  We apply the method of linear perturbations to the case of
Spin(7)-structures, showing that the only nontrivial perturbations are those
determined by a rank one nilpotent matrix.
  We consider linear perturbations of the Bryant-Salamon metric on the spin
bundle over $S^4$ that retain invariance under the action of Sp(2), showing
that the metrics obtained in this way are isometric.
