Having formulated the Clairaut second-order differential equations up
to the fourth order in superficial distortion due to Hensen's coeffici
ents in the previous article (El-Sharawy et al., 1989 III, hereafter d
enotes by SM3), we are now in a position to solve them. In this paper
we shall discuss the methods of solving the Clairaut theory, to give a
n explicit form about the distortion of the surfaces of Jupiter and Sa
turn, numerically up to the fourth-order.