  Recent data from the LHC makes it possible to examine an old speculation that
at very high energy the total multiplicity and the cross section in elementary
particle interactions vary in parallel with energy. Using fits incorporating
the new data, it appears that the ratios of the total, elastic, and inelastic
cross sections to the average multiplicity N can in fact approach constants at
very high energy. The approach to the limit is however quite slow for the total
and inelastic cross sections and is not yet reached at LHC energies. The
elastic ratio sigma^{el}/N at 7 TeV, however, is not far from its asymptotic
value.
