# 1911 Encyclopædia Britannica/Vernier, Pierre

in contact with AB for convenience) graduated so that 10 divisions equal 11 divisions of the scale AB, and EF a scale placed similarly and graduated so that 10 divisions equal 9 divisions of the scale AB. Consider the combination AB and CD. Obviously each division of CD is ${\displaystyle {\tfrac {1}{16}}}$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 10. 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 i-i 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 the, scales AB and EF, and let /S be the length to be measured; the scale EF being placed so that the zero end is in contact with an end of 0. Obviously each division of EF is ${\displaystyle {\tfrac {1}{16}}}$th 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 β 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 ${\displaystyle {\tfrac {1}{25}}}$ths 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 ${\displaystyle {\tfrac {1}{500}}}$ fostfi 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.