We have studied γ-ray line emission from fusion of accelerated α-particles with ambient helium in 19 solar flares observed by the Solar Maximum Mission Gamma-Ray Spectrometer from 1980 to 1989. An isotropic or fan-beam distribution of accelerated particles provides good fits to the line profiles for most of the flares. In contrast, a downward beam of accelerated particles can be ruled out at high confidence levels, 99.99% and 99.8%, for the two most intense flares and provides significantly poorer fits than isotropic or fan-beam distributions in two other flares. The fluences in the α-α lines, with a few exceptions, show a correlation with fluences of the narrow nuclear de-excitation lines from elements with high first ionization potential. If we assume that all accelerated ions have the same spectral shape, and if we adopt accelerated particle and ambient abundances derived from other γ-ray line studies, we find that an accelerated α/proton ratio of 0.5 is consistent with the spectra from the 19 flares, whereas a ratio of 0.1 is not. We also suggest the possibility that 7Be produced in α-4He fusion during the intense flares occurring in late 1989 may have reached Earth in a concentration high enough to account, in part, for 7Be observed in NASA's Long-Duration Exposure Facility satellite after its recovery in early 1990.