Fig. 2.
fulcrum knife-edge, and X, Y the knife-edges on which the scales are
bung. In order to ensure a high degree of sensitiveness, balances are
sometimes constructed so that Z is slightly below the line joining X
and Y, and is only
slightly above H, the
centre of gravity of the
beam with the scale
pans and chains
attached. The addition
of weights in. the scales
will have the effect of
raising the point H till it gets above Z, and the balance, becoming
unstable, will turn till it is brought up by a stop of some kind.
Fig. 3 represents a precision balance constructed to weigh with great accuracy. The beam is of bronze in a single deep casting, cored out in the middle so as to allow the saddle at the top of the stand to pass through the beam and afford a continuous bearing for the fulcrum knife-edge. The knife-edge and its bearing are both of steel or agate, and the bearing surface is flat. The end knife-edges also are of steel or agate, and have continuous bearing on flat steel or agate surfaces at the upper part of the suspension links. To relieve the knife-edges from wear when the balance is not being used a triangular frame is provided, which is lifted and lowered by a cam action at the bottom, and moves vertically in guides fixed on the stand. By its upward movement the tops of the screw studs near its ends arc first received by the projecting studs on each side of the suspension links, and the suspension links are lifted off the end knife-edges; and next, as the sliding frame continues its upward motion, the horizontal studs at the two ends of the beam are received in the forks at the ends of the sliding frame, and by them the fulcrum of the beam is lifted off its bearing.
 |
| From Airy, "On Weighing Machines," Institution of Civil Engineers, 1892. Fig. 3.—Precision Balance. |
To keep the beam truly in its place, which is very necessary, as all the bearings are flat, the recesses for the ends of the studs are formed so as to draw the beam without strain into its true position every time that it is thrown out of gear by the sliding frame. The end knife-edges are adjusted and tightly jammed into exact position by means of wedge pieces and set screws, and the beam is furnished with delicate adjusting weights at its top. The position of the beam with respect to the horizontal is shown by a horizontal pointer (not shown) projecting from one end of it, which plays past a scale, each division of which corresponds to the 110th or, 1100th of a grain according to the size and delicacy of the machine. A first-class chemical balance would be made in this manner, but in all places where there are acids and gases the knife-edges and bearings must be made of agate, as the fumes attack and corrode steel.
For the weighing of very small quantities with balances of great delicacy, the following method is adopted:—If the balance be in perfect adjustment, and l be the length of each arm, and w a very minute difference of the weights in the two scale-pans, by which the beam is deflected from the horizontal by a very small angle φ, it can easily be shown that tan φ, or φ, varies as w×l. Therefore the angle of deflection which would be produced by grain weight hung at the distance l10 (for example) from the centre is the same as would be produced by 110th of a grain in the scale-pan at the distance l. Therefore by graduating the top of the beam and shifting a rider grain weight till the beam is horizontal, it is easy to ascertain the small difference of weight in the scale-pans which caused the deflection to the 1100th or 11000th part of a grain without using a weight smaller than a grain.
The fitting of the knife-edges is of great importance. In ordinary, trade balances a triangular piece of hard steel, with a finely-ground edge, is driven through a triangular hole in the beam and jammed tight. This forms the knife-edge, and the scale-pans arc hung from the two projecting ends of the piece of steel. Similarly the two projecting ends of the central piece of steel which forms the fulcrum take bearing on two checks of the stand, between which the beam sways. It is clear that errors will arise if the pieces of steel are not truly perpendicular to the plane of the beam, and the adjustment of great accuracy would be very tedious. Therefore for balances of precision the end knife-edges are fixed on the top of the beam so as to present a continuous unbroken knife-edge, and the fulcrum knife-edge is also made continuous, the beam being cored out or cut away to admit of the introduction of the stand bearing. With this arrangement the knife-edges can be easily adjusted and examined, and the system is now rapidly extending to the better class of trade balances.
The knife-edges of weighing machines are the parts that wear out soonest, but very little is known about them experimentally, and the knife-edges made by different makers vary extremely in their angles. Those made by some of the best makers for the most delicate machines are formed to an angle of about 80° between the sides, with the finished edge ground to an angle varying from no" to 120°.
The following may be taken as the maximum loads per in. of acting or efficient knife-edge allowed by the best makers:—
1. For scale-beams of the highest accuracy—From 12 ℔ per in. for a machine of 12 ℔ capacity, to 25 ℔ per in. for a machine of 80 ℔ capacity.
2. For ordinary trade scale-beams, counter machines, and dead weight machines—From 20 ℔ per in. for a machine of 7 ℔ capacity, to 600 ℔ per in. for a machine of 12 ton capacity.
3. For platform machines and weighbridges—From 120 ℔ per in. for a machine of 4 cwt. capacity, to 1 ton per in. for a machine of 25 tons capacity.
The sensitiveness of scale-beams depends entirely upon the skill and care used in their construction. With balances of the highest precision it may be as high as 11000000th of the load weighed, while with trade balances when new it would be about 12000th of the load.
In Emery's testing machine there are no knife-edges, but their function is performed by thin steel plates, which are forced under a very heavy pressure into slots formed in the parts that are to be connected, so that the parts are united by the plate. In this case there is no friction and no sensible wear, so that very great permanency of condition and constancy of action might be expected. But the resistance to bending of the steel plates would render this arrangement unsuitable for scale-beams, in which the movement is large. In some respects it would appear to be very suitable for weighbridges, in which the movement of the lever is very small, but for general convenience of adjustment the knife-edges appear preferable.
In the comparison of standard weights, or in any weighing operations where great accuracy is required, it is necessary to use many precautions. The comparison of standard weights has to be conducted at the standard temperature, and the room must be brought to that temperature and maintained at it. The balance must be enclosed in a glass case to protect it from draughts of air or from the heat of the body of the operator. And the operations of placing and shifting the weights must be effected by mechanism which will enable this to be done without opening the case or exposing the machine.
When the weights which are to be compared are of different metals further complications arise, for the volumes of equal weights of different metals will be different, and therefore the quantity of air displaced by them will be different, and the difference of the weights of air displaced by the two weights must be allowed for. And the weight of air displaced depends upon the density of the air at the time of weighing, and therefore the barometer reading must be taken.
For this correction an exact knowledge of the specific gravities of the metals under comparison is required. In this way an exact comparison of the weights in vacuo can be computed, but of course the simplest way of arriving at the result would be by the construction of a strong air-tight case which can be completely exhausted of air by an air-pump, and in which the weighing can then be effected 'in vacuo. The difficulty about weighing in vacuo is that it is found almost impossible to exhaust the case entirely, or even to maintain a constant degree of exhaustion, by reason of the leakage connected with the weighing operations, and in consequence weighing in vacuo is not much in favour. Whatever method is adopted, very exact weighing is a difficult and troublesome work.
Counter machines have an advantage over scale-beams in not being encumbered with suspension chains and the beam above. They are usually made with two beams, each with its three knife edges, rigidly tied together or cast in one piece and some distance apart, so that the scale-pans being carried on two knife-edges, each is prevented from tipping over sideways. To prevent them from tipping over in the direction of the beams a vertical leg is rigidly fastened to the under side of each pan, the lower end of which is loosely secured by a horizontal stay to a pin in the middle of the frame. In using these machines there is seldom any question of determining the weight to any great nicety, and rapid action is generally of high importance. Hence they are very commonly made unstable, or "accelerating," i.e. they are constructed with the fulcrum knife-edges lower than the line joining the end knife-edges, and they are arranged so that the beam is horizontal when the stop of the weights-pan is hard down on its bearings. This arrangement
