**Triangulation Survey**

Triangulation survey is a technique used in surveying to determine the relative positions of points on the Earth's surface. It involves measuring the angles between selected points and using trigonometry to calculate the distances and positions of other points. One important aspect of triangulation survey is the intervisibility of stations, which refers to the ability to see one station from another.

**Methods for Checking Intervisibility**

There are several methods that can be used to check the intervisibility of stations in a triangulation survey. These methods include:

1. **Method of Least Squares:** The method of least squares is a statistical technique used to determine the best fit of a mathematical model to a set of observed data. In the context of triangulation survey, this method can be used to adjust the measured angles between stations and calculate the most probable positions of the stations. By analyzing the adjusted positions, it is possible to identify stations that are not intervisible due to obstructions such as hills or buildings.

2. **Heliotropes:** Heliotropes are instruments that use mirrors to reflect sunlight in a specific direction. In a triangulation survey, heliotropes can be used to establish a line of sight between stations. By having an observer at one station and reflecting sunlight towards another station, it is possible to determine if the second station is visible from the first. If the sunlight is reflected back to the observer, it indicates that the two stations have intervisibility.

3. **Captain G.T. McCaw's Solution:** Captain G.T. McCaw's solution is a method proposed by Captain G.T. McCaw for checking intervisibility in triangulation surveys. This method involves using a theodolite to measure the angles between stations and then calculating the distances and positions of the stations using trigonometry. By analyzing the calculated positions, it is possible to determine if the stations have intervisibility.

4. **Three-Point Problem:** The three-point problem is a method used to determine the position of a point in space based on its distances from three known points. In the context of triangulation survey, this method can be used to check the intervisibility of stations. By measuring the distances between three stations and using the three-point problem, it is possible to calculate the position of a fourth station. If the calculated position of the fourth station is within the expected range of intervisibility, it indicates that the stations have intervisibility.

**Conclusion**

In conclusion, the intervisibility of stations in a triangulation survey can be checked using various methods such as the method of least squares, heliotropes, Captain G.T. McCaw's solution, and the three-point problem. These methods involve measuring angles, calculating distances and positions, and analyzing the results to determine if stations have intervisibility. By ensuring intervisibility, accurate and reliable survey data can be obtained for various engineering and mapping purposes.