PIERRE VERNIER (c. 1580–1637), inventor of the instrument which bears his name, was born at Ornans (near Besancon) in Burgundy about 1580. He was for a considerable time commandant of the castle in his native town. In 1631 he published at Brussels a treatise entitled Construction, usage et proprietes du quadrant nouveau de mathematiques, in which
the instrument associated with his name is described. He died at Ornans in 1637.
The instrument invented by Vernier is frequently called a nonius, particularly in Germany, after Pedro Nunez (1492–1577), professor of mathematics at the university of Coimbra; but this is incorrect, as the contrivance described by the latter in his work De crepusculis (1542) is a different one, although the principle is practically the same. Nunez 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, which was divided into 90 parts, the number of degrees in a quadrant, 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 halfdegrees a movable sector of a length equal to 31 halfdegrees, 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. The idea had been mentioned by Christopher Clavius (1537–1612) in his Opera malhematica, 1612 (ii. 5 and iii. to), 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.
The principle of the vernier is readily understood from the following account: Let AB (see fig.) be the normal scale, i.e. a scale graduated according to a standard of length, CD, a scale (placed in contact with AB for convenience) graduated so that to divisions equal 11 divisions of the scale AB, and EF a scale placed similarly and graduated so that to divisions equal 9 divisions of the scale AB. Consider the combination AB and CD. Obviously each division
C1 D a
7 8 O 9 10
1 I I I
a
9 2 OIL
E F
of CD is th greater than the normal scale division. Let a represent a length to be measured, placed so that one end is at the zero of the normal scale, and the other end in contact with the end of the vernier CD marked to. It is noted that graduation 4 of the vernier coincides with a division of the standard, and the determination of the excess of a over 3 scale divisions reduces to the difference of 7 divisions of the normal scale and 6 divisions of the vernier. This is .4, since each vernier division equals 1.1 scale division. Hence the scale reading of the vernier which coincides with a graduation of the normal scale gives the decimal to be added to the normal scale reading. Now consider thq scales AB and EF, and let $ be the length to be measured; the scale EF being placed so that the zero end is in contact with an end of $. Obviously each division of EF is ,15th less than that of the normal scale. It is seen that division 6 of the vernier coincides with a normal scale division, and obviously the excess of fl over two normal scale divisions equals the difference between 6 normal scale divisions and 6 vernier divisions, i.e. 0.6. Thus again in this case the vernier reading which coincides with a scale reading gives the decimal to be added to the normal scale. The second type of vernier is that more commonly adopted, and its application to special appliances is quite simple. For example, the normal scale to an English barometer is graduated in TSths of an inch. The vernier is such that 24 divisions of the normal scale equal 25 of the vernier; each of the latter therefore is •002 or• .azth inch less than the normal division. In the scientific barometer, the normal scale is graduated in millimetres, and the vernier so that 20 scale divisions equal 19 mm. This combination reads to 0.05 mm.
End of Article: PIERRE VERNIER (c. 1580–1637) 

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