802 Transactions of the Society. 



will admit of an equal degree of perfection of image with a greater 

 aperture in objectives for homogeneous-immersion than in water- 

 immersion or dry lenses — which is also in accordance with the 

 facts. 



(c) Another point which deserves particular attention in 

 every attempt to assign the proper relation of aperture to power, 

 relates to the great influence of the illumination and the 7iature of 

 the object on the visibihty of the residual defects of the objectives. 

 If we could determine numerically the inherent angular dissipation 

 of the rays (the angle u) for a given objective, either by computation 

 or by experiment, the value of u would then indicate the visual angle 

 of the circles of indistinctness in an image which is obtained under 

 the normal amphfication of the objective (if, for instance, the 

 objective were used without an eye-piece, as a hand-magnifier) and 

 J] = v^l the same visual angle for a super-amplification of v — but 

 both elements under the obvious supposition, that the whole pencil 

 of light which is collected by the objective, is under comparison, or 

 the full area of the aperture effective at the same time. If in any 

 particular case a portion only of the clear aperture should be utilized 

 by the delineating pencils, the actual dissipation of the light will of 

 course be confined to more or less small spots than would corre- 

 spond to the angles u and U, and would accordingly become less 

 apparent. In the practical use of the Microscope we always have 

 very variable conditions, according to the illumination in use and 

 the structure of the objects under observation. With very low 

 apertures the range of difference is not so great, it is true, 

 because the illuminating cone of light will generally fill the whole 

 aperture, or at least the greater part of it. But with wide-angled 

 objectives the incident beam from the illuminating apparatus is — 

 and in most cases must be — confined to a much narrower angle 

 than the aperture of the system. How much of the aperture is 

 actually utilized by the deUneating pencils will entirely depend on 

 the dissipation of the incident rays by the structure of the object — 

 in particular the difiraction effect of the structure ; and according 

 as the illuminating cone, after its transmission through the object, 

 is spread out to a smaller or greater angular extension, smaller or 

 greater aberration-circles will disturb the image. Thus it may 

 happen that with one kind of preparation an objective may bear a 

 deep ocular very well, whilst with other objects a great deterioration 

 of the image becomes visible under even a lower ocular. Objects 

 which show a regular striation, and in general all regular periodic 

 structures, are particularly insensible to the residuary defects of the 

 objectives, because they produce only a limited number of isolated 

 diffraction-beams, and thus leave the greatest part of the objective's 

 aperture entirely unemployed. In observing an object with only 

 one set of parallel lines which are near the limit of the resolving 



