Stadia interval factor, additive constant

Stadia interval factor and additive constant

• Stadia interval factor (multiplying constant) $K$: the ratio $f/i$ of the focal length of the objective to the stadia hair interval. It is the number by which the staff intercept is multiplied to get the distance, usually 100.
• Additive constant $C$: the distance $(f+d)$ from the instrument's vertical axis to the objective's focus, in metres. About 0.3 m for an external focusing telescope, nearly zero for an internal focusing one, and exactly zero for an anallatic lens.

Distance: $D=Ks+C$.

Determination of the constants (field method)

1. On level ground, set up the instrument on a line and measure out several distances from it, say 50, 100, 150 and 200 m, with a tape. Mark with pegs.
2. Hold the staff vertical at each peg and read the stadia hairs. Compute the intercepts $s_1,s_2,\dots$ with the line of sight horizontal.
3. Write $D=Ks+C$ for two pegs and solve:

$$K=\frac{D_2-D_1}{s_2-s_1},\qquad C=D_1-Ks_1$$

4. Calculate $K$ and $C$ for several pairs and take the mean values, or fit by least squares from all readings.

Example: $D_1=50$ m, $s_1=0.497$ m; $D_2=150$ m, $s_2=1.497$ m give $K=100/1.000=100.0$, $C=50-49.7=0.30$ m.