ON THE THEORY OF THE MICROSCOPE. 223 



power objectives ; for when the focal length is less than ^th inch, 

 the relative perfection of construction perceptibly fails, on account 

 of the rapidly accumulating technical difficulties, and there cer- 

 tainly does not exist an objective of Jj inch focus whose optical 

 capacity exceeds a five-fold angular amplification. It is easy, 

 accordingly, from this, to calculate what figures indicate the 

 necessary linear amplification with objectives of diff'erent focal 

 lengths (about ^^^ for -J- inch, ^2_oo f^^ -^^ inch) ; and, further, 

 what extreme amount of magnifying power may be accepted as 

 really serviceable when we take into consideration that the mere 

 extension of an image by large visual angles of formation, with- 

 out any corresponding increase of optical capacity (especially 

 where the amplification is already so great and pr oportionately so 

 weakly illuminated), mast tend to injure, rather than to assist, 

 the clearness of visible impression. 



Prom all this may be gathered how utterly futile any efforts 

 to obtain disproportionately high amplifications by means of 

 specially constructed eyepieces must prove ; and, as regards any 

 expectation of exalting the performance of the instrument by 

 further shortening of the focal length of the objective, there stands 

 in the way one objection, which, apart from all others, in the 

 present state of our knowledge, is absolute and insuperable — 

 namely, that the imperfections resulting from residual aberra- 

 tions and defective technical manipulation increase with every 

 addition of magnifying power, through the efi*ect of diffi'action 

 occasioned by the minute surface of very high power lenses. This 

 form of diffraction, likewise, turns the image of each point in an 

 object into a dispersive circle of greater or less diameter ; but the 

 resulting diminution of optical capacity, while scarcely notice- 

 able in objectives of moderate power, compared with the effect of 

 residual aberrations, becomes very serious with the higher powers. 

 It may be shewn, as a general rule, that the influence of this 

 source of error, which has nothing to do with the optical power 

 of the microscope (or of the telescope), depends alone upon the 

 magnitude of the final aperture-image seen by the eye above the 



