The following combination is used where a great pressure is to be exerted through a very small distance:

The Elbow-joint Press.

80. Let CA, BD, and DE represent bars, with hingejoints at B and D. The bar CA, has a fulcrum at C, and the bar DE works through a guide between D and E. When A is depressed, DE is forced against the upright F, so as to compress, with great

B

D

C

Fig. 67.

force, any body placed between E and F. This machine is called the elbow-joint press, and is used in printing, in moulding bullets, in striking coins and medals, in punching holes, riveting steam boilers, &c.

Let P denote the force applied at 4, perpendicular to AC, Q the resistance in the direction DB, and R the component of Q, in the direction ED. Let C be taken as an axis of moments, and then, because P and Q are in equilibrium, we shall have,

P× AC = Q × FC, or, Q

AC

=

P×

FC

If we draw BH perpendicular to DR, we shall have,

When B is depressed, DH and DB approach equality, and FC continually diminishes; that is, the mechanical advantage increases, and finally, when B reaches ER, it becomes infinite. There is no limit to the pressure exerted at F, except that fixed by the strength of the machine.

The Balance.

81. A BALANCE is a machine for weighing bodies: it

B

consists of a lever AB, called the beam, a knife-edge fulcrum F, and two scale-pans D and E, suspended by knife-edges from the extremities of the lever arms FB and FA. These arms should be symmetrical, and of equal length; the knifeedges A, B, and F, should all lie in the same plane, and be perpendicular to a plane through their middle points and the centre of gravity of the beam; they are, therefore, parallel to each other. This condition of parallelism in the same plane, is of essential importance.

E

D

Fig. 68.

In addition to this, the middle points of the knife-edges A, B, and F, should be on the same straight line, perpendicular to the plane through the fulcrum F, and the centre of gravity of the beam. The knife-edges should be of hardened steel, and their supports should either be of polished agate, or, what is still better, of hardened steel, so as to diminish the effect of friction along the lines of contact. The fulcrum may be made horizontal, by leveling-screws passing through the foot-plate L. A needle N, projects upwards, or sometimes downwards, which, playing in front of a graduated arc GH, serves to show the deflection of the line of knifeedges from the horizontal. When the instrument is not in use, the fulcrum may be raised from its bearings by a pinion K, working into a rack in the interior of the standard FK. The knife-edges A and B may, by a similar arrangement, be raised from their bearings also.

The ordinary balances of the shops are similar in their general plan; but many of the preceding arrangements are omitted. The scale-pans being exactly alike, the balance. should remain in equilibrium, with the line AB horizontal, not only when the balance is without a load, but also when the pans are loaded with equal weights; and when AB is

deflected from the horizontal, it should return to this position. This result is attained by throwing the centre of gravity slightly below the line AB. To test a balance, let two weights be placed in the pans that will exactly counterbalance each other, then change the weights to the opposite pans; if the equilibrium is still maintained, the balance is said to be truc.

The sensibility of a balance is its capability of indicating small differences of weight. The sensibility will be greater, as the lengths of the arms increase, as the centre of gravity of the beam approaches the fulcrum, as the mass of the load decreases, and as the length of the needle increases. The centre of gravity of the beam being below the fulcrum, it may be made to approach to or recede from it, by a solid ball of metal attached to the beam by means of a screw, by which it may be raised or depressed at pleasure. The remaining conditions of sensibility will be limited by the strength of the material, and the use to which it is to be applied.

Should it be found that a balance is not true, it may still be employed, with but slight error, as indicated below.

Denote the length of the lever arms, by r and r', and the weight of the body, by W. When the weight W is applied at the extremity of the arm r, denote the counterpoising weights employed, by W'; and when it is applied at the extremity of the arm r', denote the counterpoising weights employed, by W". We shall have, from the principle of the lever,

Multiplying these equations, member by member, we have,

that is, the true weight is equal to the square root of the product of the apparent weights.

A still better method, and one that is more free from the effects of errors in construction, is to place the body to be

weighed in one scale and add counterpoising weights till the beam is horizontal; then remove the body to be weighed and replace it by known weights till the beam is again horizontal; the sum of the replacing weights will be the weight required. If, in changing the loads, the positions of the knife-edges are not moved, this method is almost exact, but this is a condition difficult to fulfill in manipulation.

The Steelyard.

82. The steelyard is an instrument used for weighing bodies. It consists of a lever AB, called the beam; a fulcrum F; a scale-pan D, attached at the extremity of one arm; and a known weight E, movable along the other arm. We shall suppose the weight of E to be 1 lb. This instrument is sometimes more conve

Fig. 69.

20

30

The con

nient than the balance, but it is more inaccurate. ditions of sensibility are essentially the same as for the balance. To graduate the instrument, place a pound-weight in the pan D, and move the counterpoise E till the beam rests horizontal-let that point be marked 1; next place a 10 lb. weight in the pan, and move the counterpoise E till the beam is again horizontal, and let that point be marked 10; divide the intermediate space into nine equal parts, and mark the points of division as shown in the figure. These spaces may be subdivided at pleasure, and the scale extended to any desirable limits. We have supposed that the centre of gravity coincides with the fulcrum; when this is not the case, the weight of the instrument must be taken into account as a force applied at its centre of gravity. We may then graduate the beam by experiment, or we may compute the lever arms, corresponding to the different weights, by the general principle of moments.

To weigh any body with the steelyard, place it in the scale-pan and move the counterpoise E along the beam till

an equilibrium is established between the two; the responding mark on the beam will indicate the weight.

cor

The bent Lever Balance.

83. This balance consists of a bent lever ACB; a fulcrum C; a scale-pan

D; and a graduated arc

EF, whose centre COincides with the centre of motion C. When a weight is placed in the scale-pan, the pan is depressed and the leverarm of the weight is

Ex

Fig. 70.

diminished; the weight B is raised, and its lever-arm increased. When the moments of the two forces become equal, the instrument will come to a state of rest, and the weight will be indicated by a needle projecting from B, and playing in front of the arc FE. The zero of the arc EF is at the point indicated by the needle when there is no load in the pan D.

The instrument may be graduated experimentally by placing weights of 1, 2, 3, &c., pounds in the pan, and marking the points at which the needle comes to rest, or it may be graduated by means of the general principle of moments. We need not explain this method of graduation.

To weigh a body with the bent lever balance, place it in the scale-pan, and note the point at which the needle comes to rest; the reading will make known the weight sought.

Compound Balances.

84. Compound balances are much used in weighing heavy articles, as merchandise, coal, freight for shipping, &c. A great variety of combinations have been employed, one of which is annexed.

AB is a platform, on which the object to be weighed is