisor, to make the complete divisor. Multiply the complete divisor by the last figure in the answer and subtract this result from the remainder. Bring down the next period and repeat the operation. Continue in the same way until there is no remainder, or until the root has been found to as many decimal places as desired.

The arithmetical work is as follows:

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To find the square root of a number which contains a decimal, proceed in the same way, taking care to begin at the decimal point to divide the number into periods.

For example: The square root of 6.25 is 2.5. But suppose we are to find the square root of 62.5. The work is as follows:

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1. Find the square root of 576.- Answer, 24. 2. The area of a square floor is 256 square feet. What is the length of one side? Answer, 16 feet.

3. I wish to make a bin to hold 100 tons of coal. The coal requires 44.1 cubic feet to the ton. If the bin is 10 feet high and the bottom square, what is the length of one side? Answer, 21 feet.

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4. What is the radius of a piston if its area is 201.0624 square inches? Divide by 3.1416 and find the square root of the quotient.- Answer, 8 inches.

5. What is the radius of a piston if its area is 226.9806 square inches? - Answer, 8.5 inches.

6. A safety valve is to be designed for a total pressure of 600 pounds, 50 pounds per square inch. What must be the radius of the valve? Divide 600 by 50 to find area, and this result by to find r2. Then find the square root.- Answer, 1.9 inches.

Cube Root.

The cube root of a number is the quantity which, multiplied by itself three times, will produce the given number. The cube root may be regarded as the length of the edge of a cube, the volume of the cube being the given number.

Square root and cube root of numbers may be found from Table IX.

Heating and Ventilation.

We shall explain here heating and ventilating calculations, as affecting the work of the operating engi

neer.

Following are some facts which the engineer should know regarding his heating plant:

One horse-power is equivalent to 42.7 heat units per minute.

One horse-power represents the energy required to evaporate .044 pound of water per minute.

With steam heat, 1 horse-power is sufficient to supply 100 square feet of direct cast-iron radiation, or 90 square feet of pipe or heating-coil radiation.

The heat that will raise 1 pound of water 1 degree will raise 41⁄2 pounds of air, or 9 pounds of iron, 1 degree.

At ordinary pressure and temperature, about 12 cubic feet of air weigh 1 pound.

One square foot of grate surface supplies 36 square feet of boiler surface, and this carries 196 square feet of dried radiating surface for heating. Area of chimney should allow 49 square inches for 1 square foot of grate surface.

For low-pressure steam heating, the size of the chimney may be somewhat less.

A cast-iron radiator will radiate much less heat when enameled than when painted with bronze or a mineral paint.

In estimating radiation, a square foot of glass and a square yard of ordinary outside wall have about the same cooling value.

Mills' rule for computing amount of radiation: "To find the amount of radiation required to heat a room with low-pressure steam to 70° F. when the outside temperature is at 0° F., allow 1 square foot of radiation for each 200 cubic feet of contents, 1 square foot of radiation for each 20 square feet of outside wall surface, and 1 square foot of radiation for each 2 square feet of glass surface (counting outside doors as glass surface). The sum of these results will be the amount of radiation required. For hot water, add 60 per cent to this result."

Amount of carbon dioxid usually present in air is 2 to 4 parts in 10,000, and this amount is not harmful.

Effect of Different Modes of Lighting on the Air, According to Doctor Tidy.

Material sufficient to produce Cubic feet of

light equal to 12 standard

candles, 1 hour.

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oxygen con-
sumed.

Cubic feet of

carbon dioxid

given off.

Cubic feet of air vitiated.

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The value of electric light in keeping the air pure is apparent from this table.

The least amount of air supply essential to good ventilation is given in the following table prepared by Doctor Billings:

Shops

Hospitals

Schools and churches.

Theaters and ordinary halls of audience.
Offices and dining-rooms.

Cubic feet per hour. ..3,600 per person. .3.600 per bed. .2,400 per person. .2,000 per seat. .1,800 per person.

To find what amount of air is being supplied, use an anemometer to measure the velocity of the air in the supply pipe.

The anemometer gives velocity in feet per minute.

Velocity of air in feet per minute, multiplied by area of air pipe in square feet, gives cubic feet of air per minute. This result multiplied by 60 gives cubic feet per hour.

Another method is to find the pressure of the air by means of a water-pressure gauge. Then its velocity can be found from Table 13.

The amount of moisture in the air is important. For health the air, whatever its temperature, should contain about 70 per cent as much moisture as it can hold at that temperature.

Warm air can hold more moisture than cold air. The effect of heating air on its humidity is shown in the following table. This table supposes the outside air to be saturated, and gives the humidity when brought in and heated to 70° F.

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Per cent of humidity is found by means of a wet and dry bulb hygrometer. This consists of two thermometers, one having the bulb wrapped with a wick which dips in water The dryer the air the more rapidly water evaporates from the wick and the lower the

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