The emulsion technique was used to set certain upper limits for the fission cross sections of some naturally occurring heavy elements bombarded with 21 Mev neutrons. It is established that the fission cross-sections for these elements (Bi, Pb. Au, Pt and W) are less than 4 X 10-5 of that of U238. These results are in disagreement with the fission threshold derived from the theory of fission based on the liquid drop model for heavy nuclei, but support a simple argument about the minimum neutron energy required to produce fission by Tsien San-Tsiang.