ence between where the water strikes the wheel, and the tail water; the sum is the effective power.

EXAMPLE. What would be the power of a breast wheel applied to a stream 2×80 inches, 14 feet from the surface, the rest of the fall being 11 feet?

14×6.5×60 : = 1458.6 feet velocity of water per minute. And 2x80x1458 × 12÷÷1728 1620 cubic feet 62.5=101250 lbs. of water discharged in one minute.

Then 101250 100000 1.012 horses' power as an undershot. 11x6.5x60 = 1290 feet velocity of water per minute.

And 2×80x1290×12÷1728 1433 cubic feet X 62.5=89562 lbs. of water discharged in one minute.

X11 height of fall ÷50000 = 19.703 horses, which, added to the above, 20.715, Ans.

When the fall exceeds 10 feet, it may be divided into two, and two breast wheels applied to it.

When the fall is between 4 and 10 feet, a breast wheel should be applied.

The power of a water wheel ought to be taken off opposite to the point where the water is producing its greatest action upon the wheel.

BARKER'S MILL.

The effect of this mill is considerably greater than that which the same quantity of water would produce if applied to an undershot wheel, but less than that which it would produce if properly applied to an overshot wheel.

For a description of it, see Grier's Mechanics' Calculator, page 234.

Make each arm of the horizontal tube, from the centre of motion to the centre of the aperture of any convenient length, not less than of the perpendicular height of the water's surface above these centres.

Multiply the length of the arm in feet by .61365, and the square root of the product will be the proper time for a revolution in seconds; then adapt the geering to this velocity. Or, if the time of a revolution be given, multiply the square of it by 1.6296 for the proportional length of the arm in feet.

Divide the continued product of the breadth, depth, and velocity of the stream in feet by 14.27; multiply the quotient by the square root of the height, and the result is the area of either aperture.

Multiply the area of either aperture by the height of the head of water, and this product by 56; the result is the moving force in lbs. at the centre of the apertures.

EXAMPLE. If the fall be 18 feet from the head to the centre of the apertures, then the arm must not be less than 2 feet (as of 18= 2), √2.613651.107, the time of a revolution in seconds; the breadth of the race 17 inches, the depth 9, and the velocity 6 feet per second; what is the moving force?

17 inches 1.41 feet, 9 inches.75 feet; then 1.41X.75×6÷ 14.27X18X18×561895 lbs., Ans.

To find the Centre of Gyration of a Water Wheel. RULE. Take the radius of the wheel, the weight of its arms, and the weight of its rim, as composed of floats, shrouding, &c.

Let R represent the weight of rim,

the radius of the wheel,

66 T

“... A "W

66

the weight of arms,

the weight of the water in action when the buck

ets are filled, as in operation.

Then √(Rxr2×2+A×r2×2+W×r2÷R+A+Wx2)= centre of gyration.

EXAMPLE. In a wheel 20 feet diameter, the weight of the rim is 3 tons, the weight of the arms 2 tons, and the weight of the water I ton; what is the distance of the centre of gyration from the centre of the wheel?

NOTES. At the mill of Mr. Samuel Newlin, at Fishkill Creek, N. Y., 5 barrels of flour can be ground, and 400 bushels of grain elevated 36 feet per hour with a stream and overshot wheel of the following dimensions, viz.:

Height of head to centre of opening, 24 inches; opening, 13 by 80 inches; wheel, 22 feet diameter by 8 feet face; 52 buckets, each 1 foot in depth.

The wheel making 34 revolutions, driving 3 run of 4 feet stones 130 turns in a minute, with all the attendant machinery.

This is a case of maximum effect, in consequence of the gearing being well set up, and kept in good order.

At the furnace of Mr. Peter Townsend, Monroe Works, N. J., 30 to 34 tons of No. 1 Iron are made per week, with the blast from two 5 feet by 5 feet 1 inch blowing cylinders. The wheel (overshot) being 24 feet diameter, by 6 feet in width, having 70 buckets of 14 inches in depth. The stream is by 51 inches, having a head 64 feet; the wheel and cylinders each making 44 revolutions per minute.

Rocky Glen Factory, Fishkill, N. Y., containing 6144 self-acting mule spindles, 160 looms, weaving printing cloths 27 inches wide of No. 33 yarn (33 hanks to a pound), and producing 24,000 hanks in a day of 11 hours, is driven by a breast wheel and stream of the following dimensions, viz. :

Stream 18 feet by 2 inches, head 20 feet, height of water upon wheel 16 feet, diameter of wheel 20 feet 4 inches, face of wheel 20 feet 9 inches, depth of buckets 15 inches, number of buckets 70.

