of the Microscope. 423 



difficulty and the expense necessarily attending their processes, 

 are so great, that but few persons can derive any benefit from 

 their exertions*. 



In making a comparison between the telescope and microscope, 

 it must be observed, that some difficulties, and sources of error, 

 which in the former are so small as to have been overlooked, 

 are in the latter of the greatest and most palpable importance. 

 The image produced by the object glass of a telescope is usually 

 considered as perfectly plane, and equally distinct in all its 

 parts, and this supposition is quite sufficiently accurate, because 

 although the image given by a lens with centrical pencils, is 

 on the whole very much curved and very indistinct, so small 

 a part of it is employed in this case, and that only the most 

 perfect, that the defects are usually quite insensible in practice. 



I have shownf, after Dr. Young and Professor Airy, that 

 if we represent by 



X, the aperture of the object-glass, 

 z, the distance of a point of the image from the axis, 

 /, the focal length of the lens, 

 k, the distance of the image from the lens, 



the indistinctness is proportional to the diameter of the least 

 space over which a pencil is diffused, the value of which is 



Xz- 



ikf 



* Mr. TuUey has just finished an achromatic microscope ordered for Lord Ashlej', 

 about six months ago. This instrument, which I have seen, is a masterpiece of art, but 

 I believe that the above eminent optician has been obliged to make the object-glass 

 with bis own hands, and the price is far beyond the reach of most naturalists. 



f Treatise on the Reflexion and Refraction of Light, Art. 145. 



Vol. III. Fart III. 3 I 



