  We report measurements of transverse momentum $p_t$ spectra for ten event
multiplicity classes of p-p collisions at $\sqrt{s} = 200$ GeV. By analyzing
the multiplicity dependence we find that the spectrum shape can be decomposed
into a part with amplitude proportional to multiplicity and described by a
L\'evy distribution on transverse mass $m_t$, and a part with amplitude
proportional to multiplicity squared and described by a gaussian distribution
on transverse rapidity $y_t$. The functional forms of the two parts are nearly
independent of event multiplicity. The two parts can be identified with the
soft and hard components of a two-component model of p-p collisions. This
analysis then provides the first isolation of the hard component of the $p_t$
spectrum as a distribution of simple form on $y_t$.
