(2.) The diameter of the barrel, the length of the handle, and the force applied given, to find the number of revolutions of the pinion to one of the wheel.

RULE. Multiply the weight to be raised in lbs. by the diameter of the barrel in inches, and divide the product by the diameter of the circle described by the handle in inches, multiplied by the power applied in lbs.,

pinion to one of the wh the quotient is the revolutions of the

(3.) The diameter of the barrel, the number of revolutions of the pinion to one of the wheel, and the power applied given, to find the length of the handles.

RULE Multiply the weight to be raised in lbs. by the barrel's diameter in inches, and divide the product by the power applied in lbs., multiplied by the number of revolutions of the pinion to one of the wheel, and half the quotient is the length of the handles.

(4.) The diameter of the barrel, the revolutions of the pinion to one of the wheel, and length of handles given, to find the power required.

RUB Meltiply the weight to be raised in lbs. by the diameter of the barrel in inches, product by the diameter of the circle described by the handle multiplied by the revolutions of the pinion to one of the wheel, and the quotient is the power applied.

The handles of a crane should not be less than 2 feet 11 inches or 3 feet from the ground, and the jib to stand at an angle of about 45 degrees.

Equilibrium and Pressure of Beams.

The Parallelogram of Forces.

It has been proved by experiment that three forces, proportional to the two sides of a parallelogram and its diagonal, are in a state of equilibrium when their directions are in the direction of these lines.

tion

and

Let two forces, represented in direct out stalls? OT
magnitude by lines

and BO act at the point then will #1960
third force CO in direction and
tude can be

found, so that the three

forces are in a state of equilibrium.
Draw A D, BD, parallel to OB, O A,

respectively join DO, and produce it th
to C making CO equal to OD, then
OC is the force required.

The two forces 40, BO are called components, and CO the resultant of the

components. The components and resultant are called the parallelogram of forces.

Any resultant force can be readily decomposed into two compo nents, which will be the sides of a parallelogram whose diagonal is the resultant.

E

Let the beams O E, O B sustain a weight (W) tons at the point 0; draw OD verti cal, and make it equal to (W) inches, then draw DA, DB parallel to O F and OE respectively; measure D A, D B in inches which will be the pressure in tons in the directions OF and OE.

In this case E Fis a tie beam to prevent the lower ends of the beams OE, OF from spreading. Draw OD vertically equal to (W) inches, then draw DA, DB parallel to OF, OE and a A, b B, parallel to EF, then AD will be

the thrust in O F, and D B in CE, and Aa equal to bB will be the thrust in the direction of the tie beam EF

A

Let A B be a beam whose centre of gravity is, and resting against an upright wall BE, the lower end resting on an abutment cut in the beam A E at A..

O draw

Through the centre of gravity the line CD vertically equal to the weight of the beam, draw B C, D F parallel to EA, join CA; then CF represents the thrust at A in the direction CF, and FD represents the thrust at B, and also the horizontal thrust at A.

To Compute the Tension of the guise' and Shear-leg of a pair of Shears.

Let BC be the shear-leg and AC the guise, and (W) weight in tons supported at C.

To Compute the Tension on the guise arithmetically." Put A Bċ, BC= a, and A C± b.

THE Comparative density of various substances, expressed by the term Specific Gravity, affords the means of readily determining the bulk from the known weight, or the weight from the known bulk; and this will be found more especially useful, in cases where the substance is too large to admit of being weighed, or too irregular in shape to allow of correct measurement. The standard with which all solids and liquids are thus compared, is that of distilled water, one cubic foot of which weighs 1000 ounces avoirdupois; and the specific gravity of a solid body is determined by the difference between its weight in the air and in water. Thus,

If the body be heavier than water, it will displace a quantity of fluid equal to it in bulk, and will lose as much weight on immersion as that of an equal bulk of the fluid. Let it be weighed first, therefore, in the air, and then in water, and its weight in the air be divided by the difference between the two weights, and the quotient will be its specific gravity, that of water being unity. Example. A piece of and 431 ounces in water: required its specific gravity. copper ore weighs 561 ounces in the air,

56.25—43·75 12.5 and 56·25 ÷ 12·5 —= 4·5, the specific gravity. If the body be lighter than water it will float, and displace a quantity of fluid equal to it in weight, the bulk of which will be equal to that only of the part immersed. A heavier substance

must therefore be attached to it, so that the two may sink in the fluid. Then, the weight of the lighter substance in the air must be added to that of the heavier substance in water, and the weight both united, in water, be subtracted from the sum; the weights the lighter body in the air must then be divided by the differen and the quotient will be the specific gravity of the lighter substan required.

а

Example. A piece of fir weighs 40 ounces in the air, and, immersed in water attached to a piece of iron Weighing 30 oune the two together are found to weigh 3.3 ounces in water, and tl iron alone 25.8 ounces in the water: required the specific gravi of the wood.

40 + 25.8 = 65 8 cific gravity of the fir.

3·362·5; and 40 ÷ 62·5 = 0.64, the sp

The specific gravity of a fluid may be determined by taking a solid body, heavy enough to sink in the fluid, and of known specific gravity, and weighing it both in the air and in the fluid. The dif ference between the two weights must be multiplied by the specific gravity of the solid body, and the product divided by the weight of the solid in the air; the quotient will be the specific gravity of the fluid, that of water being unity.

Example. Required the specific gravity of a given mixture of muriatic acid and water, a piece of glass, the specific gravity of which is 3, weighting 32 ounces when immersed in it, and 6 ounces

in the air.

6 — 3·75 = 2·25 × 3 = 675 ÷ 6 — 1·125, the specific gravity, Since the weight of a cubic foot of distilled water, at the tempe rature of 60 degrees (Fahrenheit), has been ascertained to be 1000 avoirdupois ounces, it follows that the specific gravities of all bodies the weight, in ounces,

compared with it, may be by multiplying these specific gravities

of a cubic foot of each,

(compared with that of water as unity) by 1000. Thus, that of water being 1, and that of silver, as compared with it, being 10474, the multiplication of each by 1000 will give 1000 ounces for the cubic foot of water, and 10474 ounces for the cubic foot of silver.

Dog or the weight is at one

Weights of given bulks of water and air for cale the ngr insulutė

weights from the specific gravities of bodies.

Cubic inch of distilled water (bar. 30, therm. 62)

foot

Logarithms,

2.40219

2.99875

62-32106061-79463

30.49

148416

.in ounces avoir. 997 1369691 ..in pounds do.

Weight of 100 cubic in. of air in grains do.

THE simple Mechanical Powers are six in number, viz. the Lever, the Pulley, the Wheel and Axle, the Inclined Plane, the Wedge, and the Screw. All machines are formed by combinations to a greater or less extent of these six elements. The mechanical effects, how. ever, of the whole, are ultimately resolvable into that of the lever. By means of the Mechanical Powers a great weight may be sus tained, or a great resistance slowly overcome, by the application of a small force. Or, a great velocity may be imparted to a small weight or resistance, by the use of a great force or power.

The Lever.

Levers are of three orders: of 1976

In the first order, the fulcrum is between the weight and the power. Idw 0901 vd ons to nitroite,stum song In the second order, the weight is between the fulcrum and the power

In the third order, the power is between the weight and the fulcrum.

The bent lever has no peculiarity except that of form, which is given to it for convenience in use. Its properties are those of the first order. Ansage dond

In order to preserve an equilibrium between the power and the weight, they must be to each other inversely as their distances from the fulcrum. Jodosi A

Case 1. When the Lever is of the first order, or when the fulcrum is between the power and the weight.

RULE Divide the weight to be raised by the power to be applied;