whence

CI
CD = ------------------ or CD = CI cos squared[alpha]. (1)
I + tang squared[alpha]

[TEX: CD = \frac{CI}{I + \tan^2 \alpha}\ \text{or}\ CD = CI \cos^2
\alpha.]

9. If the instrument is jointed, the absolute values being

_____________
/
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