Although the temporal tilting of Listing’s plane may suffice to
account for the observed anterior position of the MR pulley, there are
theoretical grounds to anticipate that the effect might be further
magnified by convergence. During convergence, the Listing’s planes for
the two eyes are reported by various authors to rotate temporally by
between 16% and 100% of the vergence angle, but most commonly
25%,
26 corresponding to the relative excyclotorsion in
depression and incyclotorsion in elevation
27 28 necessary
to maintain alignment of corresponding retinal meridia during near
viewing. Thus, during binocular viewing of near and far targets aligned
on one eye, the Listing plane for that unmoving eye nevertheless tilts
in association with the vergence movement of the other
eye.
29 In the present experiment, convergence to the near
target may have occurred in some subjects despite the nonaccommodative
target’s monocular presentation aligned to the scanned eye.
Figure 8 (bottom) depicts a situation in which a near target is aligned to the
diagrammed eye, with the entire vergence angle generated by the fellow
eye (not shown). In such a convergent situation, pulleys could
implement a linear plant with a temporal shift of Listing’s primary
position by anterior displacement of the MR pulley, nasal and anterior
displacement of the SR pulley, and posterior displacement of the LR
pulley. The peribulbar smooth muscle is anatomically situated to
accomplish much of the required pulley displacements.
19 Note that in the convergent case where Listing’s primary position is
oriented temporally from central gaze to angle α, the distance
D
1 from the LR pulley to globe center can be
equal to the distance D
2 from globe center to the
LR insertion, and distance D
3 from the MR pulley
to globe center can be equal to distance D
4 from
globe center to the MR insertion, although D
1 >
D
3. Suitable MRI studies during controlled
convergence could test this hypothesis.