572 THE SENSES AND SENSORY ORGANS. 
there is undoubtedly binocular vision, and possibly for very 
near objects this may be stereoscopic. I do not know, nor 
does it appear to me likely that we shall ever know, whether 
such binocular vision has any physiological importance amongst 
the Arthropoda. 
8. FURTHER REMARKS ON THE OPTICAL PROPERTIES OF 
THE COMPOUND EYE. 
It has been thought unadvisable to complicate the foregoing 
section with certain problems of a somewhat more difficult 
character, which will occur to some who are more fully 
acquainted with the science of optics, than is needed for a 
perusal of the thesis which I have endeavoured to establish. 
These problems will be now examined, and although they 
necessarily require some mathematical knowledge, every 
endeavour has been made to render the explanations of the 
views advocated as simple as possible. The student of evolu- 
tion will probably be chiefly interested in the conclusions 
arrived at by the author, as the result of Exner’s theory of re- 
fractive cylinders, which will be found upon page 574. 
a. On the Optical Properties of Refractive Cylinders, and the 
Probable Relation of the Several Types of Compound Eye 
in the Arthropoda. 
The following account of the optical properties of a refractive 
cylinder is taken from Exner [252]; it is extracted by him from 
his brother’s paper in Ann. f. Physik und Chemie, xxvii., 1868 : 
Let ss, ss (Pl. XL., Fig. 2, B) be a cylinder, the refractive 
index of which is a maximum in its axis; let the refractive 
index diminish on the line yy. A ray of light proceeding from 
x, when it crosses the line yy, instead of proceeding to will be 
refracted from the perpendicular to q¢; when it again crosses 
the surface y y, it will be bent towards the perpendicular, and 
instead of proceeding to z will pass to x’. Ifa series of such 
planes occur, the course of the ray will be a curve x q x’. 
