IXTRODUCTIOX. 3 



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of the eye-piece by - ^- . The combination of the two in the 



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 Microscope gives therefore an amplification of --* ^~ 1 times. 



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In order that the image seen by the eye may be distinct and 

 bright, the spherical and chromatic aberration must be reduced to 

 a minimum, and the apertures of the lenses must be as large as 

 possible. These conditions are, however, in antagonism, as the 

 aberrations of a single lens increase with its aperture. Distinct- 

 ness can, therefore, be gained only at the cost of brightness, and 

 conversely. This inconvenience reaches such a pitch in the older 

 Microscopes, that when their images are at all satisfactory in point 

 of distinctness they are very deficient in light, even with moderate 

 magnifying powers. 



It was only in more recent times that the happy idea was sug- 

 gested of constructing the objective of two or three compound lenses 

 approximately achromatic. It was soon found that by their skilful 

 combination both kinds of aberration could be eliminated far more 

 perfectly than had been at all feasible in the earlier arrangements 

 by merely diminishing the aperture. In addition to this, the 

 important advantage was gained, that, as the deflection of the rays 

 which form the image was divided between several lenses, their 

 curvatures might be considerably reduced, and thus a larger aper- 

 ture obtained. . 



We shall, hereafter, examine more closely the principles of 

 achromatism and aplanatism as far as they concern the construc- 

 tion of the Microscope, and will for the present assume that we 

 have an ordinary objective composed of three compound lenses, 

 just as it leaves the hands of the optician, and will trace the course 

 of the rays of light from the object to their reunion in the image. 

 Our explanation will be based upon the dioptric investigations of 

 Gauss, 1 which expound the laws of the refraction of light in the 

 case of a concentric system of any number of spherical surfaces, 

 between which lie media with varying refractive indices. Though 

 the suppositions which form the basis of these investigations are 

 not applicable, in certain essential points, to the course of the rays 

 in the Microscope, still the results furnish an excellent view of the 

 conditions met with. In a subsequent chapter we shall give the 



1 C. F. Gauss : " Dioptrische Untersuchungen." Abhandl. Gottinger Gesell., I., 

 1843. 



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