Let's solve the problem step by step: --- ## **Step 1: Interpret the Data** - **BM A (initial elevation):** 687.68 ft - **Back Sight (B.S.):** Reading taken on a point of known elevation (add to get H.I.) - **Fore Sight (F.S.):** Reading taken on a point of unknown elevation (subtract from H.I. to get new elevation) - We move from BM A through points 1 to 8, then back to BM A. --- ## **Step 2: Calculate Elevations** We'll use the **Rise and Fall Method**: \[ \text{New Elevation} = \text{Previous Elevation} + \text{B.S.} - \text{F.S.} \] Let's tabulate the calculations: | Points | B.S. | F.S. | Elevation (ft) | Calculation | |---------|-------|-------|----------------|------------------------------------------| | BM A | 3.33 | | 687.68 | Given | | 1 | 4.20 | 3.45 | 687.68 + 3.33 - 3.45 = 687.56 | 687.68 + 3.33 - 3.45 = **687.56** | | 2 | 4.23 | 4.85 | 687.56 + 4.20 - 4.85 = 686.91 | 687.56 + 4.20 - 4.85 = **686.91** | | 3 | 5.55 | 5.45 | 686.91 + 4.23 - 5.45 = 685.69 | 686.91 + 4.23 - 5.45 = **685.69** | | 4 | 6.18 | 4.87 | 685.69 + 5.55 - 4.87 = 686.37 | 685.69 + 5.55 - 4.87 = **686.37** | | 5 | 4.32 | 6.64 | 686.37 + 6.18 - 6.64 = 685.91 | 686.37 + 6.18 - 6.64 = **685.91** | | 6 | 5.58 | 3.97 | 685.91 + 4.32 - 3.97 = 686.26 | 685.91 + 4.32 - 3.97 = **686.26** | | 7 | 4.43 | 5.54 | 686.26 + 5.58 - 5.54 = 686.30 | 686.26 + 5.58 - 5.54 = **686.30** | | 8 | 5.35 | 3.85 | 686.30 + 4.43 - 3.85 = 686.88 | 686.30 + 4.43 - 3.85 = **686.88** | | BM A | | 5.12 | 686.88 + 5.35 - 5.12 = 687.11 | 686.88 + 5.35 - 5.12 = **687.11** | --- ### **Corrected Table** Let's recalculate using the correct formula at each step: - **At each point:** Elevation = Previous Elevation + B.S. - F.S. #### **Tabulated Calculations** | Station | B.S. | F.S. | Elevation (ft) | Explanation | |---------|-------|-------|----------------|--------------------------------| | BM A | 3.33 | | 687.68 | Given | | 1 | 4.20 | 3.45 | 687.68 + 3.33 - 3.45 = 687.56 | | 2 | 4.23 | 4.85 | 687.56 + 4.20 - 4.85 = 686.91 | | 3 | 5.55 | 5.45 | 686.91 + 4.23 - 5.45 = 685.69 | | 4 | 6.18 | 4.87 | 685.69 + 5.55 - 4.87 = 686.37 | | 5 | 4.32 | 6.64 | 686.37 + 6.18 - 6.64 = 685.91 | | 6 | 5.58 | 3.97 | 685.91 + 4.32 - 3.97 = 686.26 | | 7 | 4.43 | 5.54 | 686.26 + 5.58 - 5.54 = 686.30 | | 8 | 5.35 | 3.85 | 686.30 + 4.43 - 3.85 = 686.88 | | BM A | | 5.12 | 686.88 + 5.35 - 5.12 = 687.11 | --- ## **Step 3: Calculate Loop Misclosure** \[ \text{Loop Misclosure} = \text{Final Elevation of BM A} - \text{Known Elevation of BM A} \] \[ = 687.11 - 687.68 = -.57 \text{ ft} \] --- ## **Step 4: Permissible Error** Permissible error is generally: \[ \text{Permissible Error} = \pm .02 \sqrt{n} \] Where \( n \) is the number of instrument setups (number of B.S. or F.S., not including the initial B.S.). Here, n = 9 (since there are 9 B.S./F.S. readings, not counting the initial BM A). \[ \text{Permissible Error} = .02 \times \sqrt{9} = .02 \times 3 = .06 \text{ ft} \] --- ## **Step 5: Is the Misclosure Acceptable?** \[ |\text{Loop Misclosure}| = |{-.57}| = .57 \text{ ft} \] \[ \text{Permissible Error} = .06 \text{ ft} \] - **.57 ft > .06 ft** - **The misclosure exceeds the permissible error.** --- ## **Step 6: Final Answers (Tabulated Form)** | Step | Value | |---------------------|--------------| | Loop Misclosure | -.570 ft | | Permissible Error | ±.060 ft | | Acceptable? | **No** | --- ### **Conclusion** - **Loop Misclosure = -.570 ft** - **Permissible Error = ±.060 ft** - **Is the misclosure acceptable?** **No**, the misclosure is not acceptable because it exceeds the permissible error. --- **If you need the full tabulated elevations with two decimal places, let me know!**