DIY History | Transcribe | Scholarship at Iowa | Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no.26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903 | Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no. 26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903, Page 6

Theory of the astronomical transit instrument applied to the portable transit instrument Wuerdemann no. 26: a compilation from various authorities, with original observations by Harry Edward Burton, 1903, Page 6

division mark of the vernier counting in the direction in which the circle is graduated coincides with a mark on the circle the circle reading will be r1+n'.
In general, if n divisions of a vernier equal n-1 divisions of the circle, i.e. if ndr = (n-1)dc, we have dr = (n-1/n)dc and dc-dr = ndc-(n-1)dc/n = (1/n)dc.
Whence we have the rule: To find how [finely] we may read an arc by means of the accompanying vernier, divide the least reading of the arc by the number of divisions on the vernier which is equivalent to a number of divisions of the arc.
Sometimes the number of divisions on the vernier is one less than the number of divisions of a corresponding length of arc. In this case we have ndr=(n+1)dc and dr-dc=(n+1/n)dc-dc=dc/n. Whence we have the same rule as before, but in this case, since dr=dc+dc/n, we count the divisions of the vernier in the appropite direction to the way the arc reads

division mark of the vernier counting in the direction in which the circle is graduated coincides with a mark on the circle the circle reading will be r1+n'.
In general, if n divisions of a vernier equal n-1 divisions of the circle, i.e. if ndr = (n-1)dc, we have dr = (n-1/n)dc and dc-dr = ndc-(n-1)dc/n = (1/n)dc.
Whence we have the rule: To find how [finely] we may read an arc by means of the accompanying vernier, divide the least reading of the arc by the number of divisions on the vernier which is equivalent to a number of divisions of the arc.
Sometimes the number of divisions on the vernier is one less than the number of divisions of a corresponding length of arc. In this case we have ndr=(n+1)dc and dr-dc=(n+1/n)dc-dc=dc/n. Whence we have the same rule as before, but in this case, since dr=dc+dc/n, we count the divisions of the vernier in the appropite direction to the way the arc reads