of Binocular Vision. 186 



phenomena he observes, I think can be proved. In the first 

 place, I find that if there be any distinction between real and 

 apparent verticality for my eyes, the difference is too small to be 

 detected by the simple observation of lines drawn at right angles 

 with each other. For my own eyes really vertical lines are also 

 apparently vertical, and lines inclined 1 \ Q from verticality are not 

 at all apparently vertical. I have tried several other normal 

 eyes with the same result. But, leaving this aside, in the 

 second place, it is by no means indifferent whether the two 

 halves be combined by a " stereoscope or by squinting." If they 

 are combined by a stereoscope as stereoscopes are usually con- 

 structed, the right half is looked at by the right eye and the left 

 half by the left eye, so that the point of sight and the plane of 

 combination is beyond the diagram; coincidence in this case, 

 therefore, would be a true illustration of Professor Helmholtz's 

 principle. But if they are combined by squinting, the eyes are 

 crossed, and therefore the right eye is looking at the left half and 

 the left eye at the right half of the diagram, and therefore, in 

 Professor Helmholtz's own words, the verticals should " deviate 

 much from a right angle," viz. 2^°. I have tried many eyes 

 and I have yet found none in which the coincidence of the verti- 

 cals of Professor Helmholtz's diagram was perfect when com- 

 bined by means of a stereoscope, i. e. beyond the diagram ; but 

 I have found one person to whom the coincidence seemed to be 

 perfect when the combination was made by squinting. 



It is evident, then, that Professor Helmholtz's principle can- 

 not explain the stereoscopic coincidence by squinting in his own 

 experiment. I myself believe that if the coincidence takes place 

 only by squinting (as in the case mentioned above), it can only 

 be explained by rotation of the eyes inward. It is true that in 

 this case the horizontals ought to cross also ; but Professor Helm- 

 holtz himself admits that such is sometimes the fact, but attri- 

 butes it to fatigue. " After keeping the eyes," he says, " a long- 

 time looking at a near object, as in reading or writing, I have 

 found that the horizontal lines cross each other ; but they became 

 parallel again when I had looked for some time at a distant object." 



On reading Professor Helmholtz's lecture and finding his re- 

 sults so different from my own, I immediately tried his figure 

 by squinting, but found the verticals cross one another at an in- 

 clination much greater than in the diagram itself, while the ho- 

 rizontals also crossed but at a less angle. On turning the figure 

 upside down, however, the verticals coincided perfectly when the 

 proper distance was obtained, though the horizontals crossed as 

 before. All these phenomena are easily explained by rotation of 

 the eyes outward. To test the question still more thoroughly, I 

 then constructed other diagrams in which both verticals and 



Phd. Mag. S. 4. Vol. 38. No. 254. Sept. 1869. 



