NONIUS

A name frequently given to that useful contrivance, the vernier, for subdividing the divisions of graduated arcs or scales into minute parts, from its invention having been erroneously ascribed to Pedro Nunez, or Nonius, a Portuguese, who lived in the early part of the 16th century. The contrivance employed by Nonius was widely different from the vernier now universally used. It consisted in describing within the same quadrant 45 concentric arcs, dividing the outermost into 90 equal parts, the next into 89, the next into 88, and so on, the innermost being consequently divided into 46 only. With this instrument the observed altitude of an object could be read off on the outermost arc only to degrees, but the fractions were obtained in the following manner: — The plumb-line, or moveable index, must intersect one of the concentric arcs at, or very near, a point of division. Now, it is evident that the number of parts read off at this point must be in the same proportion to the degrees and fractions of a degree intercepted on the outermost arc, as the number of parts into which the arc containing the point is divided, is to 90°. The division read off being therefore multiplied by 90, and divided by the number of parts in the arc, gives the observed altitude to fractions of a degree. Thus, if the plumb-line intercept 25 parts exactly on the arc in which the number of parts is 78, the angle measured will be 28-840°: the fraction is easily converted into minutes and seconds. Nonius supposed that this artifice was known to Ptolemy. It was adopted by Tycho Brahe; but soon abandoned by him for the method of diagonal divisions, in consequence of the difficulty of dividing accurately the different arcs. {Bobins's Mathematical Tracts, \ol.n.) See Vernier. [s. 841]