  In the Ginzburg-Landau theory of superfluid $^{3}$He, the free energy is
expressed as an expansion of invariants of a complex order parameter. Strong
coupling effects, which increase with increasing pressure, are embodied in the
set of coefficients of these order parameter invariants\cite{Leg75,Thu87}.
Experiments can be used to determine four independent combinations of the
coefficients of the five fourth order invariants. This leaves the
phenomenological description of the thermodynamics near $T_{c}$ incomplete.
Theoretical understanding of these coefficients is also quite limited. We
analyze our measurements of the magnetic susceptibility and the NMR frequency
shift in the $B$-phase which refine the four experimental inputs to the
phenomenological theory. We propose a model based on existing experiments,
combined with calculations by Sauls and Serene\cite{Sau81} of the pressure
dependence of these coefficients, in order to determine all five fourth order
terms. This model leads us to a better understanding of the thermodynamics of
superfluid $^{3}$He in its various states. We discuss the surface tension of
bulk superfluid $^{3}$He and predictions for novel states of the superfluid
such as those that are stabilized by elastic scattering of quasiparticles from
a highly porous silica aerogel.
