Royal Society. 215 



being sufficiently oblique, no part of them is refracted beyond the 

 angular aperture of the object-glass ; the second, being more oblique, 

 are refracted out of the field by certain parts of the object and not 

 by others, and thus contribute to render its different parts distin- 

 guishable by contrast of darkness and illumination. The first set of 

 rays, by illuminating all parts of the object, tend to diminish this 

 contrast, and consequently do not add to but impair the discrimina- 

 tive power of the object-glass for the fine markings of transparent 

 objects, and accordingly these are rendered more distinctly visible 

 by intercepting the less oblique rays by means of a central stop. 



It has been here assumed that the oblique light requisite for the 

 display of the markings upon objects is separated into two sets of 

 rays by refraction ; but the author observes that it might be ques- 

 tioned whether they are not separated by reflexion. There can be 

 no doubt that the latter is not generally the case ; perhaps the most 

 important reason which may be assigned for this is, the considerable 

 comparative breadth of the luminous portions of the valve of the 

 Gyrosigma for instance. On transmitting unilateral light obliquely 

 through the valve of an Isthmia, in which the depressions are so 

 large, in such manner that part of it is reflected by portions of them, 

 it is easily seen how small the amount of reflected light is ; and this 

 because the surface of the depressions is curved, and thus the por- 

 tions inclined at the requisite angle for reflexion are also very small. 

 As the amount of light reflected is so small in this case, it would 

 be inappreciable in that of the Gyrosigma, in which the depressions 

 are so exceedingly minute. In fact, attention to this point affords 

 a ready means of distinguishing whether an object is illuminated by 

 reflexion or refraction. 



The author next considers the relation of the penetrating power of 

 an object-glass to its defining power. Penetrating power depends 

 upon angular aperture, and consequently on oblique light. The 

 question whether there be any essential difference between pene- 

 trating and defining power is best answered by experiment. If we 

 take a fragment of the valve of an Isthmia and examine it under a 

 high power of small aperture, all the parts are very distinctly seen 

 by the ordinary light of the mirror; and the various depths of shadow 

 of the different parts of the depressions and the undepressed por- 

 tions render these also clearly distinguishable ; and when an object- 

 glass of very large aperture is used, the distinctness is rather im- 

 paired than improved. But if we examine a fragment of the valve 

 of a Gyrosigma, and this requires an object-glass of large aperture 

 to render the markings visible, no distinction of the various parts of 

 the depressions and the undepressed portions is visible ; all we see is, 

 that the depressions as a whole are dark and the undepressed por- 

 tions are luminous. Hence the Isthmia requires defining power, 

 whilst the Gyrosigma requires penetrating power or large angle of 

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

 size. Aud 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 



