Figure 20a shows an example of the type of data frequently displayed on stereograms. The points represent the long axes of clasts measured in a till. The reason for measuring and plotting these data is not to show the orientations of individual axes but to analyse the pattern of orientations shown by the whole sample. The pattern of preferred orientation of till clasts is indicative of the flow direction of the ice. Before we can recognize such patterns confidently we need to know whether the stereographic projection faithfully represents the true clustering of directions in space.

One way of checking for possible distortion is to plot data that are known to be devoid of any preferred orientation. Figure 20b shows 2000 directions randomly chosen by the computer, plotted using the stereographic (Wulff) net (Fig. 20d). These directions are not evenly distributed across the stereogram (Fig. 20b) as we would expect but are more crowded in the central part of the net. This crowding is the direct result of the method of projection used. Our conclusion must be that the stereographic projection introduces an artificial preferred orientation of line directions, crowding the projected directions in the centre of the stereogram.

It is easy to understand this effect when we see how cones of identical size but different orientations are projected stereographically The small circles in Figure 20f represent two such cones.