The plane of dip circle is set in the geographic meridian and the apparent dip is `theta_(1)`. It is then set in a vertical plane perpendicular to the geographic meridian. Now, the apparent dip is `theta_(2)`. The angle of declination `theta` at that place is

Explanation

Let the true angle of dip at the place be `theta` and the declination be `delta` .
So we can relate apparent angle of dip measured in geographic meridian `(theta_(1))` with true angle of dip `theta` as
`tan theta_(1) = (tan theta)/(cos delta) " " ... (i)`
For a plane `bot` to geographic meridian , the apparent angle of dip is related to true angle of dip as
`tan theta_(2) = (tan theta)/(cos (90 - delta)) = (tan theta)/(sin delta) " " ... (ii)`
By eliminating `theta` between the result (i) and (ii) , we get
`tan theta_(1) cos delta = tan theta_(2) sin delta `
`implies tan delta = (tan theta_(1))/(tan theta_(2))`
`implies delta = tan^(-1) ((tan theta_(1))/(tan theta_(2)))`