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In levelling, the effect of refraction may be taken as:

One-seventh

The effect of refraction is generally considered to be about one-seventh of the effect due to the curvature of the Earth.

The method of surveying used for determining the relative height of points on the surface of the Earth is called:

Levelling

Levelling is the general process of determining the elevation of points and the difference in elevation between them. Differential levelling is a specific type of levelling used to find the difference in height between two points.

profile levelling 

Answer: 0.0673 D²

The length of a long chord is equal to:

2 R sin(θ/2)

where RRR is the radius of the curve and θθθ is the central angle in radians. The long chord is the straight line connecting the two ends of the arc of the curve.

To find the back bearing of a line when the fore bearing is \(36^\circ 15'\), you add \(180^\circ\) to the fore bearing and then adjust for any values exceeding \(360^\circ\).

Given:
- Fore bearing = \(36^\circ 15'\)

Calculate:
- Back bearing = \(36^\circ 15' + 180^\circ = 216^\circ 15'\)

So, the back bearing is:

216° 15

The correction for slope required is: 2l sin² θ/2

Explanation:

• l is the length of the chain along the slope.

• θ is the angle of slope.

The correction is always subtractive because the measured length along the slope is longer than the horizontal distance.

This formula is derived from trigonometric relationships and is used to accurately determine the horizontal distance when measurements are taken along a slope.

Would you like to know more about other corrections applied in chaining, such as temperature correction or pull correction?

Yes, you’re correct. Given the true bearing of the sun at noon is 180° (due south) and the magnetic declination is 5° 20' east, you subtract the declination from the true bearing to find the magnetic bearing:

\[ \text{Magnetic Bearing} = 180^\circ - 5^\circ 20' \]

Converting 5° 20' to decimal degrees:

5° 20' = 5.333°

Calculate the magnetic bearing:

\[ \text{Magnetic Bearing} = 180^\circ - 5.333^\circ = 174.667^\circ \]

Which is:

\[ 174^\circ 40' \]

So, the magnetic bearing of the sun at noon is indeed 174° 40

The object of introducing a transition curve at each end of the circular curve is:

All of the above

A transition curve serves multiple purposes:

1. To provide a satisfactory means of obtaining a gradual increase of super-elevation from zero on the tangent point to the specified amount on the main circular curve.

2. To accomplish gradually the transition from the tangent to the circular curve and from the circular curve to the tangent, ensuring smooth changes in alignment and reducing abrupt transitions.

3. To obtain a gradual increase of curvature from zero at the tangent point to the specified quantity at the junction of the transition curve with the circular curve, helping in smooth vehicle movement and comfort.