The transverse spin dependence of the proton-proton total cross-section, (DELTA)(sigma)(,T), the difference between the proton-proton total cross-sections for protons in anti-parallel and parallel transverse spin states, was measured from 300 MeV to 800 MeV at LAMPF (Los Alamos Meson Physics Facility). The detectors, ionization chambers, had current- and position-dependent responses which resulted in large systematic dependences in the data. These dependences were removed by means of a multiple regression technique. In the course of a (DELTA)(sigma)(,T) measurement at a particular energy, radiation damage caused the target polarizability to decrease by as much as 30%. To correct for this effect, elastic scattering measurements were made before and after the (DELTA)(sigma)(,T) measurements at each energy to establish a calibration factor for the NMR target polarization monitor. Cancellation of systematic errors was also achieved through randomization. Randomization of the data with respect to systematic errors was achieved by periodically reversing the target polarity. Systematic errors due to causes such as single-spin asymmetry and varying beam and target polarizations cancel when the positive and negative target polarity data are averaged. A sharp peak, found at 2.14 GeV center of mass energy, the mass of the proposed ('1)D(,2) dibaryon resonance, is confirmed by data taken by other groups using substantially different types of equipment {AXE81, BYS81, DIT83}. Data taken previously at the Argonne ZGS (Zero Gradient Synchrotron) show a peak at 2.43 GeV center of mass energy, the mass of the proposed ('1)G(,4) dibaryon. When the data sets are combined with (DELTA)(sigma)(,L) data {AUE81} to form the triplet projector {LOC83} a third peak is revealed at 2.22 GeV center of mass energy, the mass of the proposed ('3)F(,3) dibaryon resonance. As no theory or phase-shift analysis completely describes the structure in (DELTA)(sigma)(,T), the data should provide theorists with a testing ground for candidate strong interaction theories.