DETERMINATION OF THE ANGLE OF APERTUKE. 177 



the size of the plate is rendered more convenient, and the illu- 

 mination is stronger. 



Whichever method is employed, the determination is but ap- 

 proximately accurate, and with higher powers the possible error 

 may attain two degrees. It follows that light and shadow in the 

 field of view, or on the illuminated screen, do not appear sharply 

 defined on account of the various losses which the marginal rays 

 suffer in fact, they pass gradually into each other, so that the 

 limiting points must always be somewhat arbitrarily chosen. This 

 disadvantage is not practically important, since it is perfectly 

 immaterial whether the angle of aperture of a Microscope amounts, 

 for instance, to 70 or only 69. It is absurd, as Harting justly 

 remarks, to record the angle of aperture, as many have done, up to 

 a fraction of a degree. And it is just as absurd as it is unpractical 

 to manufacture objectives with angles of aperture of 160 and 

 upwards, if at least 40 to 50 belong to a totally useless peripheral 

 part of the system, as obtains in certain objectives of English 

 manufacture. 



Finally, we remark, that in those objectives which are provided 

 with correction-adjustment, for use with immersion, or to com- 

 pensate for different thicknesses of the cover-glass, the angle of 

 aperture is necessarily altered if the distance of the lowest lens 

 from the next one is increased or diminished, because an alteration 

 of the focal length of the whole system of lenses is produced 

 thereby. On the other hand, the influence which the eye-piece 

 magnification exercises upon the angle of aperture is by no means 

 so considerable as would be supposed from the representation of 

 Harting. The magnification itself does not come into the con- 

 sideration, but merely the fact that with shorter eye-pieces the 

 distance of the field-lens from the objective is somewhat greater, 

 which, as a rule, necessitates also a slight increase of the posterior 

 focal length of the latter, and consequently a diminution of the 

 object-distance. The angle of aperture is consequently somewhat 

 increased ; but it is equally clear that the refractions, which take 

 place after the formation of the real image, do not alter the angle 

 of aperture, since the path of the rays in the objective is quite 

 independent of them. With a given position of the objective- 

 image it is therefore quite immaterial whether the eye-piece 

 magnifies five or fifty linear. 



K 



