EXPLANATION OF OBSERVATIONS 169 



front of his eye. Although we saw the point of light 

 move through relatively long distances both horizon- 

 tally and vertically, no sort of deflection in its pathway 

 could be noted. Berlin's exposition does not hold true 

 for the eyes of the horses, either living or dead, which 

 were examined by us. 



But in the case of some of the horses in whom Berlin 

 had seen the phenomenon for which we sought in vain, 

 he himself tells us, the deflection was very slight. In 

 that case, it would appear, no great advantage would 

 be gained along the lines indicated. But even assuming 

 the degree of deflection to be very great, his theory goes 

 to pieces on the very point it was supposed to explain. 

 A concrete example will make this clear. If Mr. von 

 Osten, standing two feet away from the horse, raised 

 his head }i millimeter (which figure by no means rep- 

 resents 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 milli- 

 meter (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 ; in- 

 deed we can imagine cases in which the circuitous path 



