STANDARD - Survey Instrument Antique Center!

35
To express the relation between the vernier and circle divisions, let d=the rn tu
of one division of the circle; d'=the value of one division of the vernier; d-d'=
the least count of the vernier, or, in other words, the smallest reading of the circle.
n= the number of spaces of the vernier which correspond to (n 1) spaces of
the circle.
We then have the three formulas ;
(1.)
(20
(3.) d d'=
Thug, for example, suppose the circle was divided to 15', and it was desired to
read to 20". Here,d=15'
d d', or, the least count:
Then, by formula (1)
n =45
Therefore, 45 spaces of the vernier must correspond to 44 or(n-l) spaces of the
circle.
Suppose again the arc to be divided to 2CK, and to be read to 30". In this case
we have
Therefore, 40 spaces of the vernier must correspond to 39, or (n 1) spaces of
the circle. These are the graduations which Messrs. C. L. Berger & Sons usually
adopt for engineers' transits.
2.2.0
The cut fihows a portion of the circle and vernier, to illustrate the method of
reading to thirty seconds.
The lines marked 130, 140, and 150 denote 10 each. The shorter lines half way
between them denote 135 and 145. The next shorter lines denote whole degrees,
while the shortest lines are one-third of a degree, or 20 /
apart.
The vernier comprises the upper series of lines. Of this series only that half
lying to the right of the vertical arrow, or zero, and having the figures 10 and 20
inclined in the same direction as the 130, 140, and 150 of the arc, is to be used in
connection with these figures. The vernier is double, one half to be used with
one set of graduations of the arc, the other half to be used when angles are laid off
in the opposite direction, and then the lower set offigured, 210, 220, and 230 are used.
It is to be especially remembered that the figures on the vernier are inclined in
the same direction as the figures on the arc to which they belong.
To read the vernier, first note the whole degrees, and 20 7
spaces lying between
the last 10 degree division and the zero division of the vernier.
Thus in the cut, using the upper line of figures, the zero of the vernier has passed