Kinematics of the Eye. 687 



Hence the transition from P to any other position what- 

 ever, such as Q or lit in the figure, is represented by some 

 great-circle arc through X ; i. e. it is equivalent to a 

 rotation about some axis at right angles to OX. This line 



Ficy. 1. 



OX is therefore called by Helmholtz the ' atropic line ' for 

 the position P. He remarks, further, that the existence of 

 an atropic line in the case of infinitely small displacements 

 from P is an immediate consequence of the limitation to two 

 degrees of freedom, without restriction to any particular 

 law, such as Listing's. For if 01, OJ be the instantaneous 

 axes for two such displacements, any other displacement 

 from P will be compounded of rotations about these lines, 

 and will therefore consist of a rotation about some axis in 

 their plane. We have thus an 'atropic line/ viz. the normal 

 to this plane. 



A straight line in the external space is represented in the 

 spherical field by a great circle. If this circle passes through 

 the primary point A, then as the fixation point travels along 

 the line the successive portions are imaged on identically the 

 same elements of the central region of the retina *, in virtue 

 of Listing's law. In other words, the various parts of the 

 line appear to be, as they actually are, exactly superposable. 

 It is obvious, moreover, that Listing's is the only law which 

 fulfils this condition. The same statement does not, however, 

 hold with regard to straight lines which do not meet the 

 primary position of the visual axis. Exact superposition in 

 the case of all straight lines is in fact intrinsically impossible, 



* It is not necessary for the purposes of the Argument to assume that 

 the retina has any special form, spherical or other. 



313 2 



