tinued ascending line round the centre of the cylinder, and the greater the radius of the cylinder, the greater will be the length of the plane to its height, consequently, the greater the power. A lever fixed to the end of the screw will act as one of the second order, and the power gained will be as its length, to the radius of the cylinder; or the circumference of the circle described by it, to the circumference of the cylinder; hence, an addition to the rule is produced, which is,-If a lever is used, the circumference of the lever is taken for, or instead of, the circumference of the screw.

EXAMPLE I.

What is the power requisite to raise a weight of 8000 lbs. by a screw of 12 inches circumference and 1 inch pitch?

As 12 1 8000: 666 lbs. = power at the circumference of the screw.

EXAMPLE II.

How much would be the power if a lever of 30 inches were applied to the screw?

1884.

power with a lever

Circumference of 30 inches 1 As 1884 1: 8000: 425 560 lbs. = of 30 inches long.

1320

VELOCITY OF WHEELS.

Wheels are for conveying motion to the different parts of a machine, at the same, or at a greater or less velocity, as may be required. When two wheels are in motion, their teeth act on one another alternately, and consequently, if one of these wheels has 40 teeth, and the other 20 teeth, the one with 20 will turn twice upon its axis for one revolution of the wheel with 40 teeth. From this the rule is taken, which is,-As the velocity required is to the num

ber of teeth in the driver, so is the velocity of the driver to the number of teeth in the driven.

Note. To find the proportion that the velocities of the wheels in a train should bear to one another, subtract the less velocity from the greater, and divide the remainder by the number of one less than the wheels in the train; the quotient will be the number rising in arithmetical progression, from the least to the greatest velocity of the train of wheels.

EXAMPLE 1.

What is the number of teeth in each of three wheels to produce 17 revolutions per minute, the driver having 107 teeth, and making three revolutions per minute?

17-3=14

3—1=2

=7, therefore 3 10 17 are the velocities of

What is the number of teeth in each of 7 wheels, to produce one revolution per minute, the driver having 25 teeth, and making 56 revolutions per minute?

56-1=55

=9, therefore 56 46 37 28 19 10 1, are the

7-1=6 progressional velocities.

46 : 25 :: 56
: 30

37

46

It will be observed that the last wheel, in the foregoing example, is of a size too great for application; to obviate this difficulty, which frequently arises in this kind of train

ing, wheels and pinions are used, which give a great command of velocity.-Suppose the velocities of last example, and the train only of 2 wheels and 2 pinions.

56-1-55

4-1=3

=18, therefore 56 19 1, are the progres

sional velocities.

10 25 56: 74 teeth in the wheel driven by the first driver, and 1: 10 :: 19: 190 : = teeth, in the second driven wheel, 10 teeth being in the driving pinion.

25 drivers
10

74 driven. 190

STEAM ENGINE.

BOILERS-are of various forms, but the most general is proportioned as follows, viz. width 1, depth 1.1, length 2.5; their capacity being, for the most part, two horse more than the power of the engine for which they are intended.

Boulton and Watt allow 25 cubic feet of space for each horse power; some of the other engineers allow 5 feet of surface of water.

STEAM-arising from water at the boiling point, is equal to the pressure of the atmosphere, which is, in round numbers, 15 lbs. on the square inch; but to allow for a constant and uniform supply of steam to the engine, the safety valve of the boiler is loaded with three lbs. on each square inch.

The following table exhibits the expansive force of steam, expressing the degrees of heat at each lb. of pressure on the safety valve.

By the following rule the quantity of steam required to raise a given quantity of water to any given temperature is found.

RULE.-Multiply the water to be warmed by the difference of temperature between the cold water and that to which it is to be raised, for a dividend, then to the temperature of the steam add 900 degrees, and from that sum take the required temperature of the water: this last remainder being made a divisor to the above dividend, the quotient will be the quantity of steam in the same terms as the water.

Z 2

EXAMPLE.

What quantity of steam at 212° will raise 100 gallons of water of 60° up to 212° ?

212° 60° x 100 212°+900°-212

17 gallons of water formed into steam.

Now steam, at the temperature of 212°, is 1800 times its bulk in water; or 1 cubic foot of steam, when its elasticity is equal to 30 inches of mercury, contains 1 cubic inch of water. Therefore, 17 gallons of water converted into steam, occupies a space of 4090 cubic feet, having a pressure of 15 lbs. on the square inch.

In boiling by steam, using a jacket instead of blowing the steam into the water, about 10.5 square feet of surface are allowed for each horse capacity of boiler; that is, a 14 horse boiler will boil water in a pan set in a jacket, exposing a surface of 10.5×14=147 square feet.

HORSE POWER.-Boulton and Watt suppose a horse able to raise 32,000 lbs. avoirdupois 1 foot high in a minute. Desaguliers makes it 27,500 lbs.

Smeaton

do. 22,916 do.

It is common in calculating the power of engines, to suppose a horse to draw 200 lbs. at the rate of 24 miles in an hour, or 220 feet per minute, with a continuance, drawing the weight over a pulley-now, 200 × 220 = 44000, i. e. 44000 lbs. at 1 foot per minute, or 1 lb. at 44000 feet per minute. In the following table 32,000 is used. One horse power is equal to raise feet high per minute.

lbs.

gallons or