Kinematics of the Eye. 689" 



But in order that this type of motion may be possible, the 

 atropic line, being at right angles always to the axis of 

 rotation, must describe the parallel great circle (MN). It' 

 P be any point on the small circle, and OX the corresponding- 

 position of the atropic line, we have seen that AX = XP. 

 As a particular case AM = MC, in the figure, and it follows 

 that the small circle must pass through the 'occipital 

 point'' 12 of the spherical field, i. e. the point diametrically 

 opposite to A. Conversely it appears that as the fixation 

 point describes any circle through 12 the eye rotates about 

 a fixed axis, and the required condition is fulfilled. 



The various circles through 12 are called by Helmholtz. 

 'direction circles,' since they correspond to lines in the 

 external field which have apparently a constant direction. 

 Moreover it appears that circles which have a common 

 tangent line at 12 will correspond to lines having the same 

 direction. It is of course only the portions of the circles 

 within a moderate distance (say 40° at most) from A which 

 have any real significance. 



An interesting alternative proof of the preceding result 

 may be given. Let the spherical field be projected from 

 12 on the tangent plane at A. In this projection let PP r 

 represent an element of a line of constant direction, and 

 let AA be the line whose image falls on the same linear 

 element of the retina when the gaze is directed to A. By 

 hypothesis AA' has the same direction whatever the position 

 of P on the line considered. The position of the eyeball 



when the visual axis points to P is derived from the primary 

 position by a rotation now represented by the straight line 

 AP, by Listing's law. Since angles are unaltered in stereo- 

 graphic projection, it follows that the angles P'PQ, A'AQ 

 in the figure are equal. Hence PP' is parallel to AA' ; the 

 locus of P is a straight line ; and the corresponding locus 

 in the spherical field is a circle through 12. 



The lines in the external field which are apparently straight 

 are accordingly those which project from into direction 



