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Stereographic projections of the highest accuracy are obtained by the constructions described in the previous section, and they have been described first because they lead to an understanding of the principles involved. However, it is often more convenient to prepare stereograms with the help of stereographic nets, and although the accuracy obtained is usually lower it is sufficient for most purposes.

A stereographic net is simply a stereographic projection of the lines of
latitude and longitude of a sphere on to a central plane. The most obvious form
of stereographic net is shown in Fig. 12. The *N*-pole projects to the centre
as discussed in Section 1, the lines of latitude project to a set of concentric
circles, and the lines of longitude to a set of diameters of the primitive.
Such a net, if graduated sufficiently finely, could be used directly to obtain
the same results as constructions (i) and (iv) of Section 3. However, other
nets are possible. If we imagine a terrestrial globe tilted over as shown in
Fig. 13a, and we project all points on it, not to the geographical *S*-pole but
to the lowest point of the sphere, then the projection of the lines of latitude
and longitude would be as shown in Fig. 13b. We shall revert to this idea in
Section 5, but the most generally useful result is if we tilt the globe right
over so that its *N*-*S* axis is horizontal. The projection is then as shown
in Fig. 13c. It is equivalent to what we would have obtained by projecting to
its *S*-pole a globe that was inscribed with lines of latitude and longitude
referred to as `east pole` and `west pole`. This is the *Wulff net* , and
is so generally useful that it is commonly referred to as *the*
stereographic net. A commercially available Wulff net of 5 inch diameter
graduated in 2 intervals is shown in Fig. 14. On this figure all the
(nearly) vertical lines represent great circles, and all the (nearly) horizontal
lines represent small circles round a point on the primitive.

In order to construct stereograms with the help of the Wulff net it is most convenient to work on tracing paper over the net.

To plot a point at a given angle from the *N*-pole (equivalent to construction
(i)) one simply uses the scale along either of the graduated diameters of the
net.

To draw a great circle through two points (equivalent to construction (iii)) rotate the stereogram over the net until both points lie on one of the projected great circles (or an interpolated circle between two of them) and then trace the required arc on to the stereogram. Because of the simplicity of this procedure one does not need construction (ii). If the two points have been projected to opposite poles (i.e. one is a and the other a ) then rotate the stereogram until they lie on projected great circles at equal distances on opposite sides of the vertical diameter of the net.

To draw a small circle of given radius about a point *p* (equivalent to
construction (iv)) rotate the stereogram over the net so that the *p* point lies
on the vertical diameter. If there are two points at the appropriate scale
distances on opposite sides of *p* and within the primitive, then mark these two
points and draw a circle through them centred at their mid point (Fig. 15a). If
*p* is closer to the primitive than the required angular radius then only one of
the required points (a) can be found on the net. The second point required (b)
can most simply be found by using a stereographic ruler. This is a scale whose
graduations are equal to those along a diameter of the Wulff net, but which
continue appropriately to some (arbitrary) distance beyond the primitive.

However, if a stereographic ruler is not available the Wulff net itself can be
used. Position the point *p* on the horizontal diameter of the net and mark two
points *d* and (Fig. 15b) above and below *p* at distances
along the (interpolated) great circle through *p*. Then the required small
circle can be drawn through *a*, *d* and . Once the circle has been
drawn it is possible to reproject to the *N*-pole the part that lies outside the
primitive. Count divisions along the diameter from *p* to the primitive and
then continue counting back inwards until the value of is reached: this
leads to a point (Fig. 15b) and the required arc is that which goes
through and the two intersections *e* and of the small
circle with the primitive.

If the point *p* lies on the primitive, then the stereogram must be rotated so
that *p* lies at one end or the other of the vertical diameter of the Wulff net.
A projected small circle of any desired angular radius can then be traced
directly from the Wulff net.

**Copyright © 1984, 1997 International Union of
Crystallography**