88 Mr. A. Mallock. In*ect Siu/it and tl,,> [Feb. ], 



If the diameter of tlie lenses is reduced, not only is the size of the 

 sphere on which a given number of them would lie reduced, but, 

 since the definition of each lens decreases with the diameter, a less 

 number of lenses will be required to give the maximum definition 

 attainable under the changed circumstances. Thus the radius of the 

 sphere proper for the surface of a composite eye decreases as the 

 square of the defining power of the separate lenses of which it is 

 composed. 



Let A and B (tig. 2) be two adjacent lenses, C and D the sensitive 

 spots of the retina. Let be the angle between the axes of A and B, 

 and x * ne limit of definition of the lens. Then, if x = the image 

 of a distant object in the axis of A will just fall clear of the sensitive 

 point D, but, if x > 0> both C and D will be illuminated by light from 

 the same object. 



Supposing, however, x is less than 0, nothing will be gained in 

 definition unless each lens has more than one sensitive point to 

 operate on. If, then, we find that in actual composite eyes x an( i # 

 are nearly equal, that is, that the difference in the direction in which 

 the adjacent lenses point is nearly equal to the defining power of the 

 lens itself, it becomes almost certain that each lens has only one 

 sensitive point behind it. 



The following table contains measures, recently made by me, of 

 the diameters and angles between the axes of the lenses of various 

 insect eyes, and, although the measure of the angle of view was 

 necessarily rather rough, the agreement of the results, in the larger 

 number of cases, with the supposition above made seems to me 

 sufficiently remarkable. 



In estimating 6 there were two difficulties, one of which was that 

 in many eyes the curvature of the surface was sharp at the margin 

 and that the definition was probably bad there, and another that the 

 line of sight of each lens was not always normal to the outer surface 

 of the eye (fig. 3). Generally, I took the angle between the tangents 



FIG. 3. 



