Weighing scale
The balance (also balance scale, beam balance and laboratory balance) was the first mass measuring instrument invented. In its traditional form, it consists of a pivoted horizontal lever with arms of equal lengththe beamand a weighing pan suspended from each arm (hence the plural name ""scales" for a weighing instrument). The unknown mass is placed in one pan and standard masses are added to the other pan until the beam is as close to equilibrium as possible. In precision balances, a more accurate determination of the mass is given by the position of a sliding mass moved along a graduated scale. Technically, a balance compares weight rather than mass, but, in a given gravitational field (such as Earth's gravity), the weight of an object is proportional to its mass, so the standard masses used with balances are usually labeled in units of mass (e.g. g or kg).
Dialing scales
Dialing scales were first discussed by Samuel Foster in 1638. P. Pierre Bobynet, a Jesuit drew a scale in his book "L'horographie ingenieuse contenant des Connoissances, & Curiositez Agréables dans la composition des Cadrans", in 1647. It was however George Serles 1657 book, "Dialling Universal", printed by R & W Leybourn that brought them to popular attention. These scales remained virtually unchanged for 250 years. E. C. Middleton, who had been engraving dialling scales from about 1895, supplied dialling scales accompanied by a typewritten instruction book from Birmingham in 1913– these were the scales calculated by Serle. The North American Sundial Society has printed facsimiles of both the Serle and Middleton books.
The Middleton dial appeared without explanation in the 1994 "Encyclopedia de Diderot et Alembert" (French). Further work has done on these rulers by F.W. Cousins, and by Fred W Sawyer from 1997–2009.