The necessity of empirical tests has been entirely obviated by precise mathe- 

 matical computation of every detail of construction combined with exact technical 

 methods and systematic control of each phase of manufacture. This ensures an 

 extraordinary degree of uniformity in the highest as well as in the lowest 

 powers of our lenses, whilst excluding the bare possibility of inferior 

 productions. All objectives are uniformly free from spherical aberrations up 

 to the marginal zone (assuming correct thickness of the cover-glass with the 

 higher powers) and, as far as possible, from chromatic aberrations also. Special 

 consideration is also given to the compensation of the aberrations in the extra- 

 axial part of the field and to the flatness of the image. 



Free working distance. Owing to the importance of a good working 

 distance for the convenient and safe employment of the higher powers particular 

 attention has been given to this factor in calculating the formulae of the various 

 glasses. Our high power objectives possess therefore unusually large work- 

 ing distances in comparison to their focal length and aperture (see Tables on 

 pp. 9, 17, 21). 



Tube-length. The objectives specified in this catalogue, except where 

 the contrary is expressly stated, are all adjusted for a tube-length of 

 160 mm (about 6y 2 in.), reckoned from the shoulder of the objective 

 screw to the upper end of the draw-tube on which the eye-piece rests. 



The tube-length may be read off on the larger stands of our make by the 

 divisions on the draw-tube. The interposition of any apparatus, such as a revol- 

 ving nose-piece, a sliding objective- changer, &c., between the tube and the ob- 

 jective necessitates the shortening of the tube by the length of such intermediate 

 piece so as to make the whole distance between objective shoulder and eye-piece 

 equal to 160 mm (or about 6 x / 2 inches). 



The position of tlie eye-piece is usually somewhat liigher in the case of 

 various oculars of special construction, such as micrometer eye-pieces, screw micro- 

 meter eye-pieces, spectroscopic eye-pieces, &c. When using such eye-pieces this 

 must therefore be allowed for, objective-changers^ <&c., being, if necessary, omitted 

 in order to maintain the correct tube-length. 



The lower-power achromatic objectives as far as C may also, with- 

 out appreciable loss, be used on English stands with 10-inch tubes. 



All the other objectives, particularly those of the apochromatic 

 series, perform more or less imperfectly on stands of the English 

 type, unless specially adjusted. 



If the objectives are to be used with tubes differing from the usual length, 

 this fact should be expressly noted in the orders. 



Thickness of cover-glass. All objectives in fixed mounts are, unless other- 

 wise ordered, corrected for a medium thickness of cover, between 0.15 and 

 0.20 mm. In the higher powers (from the apochromatic objective 8 mm and the 



