HERMANN VON HELMHOLTZ 



have been a slight rotation of the eyeball. The coin- 

 cidence always takes place, and thus it is proved that 

 there is an involuntary rotation. Helmholtz also 

 showed that this minute rotation had the advantage of 

 enabling us to judge more correctly than we would 

 otherwise do of the position of external objects. If 

 the eyeball is thus rotated, the optic image will be 

 slightly displaced, but if its new position is parallel to 

 its former position, there is no apparent motion ; but 

 if the rotation is only through infinitely small angles, 

 the eye may move round axes perpendicular to the 

 visual line, and thus the optic images will remain 

 parallel to their first positions. Now Listing had 

 already discovered the law that, in the so-called third 

 positions of the eyeball, it rotates, not round an 

 antero-posterior axis, but round axes perpendicular to 

 the visual line. Helmholtz demonstrated the truth of 

 this law, and, finally, by the calculus of variations, 

 solved the mathematical problem. 



He next proceeded to investigate single vision with 

 both eyes. The two fields of view that seem to be 

 superposed are the corresponding or identical points of 

 Johannes Miiller. But we see things in relief; this 

 may also be done with Wheatstone's stereoscope, and 

 in neither case can we perceive the duplicity of the 

 images. Helmholtz showed, however, that if we sup- 

 pose two objects, say two stereoscopic pictures, to have 

 vertical lines or meridians that are not in reality truly 

 vertical, but each set slightly inclined to the right or 

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