# Roberval balance

This sketch shows a Roberval balance with balanced masses. Note that the masses don't need to be centered on the plates.
Old Roberval balance
Roberval balance made by W & T Avery Ltd. in England
Another example: note that the bottom horizontal beam is hidden under the protective cover

The Roberval balance is a weighing scale presented to the French Academy of Sciences by the French mathematician Gilles Personne de Roberval in 1669.

In this scale, two identical horizontal beams are attached, one directly above the other, to a vertical column, which is attached to a stable base. On each side, both horizontal beams are attached to a vertical beam. The six attachment points are pivots. Two horizontal plates, suitable for placing objects to be weighed, are fixed to the top of the two vertical beams. An arrow on the lower horizontal beam (and perpendicular to it) and a mark on the vertical column may be added to aid in leveling the scale.

The object to be weighed is placed on one plate, and calibrated masses are added to and subtracted from the other plate until level is reached. The mass of the object is equal to the mass of the calibrated masses - regardless of where on the plates items are placed. Since the vertical beams are always exactly vertical, and the weighing platforms always horizontal, the potential energy lost by a weight as its platform goes down a certain distance will always be the same, so it makes no difference where you put the weight.

The vertical column supporting a plate with an offset weight must be in axial compression and flexure. Here the axial compression is carried by the bearing at the top beam in most balance scales, the lower beam just being supported horizontally at midpoint by the body of the scales by a simple peg-in-slot arrangement, so it effectively hangs beneith the top beam and stops the platforms from rotating. The flexural force in the column (a.k.a. bending moment) is taken by a pair of equal and opposite forces in the horizontal beams. So if the offset weight is towards the outside of the platform, further from the centre of the scales, the top beam will be in axial tension and the bottom beam will be in axial compression. These tensions and compressions are carried by horizontal reactions from the central supports, the other side of the scales is not affected at all, and nor is the balance of the scales.

The Roberval balance is arguably less accurate and more difficult to manufacture than a beam balance with suspended plates. The suspended-mass balance, however, has the disadvantages of having strings in the way of the user and needing to be suspended. The Roberval balance, therefore, has, for over three hundred years, been very popular for applications where convenience and moderate accuracy are required, notably in retail trade.

Some notable manufacturers of Roberval balances are W & T Avery Ltd. and George Salter & Co. Ltd. in the United Kingdom and Trayvou in France. Henry Troemner, who designed scales for the United States Department of Treasury, was the first American to use the design.[1]

## Notes

1. ^ Child, Ernest. The Tools of the Chemist. New York: Reinhold Publishing Corporation (1940), p. 88. Cited in John Meeks Shannon and Geraldine Collins Shannon, "The Henry Troemner Company." Robert A. Paselk Scientific Instrument Museum at Humboldt State University.

## Bibliography

• J. T. Graham, Scales and Balances, Shire Publications, Aylesbury (1981) ISBN 0-85263-547-8
• Bruno Kisch, Scales and Weights. A Historical Outline, Yale University Press, New Haven (1966) ISBN 0-300-00630-6