Level book: profile levelling readings

Arranging the readings. The instrument was changed after the 3rd, 7th and 9th readings, so there are four set-ups:

• Set-up 1: 0.320 (BS), 0.530 (IS), 0.620 (FS on CP1, which is the 3rd point).
• Set-up 2: 1.780 (BS on CP1), 1.910 and 2.350 (IS), 1.750 (FS on CP2).
• Set-up 3: 0.350 (BS on CP2), 0.690 (FS on CP3).
• Set-up 4: 1.240 (BS on CP3), $-0.980$ (FS on the last point; the negative reading means the staff was held inverted, so the point is above the line of sight).

The 11 readings are on 8 points (the FS and the next BS at a change point are on the same point). The RL of the 3rd point (CP1) is 1300.250 m, so the HI of set-up 1 is $1300.250 + 0.620 = 1300.870$ m and the RLs of points 1 and 2 are found from it.

Level field book (height of instrument method)

Arithmetic check

$\Sigma BS - \Sigma FS = 3.690 - (2.080) = 1.610$ ; last RL $-$ first RL $= 1302.160 - 1300.550 = 1.610$. Both are equal, so the reduction is correct.

Gradient between the first and last point

The 8 points are 20 m apart, so the distance between the first and the last point $= 7 \times 20 = 140$ m.

$$\text{Difference of level} = 1302.160 - 1300.550 = +1.610\ \text{m} \quad (\text{a rise})$$ $$\text{Gradient} = \frac{1.610}{140} = \frac{1}{87.0}\ \text{(rising from the first to the last point)}$$

Answer: RLs of points 1 to 8 = 1300.550, 1300.340, 1300.250, 1300.120, 1299.680, 1300.280, 1299.940, 1302.160 m; the line rises from the first to the last point at a gradient of about 1 in 87.