65 



tions are luminous. Hence the Isthmia requires denning power, 

 whilst the Gyrosigma requires penetrating power or large angle of 

 aperture to exhibit the markings ; yet the structures differ only in 

 size. And there can be no doubt that if we could examine the valve 

 of the Gyrosigma under a power as high relatively to the size of the 

 depressions, as that under which we can examine the Isthmia, the 

 same relations being preserved between the angle of aperture of the 

 object-glass and the angular inclination of the refracted rays, the 

 various parts of the depressed and undepressed portions would be 

 equally recognizable in both cases. 



This is also true of fine lines scratched or etched on glass ; for 

 although the coarser lines upon glass micrometers are well seen with 

 an object-glass of small aperture with good defining power and 

 direct light, yet the finest lines upon Nobert's test-slide require 

 penetrating power in the object-glass, and oblique light. Large an- 

 gular aperture or penetrating power is but a very imperfect substitute 

 for defining power an important point which the author believes has 

 not hitherto been noticed, and to which he would invite the earnest 

 attention of object-glass makers. 



The author concludes by observing that his remarks have been 

 principally confined to one class of objects requiring penetrating 

 power, viz. the valves of the Diatomaceae. This has been done ad- 

 visedly, because the scales of insects, which may be regarded as form- 

 ing the type of the other class, involve considerations of a mixed 

 kind, which would have tended to confuse the subject. The longi- 

 tudinal ridges upon the scales of insects, in their relation to pene- 

 tration, may be viewed as representing the undepressed portions of 

 the valves of the Diatomaceae ; and the same explanation will apply 

 to the visibility of both under various conditions. The transverse 

 lines seen upon the scales are not indications of true structure ; but 

 their origin, as also that of the lines seen upon the valves of the 

 Diatomaceae, from circular or angular depressions, does not come 

 within the conditions involved in the principle which it has been the 

 object here to elucidate. It will suffice to say that the true struc- 

 tures producing the appearance of transverse markings upon the 

 scales of insects are best resolved by small angular aperture and good 

 definition. 



It has been assumed also, that the markings upon the valves of 



VOL. VII. H 



