Fackerell, Edward D.Hartley, David H.2006-07-212006-07-212000General Relativity and Gravitation. 32(5):857-8640001-7701http://hdl.handle.net/2440/12511We review the similarity solutions proposed by Waylen for a regular time–dependent axisymmetric vacuum space–time, and show that the key equation introduced to solve the invariant surface conditions is related by a Bäcklund transform to a restriction on the similarity variables. We further show that the vacuum space–times produced via this path automatically possess a (possibly homothetic) Killing vector, which may be time–like.en© Springer, Part of Springer Science+Business MediaJournal article000100153610.1023/A:1001980923501