  The determination of the centre-of-mass energies for all LEP 2 running is
presented. Accurate knowledge of these energies is of primary importance to set
the absolute energy scale for the measurement of the W boson mass. The beam
energy between 80 and 104 GeV is derived from continuous measurements of the
magnetic bending field by 16 NMR probes situated in a number of the LEP
dipoles. The relationship between the fields measured by the probes and the
beam energy is defined in the NMR model, which is calibrated against precise
measurements of the average beam energy between 41 and 61 GeV made using the
resonant depolarisation technique. The validity of the NMR model is verified by
three independent methods: the flux-loop, which is sensitive to the bending
field of all the dipoles of LEP; the spectrometer, which determines the energy
through measurements of the deflection of the beam in a magnet of known
integrated field; and an analysis of the variation of the synchrotron tune with
the total RF voltage. To obtain the centre-of-mass energies, corrections are
then applied to account for sources of bending field external to the dipoles,
and variations in the local beam energy at each interaction point. The relative
error on the centre-of-mass energy determination for the majority of LEP 2
running is 1.2 x 10^{-4}, which is sufficiently precise so as not to introduce
a dominant uncertainty on the W mass measurement.
