Let $X$ be a point on $C$.
Let $PXQ$ be the vertical circle through $X$.
If $X$ is in the northern celestial hemisphere, $DX$ is north declination.
If $X$ is in the southern celestial hemisphere, $DX$ is south declination.
It is convenient to define the declination of $X$ as between $+90 \degrees$ and $-90 \degrees$, where a south declination is a negative quantity, from $0$ at the celestial equator and $-90 \degrees$ at the south celestial pole.