1894.] Defining Power of Composite Eyes. 87 



diameter of the holes should not be less then 2000 wave-lengths of 

 light, say -^ in. Hence the thickness of the shell will be 

 7000 X Jy in., or 23 ft. 



The radius of the sphere may be determined by the condition that, 

 if the picture is to be continuous, the adjacent holes must just be in 

 contact at the internal surface of the shell, that is to say the diameter 

 of the hole, viz. : % in., must subtend 1 min. at the internal radius of 

 the shell, which makes this radius, therefore, 11 ft. 6 in. 



Thus an eye of this construction and power of definition would 

 consist of some part pf a spherical shell of 34 ft. 6 ins. external 

 radius, and 23 ft. thick, perforated with radial holes -^ in. in 

 diameter, and with their centres about apart on the external 

 surface. 



If still keeping 1 min. as the limit of definition, we substitute the 

 arrangement actually found in composite eyes, and in place of the 

 long tunnels in thick shell, we use short tunnels with a lens at the 

 outer end of each tunnel, and a diaphragm at the inner end, pierced 

 with a small central hole (fig. 2), the proportion of the eye will be 



FIG. 2. 



determined in the first place by the diameter of the lens which will 

 just define 1 min., and secondly by making that diameter subtend 

 1 min. at the centre of the sphere. 



Now the size of the image of a point formed by a lens (as seen 

 from the optic centre of the lens) is inversely as the diameter of the 

 lens, and it takes a lens 4 ins. in diameter to define 1 second, i.e., to 

 separate points 1" apart ; hence the lens which will just define 1 min. 

 is - or 0'066 in. in diameter. 



The radius at which 0'066 in. subtends 1 min. is about 19 ft. 



It is evident, therefore, that no composite eye of practicable 

 dimensions, acting as supposed above, could be made to give defini- 

 tion even approaching that of the human eye. 



much less than r the diameter of the hole may be is, to some extent, a matter of 

 judgment depending on the degree to which it is considered desirable to reduce the 

 intensity of the diffracted light. 



H 2 



