[en] The Bevatron of the Lawrence Berkeley National Laboratory operated with no permanent shielding-roof from 1954 to 1962. Neutron fluences measured at the laboratory perimeter reached a maximum in 1959, and were reported as an annual dose equivalent of 8.1 mSv (54% of the then operative radiation limit). The addition of temporary local shielding and improved operational techniques subsequently led to a steady decline in dose equivalent at the laboratory perimeter. A permanent concrete shielding-roof was constructed in 1962. In those early years of operation the reported dose equivalent, H, was derived from a measured total neutron fluence, F, and an estimated spectrum-weighted fluence to dose equivalent conversion coefficient, (g), where H=(g)F. The uncertainty in H was almost entirely due to the uncertainty in (g). While the measurements of F were accurate the estimates of (g) were quite crude and depended upon measurements of average neutron energy, on assumptions about the shape of the neutron energy spectrum, and primitive values of fluence to dose equivalent conversion coefficients for monoenergetic neutrons. These early reported dose equivalents were known to be overestimated. This paper has reappraised the dose equivalents in the light of better information now available. Environmental neutron spectra have been calculated which more accurately correspond to the operational conditions of the Bevatron in the 1950s and early 1960s, than did those spectra available at that time. A new fluence to dose equivalent conversion function based on the latest data and for isotropic irradiation geometry was developed. From these two parameters better estimates of the coefficient (g) were determined and compared with the earlier values. From this reappraisal it is shown that the early reported dose equivalents were conservative by a factor of at least five. (author)