530 Transactions of the Society. 



repeatedly, from 1830 onwards, been published in microscopical 

 text-books. These figures represent the curvature of the objective 

 image reversed by the field-lens of the Huyghenian eye-piece, 

 whereas in reality it is increased in its original direction and not 

 reversed at all. Fig. 86 shows what really takes place ; the large 

 dotted arrow represents the image due to the objective alone, and 

 the small one shows in what way it is altered by the influence of 

 the field-lens. One would have thought that a mistake such as 

 that mentioned above would long ago have been corrected, because 

 one would naturally have expected that the subject would have 

 been explained in the text-books on geometrical optics, all of 

 which deal with the Huyghenian eye-piece. The question, how- 

 ever, is evaded ; true, the position of the image arising from the 

 extreme marginal pencils is diagramatically indicated by arrows 

 drawn perpendicular to the axis ; this by itself is of small impor- 

 tance ; what everyone wants to know, and what no text-book 

 explains, is the relation of this point to that formed by the central 

 pencil. If, for instance, the point where the central pencil cuts 

 the axis, is nearer the field-lens than the position of the smaller 

 arrow in the text-book figure, then the image is curved so as to be 

 concave to the eye-lens, and therefore, the resultant image pre- 

 sented to the eye will be plane and well-defined at the edges, but 

 if, on the other hand, this point is further from the field-lens than 

 the smaller arrow, the image will be convex towards the eye-lens, 

 and the final image will be indistinct at points not far from the 

 axis. This secon.d case is what actually takes place. So impor- 

 tant is the subject, that I thought it worth the labour of making 

 an exact trigonometrical trace of the excentrical pencil passing 

 through the plano-convex field-lens of the 5-power Huyghenian 

 eye-piece for the short tube as given in Table II ; the only 

 difference being that the diaphragm was slightly widened out, so 

 that a pencil more divergent from the axis might be traced. It is 

 not my intention to trouble you with the details of the work 

 beyond mentioning that the limit of accuracy was carried out to 

 the second decimal place of a second of arc, and the sides of the 

 triangles were true to the eighth decimal place. By this means it 

 was found that the focal point of the central pencil was • 0403 of 

 an inch farther from the field-lens than that of the excentrical. 

 In brief, the image was curved, as is diagrammatically shown by 

 the small arrow in fig. 86. 



The diameter of the back focal plane of the objective was 

 assumed to be 0*6 inch, which is about that of the Zeiss 24 mm. 

 apochromat. 



It will interest mathematicians to know that the trace of the 

 second ray of the excentrical pencil only differed from that given 

 by the intersection of a line drawn in the usual manner from the 

 second Gauss point by • 007 inch. 



