March 15. 1894] 



NA TV RE 



473 



axis of the hole, which angle is of course equal to the diameter 

 of the hole -^ half its length. 



It is interes'ing to see what proportions would have to be 

 given to an eye of this kind if the definition is to be as good as 

 that of the human eye. 



The limit of definition in this case being i min., the holes 

 would have to be 7000 diameters long (since i min. is nearly 



oc. 



Fig. I. 



1/3500), and in order that diftVaction may not inteifere 

 materially with the result, ^ the diameter of the holes should not 

 be less than 2000 wave-lengths of light, say 7V in. Hence the 

 thickness of the shell will be 7000 x .j'^ 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. ^'^5 in., must subtend i 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 of a spherical shell of 34 ft. 6 ins. 

 external radius, and 23 ft. thick, perforated v?ith radial holes 

 jV in. in diameter, and with their centres about ^ apart on 

 the external surface. 



If still keeping i 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 prc- 



The radius at which 0066 in. subtends i min. is about 19 ft. 



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

 dimennons, acting as supposed above, could be made to give 

 definition even approaching that of the human eye. 



If the diameter of the 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 sutfice of a com- 

 posite eye decreases as the square of the defining power of the 

 separate lenses of which it is composed. 



Let A and B(Fig. 2) be two adjacent lenses, c and D the sen- 

 sitive spots of the retina. Let B be the angle between the axes 

 of A and B, and x ^he limit o*" 'efinition of the lens. Then, 

 if X = 9, the image of a distant oDJect in the axis of A will just 

 all clear of the sensitive point D, but if x-'^. both c and D 

 will be illuminated by light from the same object. 



Supposing, however, x is less than Q, nothing will be gained 

 in definition unless each lens has more than one sensitive p )int 

 to operate on. If, then, we find that in acUial composite eyes x 

 and Q are nearly equal, that is, that the difference in the direction 

 in v/hich the adjacent lenses point is neaily 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 ihat the line of sight of each lens was n^t always normal 

 to the outer surface of the eye (Fig. 3). Generally I took the 



Fig. 



portions of the eye will be determined in the first place by the 

 diameter of the lens which will just define i min., and secondly 

 by making that diameter subtend i 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 len^) is inversely as the diameter of 

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

 i.e. to separate points i" apart ; hence the lens which will just 

 define i min. is ij\ or o'o66in. in diameter. 



' It may be shown that the hole should not be much smaller than the first 

 Huvghens zone of a system for which, if A/r= r/R, R = the length of the 

 hole, A and /-being the wave-length of light and the radius of the zonerespect- 

 ively. How 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 

 coDiidered desirable to reduce the intensity of the diffracted light. 



angle between the tangents to the surface at the ends of a 

 measured chord, choosing the chord so that the surface outside 

 it should have faiily unilorm curvature. The length of the 

 chord was usually about three-quarters, or a little more, of 

 that of the eye. 



Taking the length of the chord as /, and r as radius of the 

 sphere which best represents the surface of the eye, we have for 

 the angle of view 0, 



sin 40 = IjZr, 



and - dfr, where d is the diameter of the lens 



hence = djb . 2 sin |0 



The other columns of the table explain themselves. 



On the whole, I think it must be concluded that insects do 

 not see well, at any rate as regards their power of defining dis- 

 tant objects, and their behaviour certainly favours this view ; 

 but they have an advantage over simple-eyed animals in the 

 fact that there is hardly any practical limit to the nearness of 

 the objects they can examine. With the composite eye, indeed, 

 the closer the object the better the sight, for the greater will be 

 the number of lenses employed to produce the impression ; 

 whereas in the simple eye the focal length of the lens limits the 

 distance at which a distinct view can be obtained. 



The best of the eyes mentioned in the table would give a pic- 

 ture about as good as if executed in rather coarse wool-work 

 and viewed at a distance of a foot ; and, although a distant 



NO. [272, VOL. 49] 



