Transversal (instrument making)

Transversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Transversals have been replaced in modern times by vernier scales. This method is based on the first Theorem of Tales.

Transversals were used at a time when finely graduated instruments were difficult to make. They were found on instruments starting in the early 14th century, but the inventor is unknown, but in 1342 Levi Ben Gerson introduced an instrument called Jacob's staff (apparently invented the previous century by Jacob Ben Makir) and described the method of the transversal scale applied to the mentioned instrument.

Thomas Digges mistakenly attributed the discovery of the transversal scale to the navigator and explorer Richard Chancellor (cited by some authors as watchmaker and with other names, among them: Richard Chansler or Richard Kantzler). Its use on astronomical instruments only began in the late 16th century. Tycho Brahe used them and did much to popularize the technique. The technique began to die out once verniers became common in the late 18th century – over a century after Pierre Vernier introduced the technique.

In the interim between transversals and the vernier scale, the nonius system, developed by Pedro Nunes, was used. However, it was never in common use. Tycho also used nonius methods, but he appears to be the only prominent astronomer to do so.

Linear transversals were used on linear graduations. A grid of lines was constructed immediately adjacent to the linear graduations. The lines extending above the graduations formed part of the grid. The number of lines perpendicular to the extended graduation lines in the grid was dependent on the degree of fineness the instrument maker wished to provide.

A grid of five lines would permit determination of the measure to one-fifth of a graduation's division. A ten-line grid would permit tenths to be measured. The distance between the lines is not critical as long as the distance is precisely uniform. Greater distances makes for greater accuracy.

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