Question

Two distance of 20 and 100m were accurately measured out and the intercepts on the staff between the outer stadia were 0.196m at the former distance and 0.996 at later. Calculate the Tacheometric Constant.​

Answer 1

Answer:

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Answer 2

Answer:

The Tacheometric Constant is 0.4.

Explanation:

Given: Distances $20$ and $100$ metres

Staff intercept $\left(\mathrm{S}_{1}\right)=0.196 \mathrm{~m}$

Staff intercept $\left(\mathrm{S}_{2}\right)=0.996 \mathrm{~m}$

We have to calculate the Tacheometric Constant.​

The constant $k = f/i$ is called the multiplying constant or stadia interval factor and the constant $(f + d) =C$ is known as the additive constant of the tacheometer but the latter one is made zero by using an analytic lens in the instrument.

$D_{1}=K S_{1}+C, \quad D_{2}=K S_{2}+C\\100=\mathrm{K} \times 0.996+\mathrm{C},\quad...(1)\\20=\mathrm{K} \times 0.196+\mathrm{C}\quad...(2)$

Subtracting Eq (1) from Eq (2):

$100-20=(0.996-0.196)K\\ 80=K \times 0.8$

$\mathrm{K}=\frac{80}{0.8}=100 \\ 100=\mathrm{K} \times 0.996+\mathrm{C} \\ \mathrm{C}=100-100 \times 0.996=0.4$

Therefore, the Tacheometric Constant is 0.4.