ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 689 



(3) In order to determine the depth of focus (4>) of a system which 

 projects virtual images to an observer's eye, we must first define the 

 degree of indistinctness which is allowed for these images. This may 

 be done in the simplest way by indicating the visual angle under 

 which the admissible circles of indistinctness (or dissipation-circles 

 arising from the deviation of focus) appear in the virtual image. If 

 to denotes this angle of allowable indistinctness (and is expressed by 



its arc — V = wtk?i = 0- 000291), /the equivalent focal length of the 



total Microscope, or whatever other system may be in question, 

 a the effective numerical aperture, and n the refractive index of the 

 medium in which the object is, the depth of focus is determined by the 

 equation 



d) = w - w 



a 



L CO 



N a 



If the whole aperture-angle of a system is utilized by the deli- 

 neating pencils (as is generally the case with low apertures), a relates 

 to the whole aperture. If, however, a narrower illuminating pencil is 

 used, and not subjected to a considerable dissipation by the structure 

 of the object, a relates to the angle of the admitted pencil only. 



The actual depth of vision is depth of accommodation (a) -\- depth 

 of focus (^). "We have therefore 



1? L w 



Depth of vision = n — A + w— -• 



W N a 



The figures resulting from this formula are obviously not affected 

 by the arbitrary value of the distance (L) of projection to which the 

 figures of the amplification (N) may relate, because with one and the 

 same system N is always proportional to L. 



(4) The absolute diameter of the field which is visible in the 

 Microscope depends on no other element but (a) on the equivalent 

 focal length of the total system, and (&) on the angle of field of the 

 eye-piece, which is the visual angle under which the clear diaphragm- 

 hole of the eye-piece appears to the observer's eye. Let u denote the 

 semi-angle of field, / the focal length, or N the total amplifica- 

 tion of the Microscope for a certain distance L of the image, the 

 linear diameter of the visible object-field is determined by the 

 equation 



L 



c? = 2 / tan M = 2 — tan «. 



N 



These are the dioptrical formulae on the basis of which the 

 examples of the foregoing discussion have been calculated. 



Abbe's Stereoscopic Eye-piece. — We should have mentioned, in 

 describing this at p. 298, 1st, that a special feature of the apparatus is 

 its capability of being used with the highest powers ; and 2nd, that 



