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

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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

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

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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