558 THE SENSES AND SENSORY ORGANS. 
seeking of the infinite scarcely compatible with the practical 
needs of life. 
Yet it appears that Notthaft’s conclusions are consistent with 
Grenacher's theory of a minimal pencil of parallel rays only 
acting upon a retina. 
If Notthaft’s paper had been written to prove the untenable 
character of Miiller’s hypothesis from an optical point of view, 
it would be intelligible; but if I understand it, Notthaft is 
serious and believes that he has aided in proving its validity. 
That he had doubts in his own mind is clear, for he quotes 
Bates, who asserts that it was long before he could distinguish 
Humming-birds from the Humming-bird Hawk-moth, Macro- 
glossa titan ; and asks ‘If it is possible that one of these little 
creatures can see well and the other hardly at all?’ He care- 
fully proves that insects see as well as birds, or appear to do 
so; and yet he apparently tries to convince himself of the truth 
of his ‘darkness hypothesis,’ as he is satisfied that the compound 
eye is constructed as Grenacher describes it, and that no other 
hypothesis can explain its function on principles which are 
optically possible. 
Effect of the Subcorneal Image.—The existence of a subcorneal 
image, in itself, renders Miiller’s theory completely untenable. 
Since the conditions of vision under the theory are most perfect 
for objects seen by pencils of parallel rays, and every lenticular 
system which tends to render the rays of light either convergent 
or divergent would render vision less distinct, and as the small 
axial pencil only could be effective, since the power of this pencil 
would be rendered less with every increase of convexity in the 
lens, it is evident that the existence of a lens would be a dis- 
advantage and not a benefit to the possessor of a compound eye. 
It has been suggested that the lens acts as a condenser, and 
causes a larger pencil to act upon the nerve end organs; but 
it is evident that this could only be effected by an increase of 
the angular aperture of the lens and a corresponding deficiency 
in the acuity of vision, as it is only by collecting the light from 
a large surface and condensing it upon a small focal point that 
a condensing lens is effective. 
