is well adapted for weighing out parcels of goods of a definite weight, though not for ascertaining the correct weight of a given article. For the latter purpose machines are used of which the beams are made stable, or "vibrating," by constructing them with the fulcrum knife-edges above the line joining the end knife-edges.
“Accelerating” machines can be used to the advantage of the
vendor in two ways. Firstly, in using them to determine the weight
Fig. 4.
of a given article. For with unstable balances, although the smallest
excess of weight in the goods-pan will cause it to descend till it is
brought up by its stop, yet being in this position, a very much greater
weight than the difference which brought it there will be required
in the weights-pan to enable it to mount again. If W be the weight
in each pan when the goods-pan commenced to sink, l the length of
each arm, m the distance of the fulcrum below the line joining the
end knife-edges, and β the angle at the fulcrum which defines the
range of sway of the beam, it can easily be shown that w, the additional
weight required in the weights-pan to enable the goods-pan
to rise from its stop, is given by the equation u =
W 2m tan β/L − m tan β.
So that if, for example, a fishmonger uses such a machine
to ascertain the weight of a piece of fish which he places in the goods-pan,
and thereby depresses it down upon its stop, and then places
weights in the weights-pan till the goods-pan rises, the customer is
charged for more than the real weight of the fish. Secondly, in using
them out of level, with the goods end of the machine lower than the
weights end. If θ be the angle of tilt of the machine, and the other
symbols be as before, it may be shown that the additional weight, w
Fig. 5.
which is needed in the weights-pan to enable the goods-pan to rise
off its stop, is given by the equation w =
W 2m tan (β−θ)/L − m tan
(β−θ).
When θ is negative, as it is when the goods end of the
machine is lower than the weights end, the value of w may be very
appreciable. With "vibrating" machines the value of m is in general
so extremely small that w is of no practical importance in either of
the above cases.
If a counter machine be made with a large flat goods-pan, as in fig. 4, an error may be caused by placing the goods eccentrically on the pan, as at D or E. Using the symbols of the diagram, it can be shown that the effect of placing the weight W at E instead of F is to cause the end of the beam to descend, as if under the action of an additional weight, w, at F such that
w＝Wα(ml −1 + tan θ)/h.
The condition that must exist in order that the balance may weigh correctly for all positions of the weight W is u = α, or tan θ = −ml −1; that is, the stay KG must be adjusted parallel to the line joining the points A and C. From the equation for w, it is seen that the larger h is the smaller w will be. Therefore for the larger counter machines, where it is not convenient to have the scale-pans raised high above the counter, and for "dead-weight" machines on the same principle, where it is not convenient to have the scale-pans raised high above the floor, there is an advantage in adopting the "inverted counter machine" arrangement (fig. 5), because the vertical leg can be produced upwards as high as is required. This arrangement is very common. As will be readily understood from the construction of the machines, there is more friction in counter machines than in scale-beams. The "sensitiveness" error allowed by the Board of Trade for counter machines is five times as great as that allowed for scale-beams.
The torsion balance made by the United States Torsion Balance
and Scale Company of New York is a counter machine made with
out knife-edges, and is very sensitive. It is constructed with two
similar beams, one above the other, which arc coupled together
at the ends to form a parallel motion for carrying the pans upright.
Fig. 6.
The coupling is effected by firmly clamping the ends of the
beams upon the top and bottom respectively of a loop of watch spring,
which is tightly stretched round the casting carrying the pan,
as is shown in the end view in fig. 6. At their middles the beams are
similarly clamped upon the top and
bottom of a loop of watch-spring
which is tightly stretched round a
casting which is bolted upon the
bed-plate. When the case which
holds the machine is adjusted horizontally
by means of its foot-screws,
and the weights in the
pans are equal, the beams remain
perfectly horizontal; but with the
slightest difference of weight in the
pans the beams are tilted, and the
elastic resistance of the springs to
torsion allows the beams to take
up a definite position of equilibrium.
The lower beam carries on
a saddle a scale which is raised
nearly to the top of the glass case
in which the machine is enclosed, and as the beams sway this scale
plays past a scratch on the glass, which is so placed that when
the zero point on the scale coincides with the scratch the beams
are horizontal. With proper care this machine should be very permanent
in its action.
Unequal-armed Balances.
Steelyards are simple, trustworthy and durable, but unless special contrivances are introduced for ascertaining the position of the travelling poise with very great accuracy there will be a little uncertainty as to the reading, and therefore steelyards are not in general so accurate as scale-beams. When carefully nicked they are well-adapted for weighing out definite quantities of goods, such as 1 ℔, 2 ℔, &c., as in such cases there is no question of estimation. The ordinary way of using a steelyard is to bring it into a horizontal position by means of movable weights, and to infer the amount of the load from the positions of these. But it is sometimes convenient to use a fixed weight on the long arm, and to infer the amount of the load from the position of the steelyard. The rule for graduation is very simple. The simplest form is that which has a single travelling poise. The more elaborate ones are made either with a heavy travelling poise to measure the bulk of the load with a light traveling poise for the remainder, or else with a knife-edge at the end of the steelyard, on which loose weights are hung to measure the bulk of the load, the remainder being measured with a light travelling poise. The advantage of the first arrangement is that the weights on the steelyard are always the same, and inconsistencies of indication arc avoided, while in the second arrangement the loose weights are lighter and handier, though they must be very accurate and consistent among themselves, or the error will be considerable, by reason of the great leverage they exert.
Steelyards, like other weighing machines, will be "accelerating," or "vibrating" according to the arrangement of the knife-edges.
