This is the fifty-fourth progress report of the Laboratory for Nuclear Science at the Massachusetts Institute of Technology. Progress reported covers the period for Physics and Chemistry through April 30,1959. Progress is reported on: (1) Chemistry of the fission elements group, (2) Nuclear chemistry (inorganic) group, (3) Nuclear chemistry (organic) group, (4) Cosmic ray group, (5) High energy accelerator physics group, (6) Bubble chamber group, (7) Liner acceleratory group, (8) Rockefeller generator group, (9) ONR generator group, (8) Radioactivity group, (9) Cyclotron group, (10) Theoretical group, (11) Personnel listing.