Vermiculite clay gels in 0.03 M butylammonium chloride solution were studied by neutron diffraction in the a range 0.02-2.2 Angstrom(-1), permitting a determination of both the distance between the clay platelets (the d spacing) and the intermediate-range structure of the interlayer solution. The structure was investigated as a function of the fraction of the clay in the condensed matter system (r) and the applied uniaxial pressure along the swelling axis (p). The d spacing of about 170 Angstrom at zero pressure and r similar to 0.01 reduces dramatically with both increasing pressure and increasing r value without changing the interlayer structure significantly. For r = 0.39 a remarkably low d value of about 50 Angstrom was obtained for a gel in equilibrium with a crystalline phase. The existence of such an equilibrium is a counterexample to DLVO theory but well accounted for by Sogami theory. Independent of the pressure, r value, and salt concentration, the clay surfaces are covered by an about 6 Angstrom thick layer of water molecules, and the majority of the butylammonium chains sit outside this water layer and form an approximately 4-5 Angstrom thick layer located 12-16 Angstrom from the center of the clay platelets, giving us a picture of a dressed macroion. Continuum electrical theories of clay swelling can thus only be valid at distances greater than the 35-40 Angstrom thickness of the clay platelet plus adsorbed layers of water molecules and counterions. Further, the results suggest that 35 Angstrom is about the lowest possible d spacing that can be achieved for the gel phase by either increasing the uniaxial pressure toward infinity or using a sufficiently high sol concentration.