The Tremaine-Weinberg equations are solved for a pattern speed that is allowed to vary with radius .
The solution method transforms an integral equation for the pattern speed to a least squares problem with well established procedures for statistical analysis .
The method applied to the H I spiral pattern of the barred , grand-design galaxy NGC 1365 produced convincing evidence for a radial dependence in the pattern speed .
The pattern speed behaves approximately as 1/ r , and is very similar to the material speed .
There are no clear indications of corotation or Lindblad resonances .
Tests show that the results are not selection biased , and that the method is not measuring the material speed .
Other methods of solving the Tremaine-Weinberg equations for shearing patterns were found to produce results in agreement with those obtained using the current method .
Previous estimates that relied on the assumptions of the density-wave interpretation of spiral structure are inconsistent with the results obtained using the current method .
The results are consistent with spiral structure theories that allow for shearing patterns , and contradict fundamental assumptions in the density-wave interpretation that are often used for finding spiral arm pattern speeds .
The spiral pattern is winding on a characteristic timescale of \sim 500 Myrs .