by no means represents the
extreme values that were obtained), then in the horse's retinal image
every point of the man's head would move through a distance of 0.0025
millimeter--assuming the horse's eye to be free from astigmatism and
assuming its focal distance to be 25.5 millimeters. If, however, other
conditions remaining the same, we presuppose an extreme form of
astigmatism, one in which the path of the retinal image is not a
straight line, but is deflected into a semicircle, then each point would
pass through a distance of nearly 0.004 millimeter. If the sensitive
retinal elements have a diameter of 0.002 millimeter (as Berlin,
somewhat inexactly, states), then from two to four elements would be
stimulated in case there were no astigmatic deflection. But in case the
deflection did take place, it would not necessarily involve more
elements, as can be seen by making a simple graph; indeed we can imagine
cases in which the circuitous path would involve even fewer elements
than the straight one. And finally, when the movement which the horse is
to perceive, does not occur in a straight line but in the form of a
curve, (which will generally be the rule), then the astigmatism will
tend in many cases to decrease the curvature of the image's path on the
retina, and sometimes even obviate it entirely. In all these cases, on
Berlin's own theory, the perception of the movements would be hindered
rather than aided.[AA]

[Footnote AA: For the benefit of specialists I would say the
following in addition to the more general remarks just made. For the
most part, the determinations of refraction made on the eye of the
horse are still rather unreliable. In sciascopy there is a dispute
among investigators concerning ambiguous shadows, and in the use of
the refraction-ophthalmoscope no definite region of the eye's
background has been adhered to by the various investigators. It
appears that Riegel, whose diligent researches mentioned on page 164
were published in 1904, knew nothing concerning the round area in
the horse's eye, discovered by I. Zuern[42] in 1902. Also, if so
great a degree of astigmatism is really the rule as is emphasized
especially by Hirschberg[43] and Berlin,[44] then the simple
refractive index usually given--sometimes within a half
diopter--would be meaningless. Berlin[45] and Bayer[46] believe the
vagueness of the retinal image resulting from the asti