114 



Angular Aperture of Object-glasses. 



Fin. 



Mr. ToUes has admitted that his judgment is not warped by any 

 theory, I must, however, trouble him with a Httie — a very Httle 



— not more abstruse than 

 that the combination of two 

 quantities produce a third, 

 or that three points make a 

 triangle. Let us take, then, 

 a diameter line of 43, and 

 a median height of 13, and 

 we have here om- angle, 

 Fig. 1, 118^, all that the object-glass can take in by carefully- 

 ascertained dimensions. Thus, in this case, from the fact of plain 

 measurement, an aperture beyond 118° is impossible. 



Were it merely my purpose to point out errors, I might now 

 stop ; but there is no benefit to the community at large unless the 

 relations of cause and effect are investigated. The appearance of ex- 

 cessive aperture has always been- a vexed question with me, having 

 seen numerous instances where extreme rays form no image. On 

 looking obliquely with a magnifier through the front lens of an 

 objective of very large aperture, the image of a flame becomes much 

 elongated or distorted towards the margin, and at last the boundary 

 is a mere indefinite ring of light. I have not believed this to con- 

 stitute true aperture, which must mean image-forming rays only. 



Fig. 2. 



Diagram Fig. 2 will demonstrate how rays beyond the true aper- 

 ture can enter the back lenses so that light may be seen up to the 

 last degree : — a, front lens of object-glass ; h h, rays forming a true 

 limiting aperture of 130^, and entering middle lens of the series on 

 line c. Take a ray, d, incident on front surface at 5° (equivalent to 

 170" aperture). This ray enters the back lenses as false light, but 

 comes -to no focus, or forms no image. If a small stop or narrow 



