The authors consider Weyl collineations (vector fields \(X\) satisfying \({\mathcal L}_X C^a_{bcd} = 0\) where \(C\) is the Weyl tensor -- the authors use, somewhat unconventionally, the symbol \(W\) for the Weyl tensor) on spacetimes. Many of the results in this short paper are either trivial or known. The authors say that no serious classification of curvature collineations has been given. This is not true [see the reviewer and \textit{J. da Costa}, J. Math. Phys. 32, No. 10, 2848-2853 (1991; Zbl 0745.53019)]. Also it is known [the reviewer, Classical general relativity, Proc. Conf., London 1983, 103-120 (1984; Zbl 0577.53021)] that except in the cases where the Weyl tensor is zero or type \(N\) the Weyl tensor components \(C^a_{bcd}\) uniquely determine the metric up to a conformal factor and hence for these spacetimes every Weyl collineation is a conformal motion. This result would simplify their paper. Also the paper of the reviewer, \textit{I. Roy} and \textit{E. G. L. R. Vaz} [Gen. Relativ. Gravitation 28, No. 3, 299-310 (1996)] contains results given in this paper. Their use of the term ``Einstein metric'' is also confusing -- it could mean ``Einstein space'' or ``Einstein's static metric'' and, in fact, means the latter! The bibliography suggests the authors are not well versed with the literature.