Figure 4.2  Different Values of $\upsilon$

This is another graph by Strange and this one shows four different values:  $\upsilon=\frac{\pi}{2.2}\:, \:\frac{\pi}{3}\:,\:\frac{\pi}{4}\:, \:\frac{\pi}{6}$
The curves have different extents along the x axis, which is the $\lambda$ angle.

In order to represent $\upsilon$ as a quantity that expresses direction, the curves must be “normalized” by making the extent of the curves along the x axis equal to 1,  similar (mathematically and conceptually) to the way vectors are normalized in order to create a unit vector or direction vector.

Once the curves are normalized, they express direction as a function of direction, without any length.