An alternative method of solving the layer scaling equations of Hamilton, Rollett and Sparks

The relationship between the methods of Dickerson (1959), Rollett & Sparks (1960), and Hamilton, Rollett & Sparks (1965) (HRS) is discussed, together with a short account of why the first two methods are unsatisfactory. An alternative iterative method (the method of 'shortest path') of solving the layer scaling equations of HRS is given which converges faster than the solution given by HRS. An exact solution of the equations of HRS is given which may be applied to situations where a simple weighting scheme may be used. The method of 'shortest path' may be important in protein crystallography where setting up the normal matrix may mean scanning 100000 reflexions and therefore the speed of convergence is of paramount importance