$(3)$ Set up a total station at station A $($the height of the instrument is $1\mathrm{.}65$ meters$)$ and observe point B $($the height of the instrument is $1\mathrm{.}35$ meters$).$ The observed horizontal distance is $1200$ meters and the elevation angle is $12{15}^{\text{'}}{00}^{\text{'}\text{'}}.$ After that, set up the total station instrument at point B again, $($The instrument height is $1\mathrm{.}45$ meters$),$ observe point A $($the instrument height is $1\mathrm{.}85$ meters$),$ The observed horizontal distance is $1200$ meters, and the depression angle is $-12{12}^{\text{'}}{35}^{\text{'}\text{'}}.$ Assume that the refractive coefficient is the same for both observations. Given that the height of point A is $350\mathrm{.}18$ meters, please find the refractive foefficient and the height of point B $.($The radius of the Earth is $6378$ km $)(20$ pts