The instrument invented by Vernier is frequently called a nonius; but this is incorrect, as the contrivance described by Pedro Nuñez in his work De crepusculis (1542) is a different one. Nuñez drew on the plane of a quadrant 44 concentric arcs divided respectively into 89,88, . . . 46 equal parts; and, if the alidade did not coincide with one of the divisions on the principal arc, it would fall more or less accurately on a division line of one of the auxiliary arcs, from which the value of the measured angle could be made out. This instrument was, however, very difficult to make, and was but little used. Vernier proposed to attach to a quadrant divided into half degrees a movable sector of a length equal to 31 half degrees, but divided into 30 equal parts, whereby single minutes could be read off by seeing which division line of the “sector” coincided with a division line of the quadrant. This movable arc was in (n +1)/ n other words divided into —parts, and the divisions were graduated in the direction opposite to that of the graduation of the principal arc. It is now usual to divide it into parts, the two graduations going in the same direction. The idea had been mentioned by Christopher Clavius (1537-1612) in his Opera mathematica, 1612 (vol. ii. p. 5 and iii. p. 10), but he did not propose to attach permanently an arc divided in this way to the alidade; this happy application of the principle at all events belongs to Vernier.