  The discovery of the planet around the solar-type star 51 Pegasi marked a
watershed in the search for extrasolar planets. Since then seven other
solar-type stars have been discovered, of which several have surprisingly short
orbital periods, like the planet around 51 Peg. These planets were detected
using the indirect technique of measuring variations in the Doppler shifts of
lines in the spectra of the primary stars. But it is possible that oscillations
of the stars themselves (or other effects) could mimic the signature of the
planets, particularly around the short-period planets. The apparent lack of
spectral and brightness variations, however, led to widespread acceptance that
there is a planet around 51 Peg. This conclusion was challenged by the
observation of systematic variations in the line profile shapes of 51 Peg,
which suggested stellar oscillations. If these observations are correct, then
there is no need to invoke a planet around 51 Peg to explain the data. Here we
report observations of 51 Peg at a much higher spectral resolution than those
in ref.9, in which we find no evidence for systematic changes in the line
shapes. The data are most consistent with a planetary companion to 51 Peg.