Revolutions, 4 per minute.

PNEUMATICS.

WEIGHT, ELASTICITY, AND RARITY OF AIR.

THE pressure of the air at the surface of the earth is, at a mean rate, equal to the support of 29.5 inches of mercury, or 33.18 feet of fresh water. It is usually estimated in round numbers at 30 inches of mercury and 34 feet of water, or 15 lbs. pressure upon the square inch.

The Elasticity of air is inversely as the space it occupies, and directly as its density.

When the altitude of the air is taken in arithmetic proportion, its Rarity will be in geometric proportion.

Thus, at 7 miles above the surface of the earth, the air is 4 times rarer or lighter than at the earth's surface; at 14 miles, 16 times; at 21 miles, 64 times, and so on.

The weight of a cubic foot of air is 527.04 grains, or 1.205 ounces avoirdupois.

At the temperature of 33°, the mean velocity of sound is 1100 feet per second. It is increased or diminished half a foot for each degree of temperature above or below 33°.

To compute Distances by Sound.

RULE.-Multiply the time in seconds by 1100, and the product is the distance in feet.

EXAMPLE.-After observing a flash of lightning, air at 50°, it was 5 seconds before I heard the thunder; what was the distance of the cloud?

1100+

50-33
2

x552801.049 miles, Ans.

Vessel.

To compute what Degree of Rarefaction may be effected in a

Let the quantity of air in the vessel, tube, and pump be represented by 1, and the proportion of the capacity of the pump to the vessel and tube by .33; consequently, it contains of the air in the united apparatus.

Upon the first stroke of the piston this fourth will be expelled, and of the original quantity will remain: 4 of this will be expelled upon the second stroke, which is equal to of the original quantity; and, consequently, there remains in the apparatus of the original quantity. Calculating in this way, the following table is easily made:

9

16

18

And so on, continually multiplying the air expelled at the preceding stroke by 3, and dividing it by 4; and the air remaining after each stroke is found by multiplying the air remaining after the preceding stroke by 3, and dividing it by 4.

Measurement of Heights by Means of the Barometer.

Approximate Rule. For a mean temperature of 550,

x=55.000x

h-h' "h+h"

Add of this result for each degree which the 440

mean temperature of the air at the two stations exceeds 550, and deduct as much for each degree below 550.

To find the Force of Wind acting perpendicularly upon a

Surface.

RULE.-Multiply the surface in feet by the square of the velocity in feet, and the product by .002288; the result is the force in avoirdupois pounds.

LET ABCD be the vertical section of a wall, behind which is a bank of earth, ADfe; let DG be the line of rupture, or natural slope which the earth would assume but for the resistance of the wall.

In sandy or loose earth, the angle G D H is generally 30°; in firmer earth it is 36°, and in some instances it is 45°.

The angle formed with the vertical by the earth, A D G, that exerts the greatest horizontal stress against a wall, is half the angle which the natural slope makes with the vertical.

If the upper surface of the earth and the wall which supports it are both in one horizontal plane,

Then the resultant In of the pressure of the bank, behind a vertical wall, is at a distance Dn of A D.

In vegetable earths, the friction is

the pressure; in sands,

The line of rupture A G in a bank of vegetable earth is = .618 of AD.
When the bank is of sand, it is .677 of A D.

If of rubble, it is .414 of A D.

Thickness of Walls, both Faces Vertical.

Brick. Weight of a cubic foot, 109 lbs. avoirdupois, bank of vegetable earth behind it, A B=.16 A D.

Unhewn stones. 135 lbs. per cubic foot, bank as before, A B.15 A D.

Brick. Bank clay, well rammed, A B.17 AD.

Hewn freestone. 170 lbs. per cubic foot, bank of vegetable earth, AB=.13 AD; if the bank is of clay, A B.14 A D.

Bricks. Bank of sand, AB=.33 AD.

Unhewn stone. Bank of sand, A B=.30 AD.

Hewn freestone. Bank of sand, A B=.26 A D.

When the bank is liable to be saturated with water, the thickness of the wall must be doubled.

For farther notes, and for the Equilibrium of Piers, see Gregory's Mathematics, pages 220 to 224.