The derivatives of $\chi ^2$

1.

${\displaystyle{\partial dr' \over \partial {\bf b}}}$

$$\begin{array}{c} {\displaystyle {\partial dr' \over \partial ... ...' , \;\;\; {\partial dr' \over \partial z_v } = 0 } \end{array}$$ (23)

2.

${\displaystyle{\partial \phi_0' \over \partial {\bf b}}}$

$$\begin{array}{c} {\displaystyle{\partial \phi_0' \over \parti... ...tial \phi_0' \over \partial\tilde{\lambda}_i } = 0} \end{array}$$ (24)

3.

${\displaystyle{\partial \kappa' \over \partial {\bf b}}}$

$$\begin{array}{c} {\displaystyle{\partial \kappa' \over \parti... ...tial \kappa' \over \partial \tilde{\kappa}_i } = 1} \end{array}$$ (25)

4.

${\displaystyle{\partial dz' \over \partial {\bf b}}}$

$$\begin{array}{c} {\displaystyle{\partial dz' \over \partial x... ... = - {\alpha\over\tilde{\kappa}_i} (\phi_0' - A) } \end{array}$$ (26)

5.

${\displaystyle{\partial \tan\lambda' \over \partial {\bf b}}}$

$$\begin{array}{c} {\displaystyle{\partial \tan\lambda' \over \... ...\lambda' \over \partial \tan\tilde{\lambda}_i} = 1} \end{array}$$ (27)