**Figure 2**
Schematic representation of the interpretation of (7) as a probabilistic version of the Harker (1956) construction. Each panel shows a contour plot of a probability distribution. (*a*) shows the probability distribution for the observed native amplitude as a function of possible values for the true native structure factor. The width of this distribution represents the estimated error in measurement of the native amplitude. (*b*) shows the probability distribution for the observed amplitude for derivative 1, again as a function of possible values for the true native structure factor. Because the derivative structure factor must be the sum of the heavy-atom contribution and the protein contribution, the centre of the circularly symmetric distribution is offset by minus the heavy-atom contribution. (*c*) overlays the first two distributions, as well as the distribution for a second derivative, and (*d*) shows the product of all three distributions as a function of the assumed true native structure factor. The combined distribution has significant values where the circles from the Harker construction come close to intersecting. |