  The relative brightnesses of standard candles have long been known to be
potentially powerful probes of distance. The distance modulus, the difference
between observed and absolute magnitudes, has been associated with the values
of the cosmological parameters: Hubble's constant H_0, the mass density Omega_M
and the cosmological constant Omega_Lambda. In the literature the relationship
between these parameters and the distance modulus is calculated for an energy
magnitude system; the Johnson-Cousins magnitude system used in observations is
in fact a photon-counting system. In this paper, we present the relation
between observed and absolute photon magnitudes in terms of the familiar energy
distance modulus and derive the correct form of the K-correction. The
differences between energy and photon systems are small relative to the
measurement errors of contemporary high-redshift supernova searches. The
distinction must be made, however, for precision cosmological measurements such
as those planned for Type Ia supernovae.
