Igo THE MICROSCOPICAL NEWS, 
diameters without an obvious loss of sharpness of the image? If 
we are able to determine that focal length, we have at the same 
time assigned the prvoger focal length for the aperture of o'50. 
1. The discussion of this subject is based on the following 
optical principles :— 
(1) If we could obtain lenses or systems of an ideal perfection, 
collecting a// rays to mathematically sharp points’ without any 
aberrations, the composition of the whole microscope would be 
absolutely unimportant. If the effect of the aberrations is dis- 
regarded, a// functions of the microscope depend solely on the 
aperture and the focal length of the emézve system, and are quite 
independent of the number and arrangement of its constituent 
elements. Upon this assumption a given short focal length of the 
whole microscope, which means high linear amplification of the 
ultimate image (which is the quotient of the distance of vision by 
the focal length) could therefore be obtained just as well by means 
of a strong ocular at the upper end of the tube, as at the lower end 
by means of a strong objective. The only reason why a difference 
of division is of importance is the accumulation of the effects of 
faults and aberrations of the lenses in the ultimate image of the 
microscope. In order to prevent an obnoxious accumulation, and 
for no other reason, we are confined to certain limits in the distri- 
bution of the total power as between objective and ocular. 
(2) The ocular is practically unimportant under the actual con- 
ditions of the microscope, so far as the sharpness of the image at 
the central portion of the field is concerned—the quality of the 
field outside the axis being disregarded. The length of the tube 
being always a considerable multiple of the clear diameter of the 
objective, the pencils of light are contracted to very small angles 
at their entrance into the ocular. The numerical computation of 
the spherical and chromatic aberrations originating in similar 
pencils, in the case of ordinary Huyghenian or Ramsden oculars, 
shows at once that in the neighbourhood of the axis their amount 
is utterly inconsiderable in comparison with the residuary aberra- 
tions of the most perfect objective. Consequently the axial 
aberrations which are inherent in the objective-image, can neither 
be increased nor diminished by any kind of ocular; they are 
enlarged only for the eye in the same ratio as the image itself is 
enlarged. Other properties of the image (outside the axis)—flat- 
ness of the field, uniform amplification, &c.—which ave influenced 
by the ocular, are doubtless of practical importance in the use of 
the instrument, but they do not touch the essential points, whether 
a given degree of sharpness and distinctness is reached with a 
given power. For it makes no difference, in regard to this ques- 
tion, whether the available field of maximum excellence is some- 
what greater or somewhat less. The interference of gross defects 
