Greens function and the conducting sphere

Can somebody explain to me, when equations 2.48 and 2.50 are applicable and what ##\Phi_s## and ##\Phi## actually are? The thing is, I want to find a general equations that determines the field produced by conducting spherical sphere in an external field and was wondering whether these are the equations I am looking for.[Reference to 2.48 and 2.50][1]
http://physics.usask.ca/~hirose/p812/notes/Ch2.pdf

Or is it rather the equation here (17.3), probably they are one and the same:
[second reference][2]
http://www.physics.udel.edu/~jim/PHY...s/Class_17.pdf