Kinematics of the Eye. 691 



There is nothing in the arrangement of the muscular attach- 

 ments of: the eyeball to suggest this particular law as natural 

 or advantageous. An explanation must therefore be sought 

 -elsewhere. The question is discussed at length by Helmholtz 

 from the empirical standpoint*. The argument is long and 

 intricate. The following investigation retains the central 

 idea, which is interesting on mathematical as well as other 

 grounds, but is simplified by the introduction of an auxiliary 

 -assumption which has (I think) something to be said for it. 



The assumption is that in the primary position of the 

 eyeball the atropic line, which necessarily exists for infini- 

 tesimal displacements, coincides with OA ; i. e. that the 

 instantaneous axis for any small displacement is perpendicular 

 to OA. In the first place, a horizontal displacement of the 

 visual axis requires only the action of the lateral muscles 

 (rectus interims and externus), and involves therefore only 

 rotation about a vertical axis. The atropic line is accordingly 

 assumed to lie in the horizontal plane through OA. Its posi- 

 tions in the two eyes must moreover obviously beysymmetr.ical. 

 ISText suppose the visual axis to be slightly displaced vertically 

 from OA. If the atropic line did not coincide with OA, 

 this displacement would involve rotations of the two eyes 

 whose components about OA would have opposite senses. 

 This would be disastrous for binocular vision in the most 

 important part of the field. 



Let us next suppose that the gaze is directed to a point P 

 of an object of small angular dimensions; let Q, P, S, ... 

 be adjacent points of the object; and let p, q, r, s, ... be the 

 points of the retina respectively affected. If the gaze be 

 shifted from P to Q, this means that a certain impression is 

 now transferred from q to p, whilst others are transferred 

 from r to r' (say), 5 to *', and so on. For the correct inter- 

 pretation of visual sensations it would be desirable that 

 exactly the same transfers from r to r', s to s', &c. should 

 be consequent on the transfer from q to />, whatever the 

 initial direction of the visual axis. When the object is near 

 the centre (A) of the field this condition is sensibly fulfilled, 

 but in excentric positions a complication is introduced by 

 the component rotation about OP which attends the transition 

 from P to Qf. 



Following Helmholtz we may regard any such component 



* Loc.cit. The mathematical calculation appeared in the first edition 

 of the Physiologische Optik. A revised version is given in Wiss. Abh. 

 vol. ii. p. 396 (1883). 



t An attempt is here made to condense the rather lengthy argument 

 of Helmholtz, wlii.lt should he studied in the original. 



