The Newman-Penrose quantities and the double-series approximation method

The double-series method is used to investigate the Newman-Penrose quantiti es (NPQ) in the case of an axially symmetric isolated source which oscillat es for a finite time. In this case there is a single NPQ. It is found that in part of spacetime this quantity is not defined because of the divergence of the Bondi-Sachs expansion used to derive it. The NPQ is conserved where it is de fined, but I argue that the conservation has little physical impo rtance.