Dip Circle and Apparent Dip

Dip Circle

Dip circle is a device used to measure the angle of dip at a place. It consists of a magnetic needle pivoted at the center of the vertical circular scale that can rotate in the plane of the scale about the horizontal axis passing through its C.G.

It consists of vertical circular scale is divided into four quadrants, each graduated from 0^o to 90^o, with 0^o- 0^o in horizontal and 90^o – 90⁰ in vertical positions. The horizontal circular scale at the bottom is graduated from 0^o to 360^o. Dip circle is shown in the figure.

Measurement of Angle of Dip

First of all the device is maintained with correct leveling and needle pointing 90^o-90^o on the vertical scale. Here the needle and vertical scale are in a plane perpendicular to the magnetic meridian. The box is then rotated through 90^o position on the horizontal circular scale. This sets the needle and vertical scale exactly in magnetic meridian. The needle rests in the direction of earth’s resultant field I and its two ends points the value of dip $\delta$ at that place.

Errors and Corrections in Dip Circle

Pivot of needle may not be at the center of circular scale:
If the center of needle and center of scale do not coincide with each other, one value of dip will be greater and the other will be smaller than the true value of dip angle. Average of these two readings will give the true value of dip angle at that place.
The line indicating 0^o – 0^o is not horizontal:
This defect will make the value of dip will be smaller or greater than the true value. To remove this defect, readings should be taken in two vertical scales: first in the magnetic meridian and then rotate it through 180^o in magnetic meridian. The average of readings is the true value.
Magnetic center of the needle may not coincide with geometric center of the needle:
In this case, the magnetic axis of the needle inclines to its geometric axis. To remove this defect, the readings are taken in magnetic meridian and then the needle is reversed on its bearing. The average of two readings is the accurate value of the angle of dip angle.
The center of mass of the needle doesn’t coincide with the pivot:
The center of mass of the needle doesn’t match as the deflection of the needle is more at one end than at the other. To remove this defect two readings are taken firstly without doing any change and secondly by interchanging the poles. We can interchange the poles by demagnetizing the needles and remagnetizing it with different poles.
We should take 16 readings of the angle of dip and average of these values gives true dip angle at that place.

Apparent Dip

The angle made by the needle with the horizontal at this plane is called the apparent dip. Let $\alpha $ be the angle made by the dip circle with the magnetic meridian. Then the effective horizontal component in this plane is $H_a = H\cos \: \alpha $ and the vertical component is still same, V. if the apparent dip at this plane is $\delta _1$ and the true dip is $\delta $, then

$$\begin{align*} \tan \delta _1 &= \frac {V}{H_a} \\ \text {or,} \: \cot \delta_1 &= \frac {H_2}{V} = \frac {H\: \cos \alpha }{V} = \frac {\cos \alpha }{\tan \delta } \\ \cot \delta _1 &= \cos \alpha \times \cot \delta \dots (i) \\ \end{align*}$$

This is the relation between true dip $\delta $ and the apparent dip $\delta _1$. If the circle makes an angle of $ (90^o - \alpha $ with the magnetic meridian and H will have the component $ H’_a = H (\cos 90^o - \alpha ) = H\sin \alpha )$ in the new plane. Then, the apparent dip $\delta _2 $ is given by

$$\begin{align*} \cot \delta _2 &= \sin \alpha \times \cot \delta \dots (ii) \\ \text {squaring and adding equation}\: (i) \:\text {and} \: (ii), \: \text {we get} \\ \cot ^2 \delta _1 + \cot^2 \delta _2 &= \cos^2 \alpha \times \cot ^2 \delta + \sin^2 \alpha \times \cot ^2 \delta \\ \cot ^2 \delta &= \cot^2\delta _1 + \cot ^2 \delta_2 \\ \end{align*}$$

Knowing the values of $\delta _1$ and $\delta _2$ we can get the value of $\delta $.