  A proper understanding of the mechanism for cuprate superconductivity can
emerge only by comparing materials in which physical parameters vary one at a
time. Here we present a variety of bulk, resonance, and scattering measurements
on the (Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_3O_y high temperature
superconductors, in which this can be done. We determine the superconducting,
Neel, glass, and pseudopage critical temperatures. In addition, we clarify
which physical parameter varies, and, equally important, which does not, with
each chemical modification. This allows us to demonstrate that a single energy
scale, set by the superexchange interaction J, controls all the critical
temperatures of the system. J, in-turn, is determined by the in plane Cu-O-Cu
buckling angle.
