  The Crab Nebula was detected with the Milagro experiment at a statistical
significance of 17 standard deviations over the lifetime of the experiment. The
experiment was sensitive to approximately 100 GeV - 100 TeV gamma ray air
showers by observing the particle footprint reaching the ground. The fraction
of detectors recording signals from photons at the ground is a suitable proxy
for the energy of the primary particle and has been used to measure the photon
energy spectrum of the Crab Nebula between ~1 and ~100 TeV. The TeV emission is
believed to be caused by inverse-Compton up-scattering scattering of ambient
photons by an energetic electron population. The location of a TeV steepening
or cutoff in the energy spectrum reveals important details about the underlying
electron population. We describe the experiment and the technique for
distinguishing gamma-ray events from the much more-abundant hadronic events. We
describe the calculation of the significance of the excess from the Crab and
how the energy spectrum is fit. The fit is consistent with values measured by
IACTs between 1 and 20 TeV. Fixing the spectral index to values that have been
measured below 1 TeV by IACT experiments (2.4 to 2.6), the fit to the Milagro
data suggests that Crab exhibits a spectral steepening or cutoff between about
20 to 40 TeV.
