268 On the Achromatic Microscope. 



The tube of the microscope should be made of variable length. 

 When the sextuple object glass is used, the length may be made to 

 vary from four to six and a half inches. The microscope will then 

 magnify the diameter, with a proper eye-piece, from ninety to one 

 hundred and eighty times. When the length is so adjusted as to 

 make it magnify the diameter one hundred times, the vision is so 

 distinct that objects are rendered visible, which cannot be seen with 

 any single glass lens. 



In constructing achromatic microscopes, it is very difficult to make 

 them free from spherical aberration in the first attempt, even when 

 we know with precision the required radii and thickness of the lens- 

 es ; as a small variation in either will materially affect the spherical 

 aberration. It is therefore found expedient not to rely on theoretical 

 calculations, but to ascertain by direct experiment, the radii that will 

 destroy, most effectually, the color and spherical aberration in glass 

 of a given density. When a standard microscope is thus obtained, 

 and several similar ones are required, the most practicable method 

 appears to be, to construct them as nearly similar as can easily be 

 done, and then change one of the curves of the first lens, until by 

 approximation, the spherical aberration be nearly corrected. When 

 this is done, the correction may be completed by changing the size of 

 the aperture, enlarging it when the aberration of the convex lens is 

 greater than that of the concave, and diminishing when less. The 

 correction may also be completed, when the aberration of the con- 

 cave is less than that of the convex, by grinding the edges of the 

 flint lens on a flat hone, so as to bring its centre and the uncemented 

 convex lens nearer together. No correction could be made by chang- 

 ing the aperture, if no secondary aberration of figure existed ; but in 

 consequence of the great increase of this aberration with the increase 

 of aperture,* on the one hand, — and the insufficiency of a great re- 

 duction, (especially if the aperture be small,) to correct the spherical 

 aberration, on the other, — the extent of this mode of correction is 

 necessarily limited. It must, therefore, be first nearly corrected by 

 changing one or both of the radii of the first lens. As these changes 

 are small, they will not much affect the secondary color. 



* It appears from calculation, that the longitudinal secondary aberration of figure, 

 in microscopes of large apertures, increases nearly as the fifth powers of the aper- 

 tures; and that when the apertures are very large, it increases in a still greater ratio. 



