198 Prof. J. LeConte on some Phenomena 



its parts coincides completely with the horizontal plane on which 

 we stand" 



These conclusions of Helmholtz are the result of refined ma- 

 thematical calculations based entirely upon the supposed constant 

 difference between the real and apparent vertical. If this principle 

 be true for all normal eyes, then it is probable that Helmholtz's 

 conclusions in regard to the form and position of the horopter 

 are also true for those cases in which the point of sight is at a 

 considerable distance, and in which, therefore, the rotation of 

 the eye is very small. I am not able to test all of Professor 

 HelmhohVs conclusions by calculations based upon this prin- 

 ciple, but I easily see that the position of the horopter lying 

 along the ground is the necessary consequence of a difference oi 

 1J° between the real and apparent vertical when the eyes are in 

 their primary direction. For if a line be drawn from each pupil 

 downward, making an angle of 2\° with each other or of 1£° 

 with the vertical, they will intersect each other at the distance 

 of about five feet below the eyes or about the feet of the observer 



standing erect. Now if these two lines be placed thus \ / be- 

 fore the observer whose eyes are in the primary direction, it is 

 plain that their stereoscopic combination would be a line lying 

 along the ground to infinite distance. If the difference between 

 the real and apparent vertical be less than 1^°, then the distance 

 below the eyes of the horopteric plane will be greater. We 

 have already show"n that if there be any such difference in our 

 own eyes, it cannot be more than lO* ; in this case the horopteric 

 plane will be at least 35 to 40 feet below the eyes. But Pro- 

 fessor Helmholtz takes no account of rotation of the eyes on the 

 optic axes, which greatly affects the form and position of the ho- 

 ropter when the point of sight is near; and we believe that it is 

 only when the point of sight is near that the form and position 

 of the horopter is of any practical importance in vision, for it is 

 only then that the doubling of images lying out of the horopter 

 is perceptible. 



It has been with much hesitation that I have ventured to cri- 

 ticise the conclusions of so distinguished a physicist. My ability 

 to do so, if well founded, I attribute entirely to a facility in the 

 use of the eyes such as I have never seen equalled in the case of 

 any other person. 



Although I believe Meissner has arrived at truer results than 

 any one who has yet written on this subject, yet I think his me- 

 thod very unsatisfactory. I have wondered at the skill and 

 patience which could attain such true results by such imperfect 

 methods. I have tried Meissner's experiments without any sa- 

 tisfactory results, and I confess I commenced these experiments 



