HELMHOLTZ IN HEIDELBERG 



left, and if we look at these through a stereoscope, the 

 'squinting' lines accurately coincide, thus showing 

 that in double vision it is not the real vertical meridians 

 of the fields of view that coincide, but the apparently- 

 vertical meridians. The horizontal meridians always 

 coincide. Thus while the retinal horizon is horizontal 

 for both eyes, the apparently vertical meridians are not 

 perpendicular to it, as had been hitherto supposed, but 

 they diverge at their upper extremity, at an angle of 

 from 2 22' to 2 33'. Corresponding points are 

 therefore equally distant from each retinal horizon, 

 and from each apparently vertical meridian. This 

 led to the examination of the true geometrical form 

 of the horopter, by which is meant the locus of 

 those points of space which are projected on cor- 

 responding retinal points, and he found that it is 

 generally a line of double curvature produced by the 

 intersection of two hyperboloids, that is to say, it is 

 a twisted cubic curve formed by the intersection of 

 two hyperboloids which have a common generator, 

 and in some special cases it is a combination of two 

 plane curves. 1 The curves pass through the nodal 

 points of both eyes. An infinite number of lines 

 may be drawn from any point of the horopter so as 

 to be seen single, and these lines lie on a cone of the 

 second order whose vertex is the point. Helmholtz 

 also showed that when we look at the horizon, the 



1 The mathematical demonstration is given in Heat/is Geometrical 

 Optics, p. 233. Cambridge, 1887. 



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