194 Prof. Helmboltz — Normal Motions of the [April 14, 



ing to tlie law of Bonders ; and in altering this rotation we should judge 

 the position of external objects wrongly. 



The same will take place when we change the direction of the visual line. 

 Suppose the amplitude of such motions to be infinitely small ; then we may 

 consider this part of the field of vision, and the corresponding part of the 

 retina on which it is projected, as plane surfaces. If during any motion of 

 the eye the optic image is displaced so that in its new position it remains 

 parallel to its former position on the retina, we shall have no apparent mo- 

 tions of the objects. When, on the contrary, the optic image of the visible 

 objects is dislocated so that it is not parallel to its former position on the 

 retina, we must expect to perceive an apparent rotation of the objects. 



As long as the motions of the eye describe infinitely small angles, the eye 

 can be moved in such a way that the optic image remains always parallel 

 to its first position. For this end the eye must be turned round axes of 

 rotation which are perpendicular to the visual line ; and we see indeed that 

 this is done, according to the law of Listing, when the eye is moving near 

 its primary position. But it is not possible to fulfil this condition com- 

 pletely when the eye is moved through a wider area which comprises a 

 larger part of the spherical field of view. For if we were to turn the eye 

 always round an axis perpendicular to the visual line, it would come into 

 very different positions after having been turned through different ways to 

 the same final direction. 



The fault, therefore, which we should strive to avoid in the motions of 

 our eye, cannot be completely avoided, but it can be made as small as pos- 

 sible for the whole field of vision. 



The problem, to find such a law for the motions of the eye that the 

 sum of all the rotations round the visual line for all possible infinitely 

 small motions of the eye throughout the whole field of vision becomes a 

 minimum^ is a problem to be solved by the calculus of variations. I have 

 found that the solution for a circular field of vision, which corresponds 

 nearly to the forms of the actual field of vision, gives indeed the law of 

 Listing. 



I conclude from these researches, that the actual mode of moving the 

 eye is that mode by which the perception of the steadiness of the objects 

 through the whole field of vision can be kept up the best ; and I suppose, 

 therefore, that this mode of motion is produced by experience and exercise, 

 because it is the best suited for accurate perception of the position of ex- 

 ternal objects. 



But in this mode of moving, rotations round the visual line are not com- 

 pletely avoided when the eye is moved in a circular direction round the 

 primary position of the visual line ; and it is easy to recognize that in such 

 a case we are subject to optical illusions. 



Turn your eyes to a horizontal hue situated in the highest part of the 

 field of vision, and let them follow this line from one end to the other. 



