6.8'8 



Prof. Horace Lamb on the 



apart altogether from the validity of Listing's law. For 

 consider any triangle PQR of the spherical field, and imagine 

 the fixation point to travel round it in the order of the letters. 

 In order to satisfy the above condition of exact superposition 

 the movements or! the eye must consist of successive rotations 

 represented by the arcs PQ, QR, RP. By a beautiful 

 theorem due to Hamilton *, the result would be a rotation 

 about OP through an angle equal to the spherical excess of 

 the triangle PQR. This is incompatible with Bonders' 

 fundamental principle that the position of the eyeball depends 

 only on the direction of the visual axis. 



It is therefore a matter of interest to ascertain what lines, 

 if any, in the external field satisfy the requirement of super- 

 position as tested by the retinal image. Now if the eye can 



rotate continuously about a fixed axis (LT) through 0, the 

 visual axis will trace out a small circle on the spherical field, 

 and the projection of this from on any plane (or other 

 surface) will evidently give a line having the desired property. 



* 'Lectures on Quaternions/ p. 335. The theorem is most easily 

 proved by examining the successive positions of the great-circle arc 

 which is initially coincident with PQ. 



