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The reason for Listing's Law

What is the reason of the existence of Listing's Law or, in other words, why is there a primary position, from which all other eye positions can be reached by simple rotation about a single axis or, in other words, why isn't the primary position in left upper gaze for instance ? Von Helmholtz' compared Listing's Law with the minimal energy condition in physics (1863). Applying this principle in a broader sense, one could say that Listing's law is probably the consequence of the facts that the primary position is the average of all eye positions during the day, that most eye movements are directed radially from or to the primary position and that rotations about a single axis are easier to perform than rotation about two axes or about an axis that changes during the movement. Eye movements from tertiary positions to other tertiary positions do occur, but are less frequent and do not occur predominantly in down-, up-, right- or left-gaze. During eye movement from one tertiary to another tertiary position, Listing's law is fulfilled only if the rotation takes place about an axis that is tilted to Listing's plane by half the angle between the momentary tertiary position and primary position (von Helmholtz, 1863): hence an axis that can change during the movement. (That is probably why Ferman (1987b) quantifying Listing's Law with a double-looped search coil for simultaneous recording of horizontal, vertical and torsional eye position (Ferman et al. 1987a; Collewijn et al. 1985) found that during pursuit of a target that circled around the primary position the torsion of the eye lagged behind, relative to what would be expected from Listing's Law.)
The primary position (Ruete, 1853), as determined with afterimages (Hering, 1868, p.74-83) varies over time (von Helmholtz, 1910; Schubert, 1927), is in down-gaze for convergence (Donders, 1876, see below) and varies with head position (Fisher, 1922). The reader interested in Listing's Law and the coordinate systems employed to describe eye positions is referred for further reading to the section at the end of the Methods chapter describing the modification in the computerized model concerning the coordinate system used.

Excyclotropia on convergence

A third kind of torsion that has confused investigators is excyclotropia on convergence. Excyclotropia (vertical retina meridians tilting clockwise in the right eye and anti-clockwise in the left eye as seen from the patient's side) on convergence was found by Hering (1868), Donders (1876), Landolt (1876), Allen (1954) and others. We also found it to occur during voluntary convergence using a double-looped scleral search coil (Simonsz and Zee, unpublished results). Why should excyclotropia occur during convergence ? The most likely reason was formulated by Donders (1876): Convergence occurs during near vision and near vision is done mostly in down-gaze. If the primary position for near vision is in down-gaze (for the same reason as why the primary position for far gaze is approximately ahead, as discussed above) excyclotropia will occur when converging from gaze ahead. One can calculate and extrapolate the primary position for near vision from the excyclotropia that occurs during convergence from gaze ahead. Only when converging the eyes by more than 10 deg, corresponding to a target distance of less than 35 cm, excess excyclotropia has been found to occur, not accounted for by assuming a lower primary position for down-gaze, but more than 10 degrees of convergence is of course a very unnatural condition.