  The first direct measurement of the dependence on target nuclear mass of the
average squared transverse momentum <pt**2> of pi+, pi-, and K+ mesons from
deep-inelastic lepton scattering is obtained as a function of several kinematic
variables. The data were accumulated at the HERMES experiment at DESY, in which
the HERA 27.6 GeV lepton beam was scattered off several nuclear gas targets.
The average squared transverse momentum was clearly observed to increase with
atomic mass number. The effect increases as a function of Q**2 and x and
remains constant as a function of both the virtual photon energy nu and the
fractional hadron energy z, except that it vanishes as z approaches unity.
