_____________
/
AD = \ / CD(CI - CD) , (2)
\/
[TEX: AD = \sqrt{CD(CI - CD)}]
it suffices to take for CD a suitable value and to calculate AD.
If, for example, the value of C D is represented by C D', the instrument
takes the position A' C B', and the needles will be inserted at A' and
B' on the line A' D' B', which is perpendicular to C I.
10. If the position of the instrument, and consequently that of the
needles, has been established, and we wish to know the distance C I, we
will have
CD
CI = ------------ ; (3)
cos²[alpha]
[TEX: CI = \frac{CD}{\cos^2 \alpha}]
or, again,
___
AC²
CI = ----- (4)
CD'
[TEX: CI = \frac{\overline{AC^2}}{CD'}]
11. In order to avoid all calculation, we may proceed thus: If I wish to
arrange the instrument so that C I represents a given quantity (§ 8),
I take (Fig. 7) the length Ci = CI/n, where n is any entire number
whatever.
[Illustration: Fig. 7.]
In other terms, Ci is the reduction to the scale of CI.
I describe the circumference C b i a, and arrange the instrument as seen
in the figure, and measure the length C b.