24 Transactions of the Society. 



What is the difference between these two cases ? The small 

 dissipation circles in the first case may still be capable of affording 

 a pretty distinct vision of the upper layer at the same time as the 

 lower, and we say that the depth of the object is within the range 

 of the depth of distinct vision for pencils of narrow aperture. 

 The broad dissipation circles resulting from the wide pencils of the 

 full aperture will in all probabihty render the image of the upper 

 layer very indistinct, so that the image of the ivliole object will 

 appear indistinct also. The causa efficiens of this indistinctness is 

 simply too great a depth of the object compared with the small 

 depth of vision attendant upon a wider aperture. If we take a 

 similar sohd object, but of much smaller depth, we should see its 

 upper and lower layers in sufficient distinctness, notwithstanding 

 the wide aperture. 



Consequently the indistinctness of an object which is not quite 

 flat if observed with a wide aperture, does not arise from any 

 dissimilarity of the images by axial and by oblique pencils, but 

 solely on account of the reduction of the depth of vision. 



Suppose now (3) an image projected by narrow ollique 

 pencils a m and yS m through a marginal or intermediate part of 

 the aperture. The sharp images of hoth layers A B and Aj, B,, 

 will be exactly the same as the sharp images by the axial pencils 

 a a and /3 a, or the sharp images by the whole pencils a and ^. 

 But as these images occur at different planes they will show a 

 parallactic displacement. If the ocular and the eye are focused 

 to the level of A^* B*, the points A* and B* will appear projected 

 to the points a* h* and will be seen as dissipation circles with 

 those points as centres. We have once more always similar images, 

 only displaced horizontally. 



This must give rise to a mode of projection of solid objects 

 which is essentially different from the ordinary perspective projec- 

 tion under oblique vision. Suppose the die (fig. 1) delineated at 

 an oblique direction of 60°. A true perspective image, such as 

 would be obtained by an eye receiving it in 

 ^i<^- 6- the direction r, or if the Microscope were 



„i ,,--;. directed to it in this direction, would give 

 ^z^^'''''''''^' the projection on a ground plane perpen- 



'-''' P&'' --''''^ ^*^*^ ^^ ^^^ ^^^^ ^' "^^^ *^® image of 

 d^-_<:l.c.r:g!^.dlX '^'' the die as depicted by the oblique pencils 



in an objective of 120° aperture-angle will 

 be a projection to a ground plane perpen- 

 dicular to the axis of the Microscope (fig. 6), 

 and not to the rays r. Both surfaces, a h and c d, will therefore 

 be projected with their true diameter, but displaced horizontally, 

 and not shortened as in fig. 1. 



If we compare now the image of the solid object by the oblique 



