Derivation of the angle of torsion of the eye

The angle of torsion of the eye, that is the amount by which the eye rotates about its anterio-posterior axis, changes with the direction of the line of fixation. If the eye can be considered as a rigid body under an elaborate system for constraints its motion can be described by the laws of kinematics. The techniques of linear algebra can then be used to derive an explicit relationship between the angles defining the direction of fixation and the angle of torsion of the eye. The angle of torsion can then be expressed as a function of the angle of rotation of the eye and the direction cosines of the axis of rotation. However, under conditions in which Listing's Law holds these angles, are well defined functions of the angles defining the direction of fixation, and so the angle of torsion, in this case, can be expressed as an explicit function of this direction.