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 Chcmic, xxvii., 1868: 



Let us, ss (PI. 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_yj'. A ray of light proceeding from 

 .v, when it crosses the linej'jy, instead of proceeding top will be 

 refracted from the perpendicular to q; when it again crosses 

 the surfacejy y, it will be bent towards the perpendicular, and 

 instead of procivding to z will pass to x '. If a series of such 

 planes occur, the course of the ray will be a curve .v q .v'. 



