ON APEETURE AND DEFINITION OF MICROSCOPE OBJECT GLASS 445 



whicli shall allow these lines to be separately visible to the eye 

 may be computed.* 



And he himself gives the following arithmetical calculation in 

 accordance with his formula: — Taking -00055 mm. (= ^-Jj-^ mm.) 

 as the wave length of medium rays, and 90° as angular divergence 

 of a dry lens (or a lens constructed on immersion principle used 

 dry), and assuming perfect correction and adjustment of lens and 

 instrument, then ^^\^ -h 2 = ^-J^g- mm. (or ^^ Jo^ inch). 



This is the same calculation and gives the same result as that in 

 Mr, Sorby's table for mean rays and 180° aperture (twice the 

 divergence angle). 



Helmholtz next points out that if the rays could be transmitted 

 through water with the same divergence as through air, then the 

 wave length \ would be •00055Xf=*0004125 =24^42 ^ini. And 

 a being supposed = 90?, it follows that e =2"5 2 4"^''^'=48V8 ^^' 



or T2 2^0^ i^ich. 



The extreme limit of minuteness is then shown to be dependent 

 on the wave length of illuminating rays. And this appears more 

 distinctly from the calculation when blue rays are employed whose 

 wave length ='0004282, as e is then =45^0" ^^- ^^ ttbVoo inch, 

 with the immersion lens as at present used. 



The figures in Mr. Sorby's table show (what has, however, been 

 long known), firstly, that red light is the worst for rendering 

 minute objects visible, whilst blue, if collected in sufficient quality 

 to supply brightness of image as well as to bear high amplifications, 

 would be best. This inference is, indeed, sufficiently justified by 

 the known diff'erences of susceptibility of the retinal nerves to 

 colour (i.e., for undulations of such widely different wave lengths 

 as those of red and blue), and by the different course of these rays 



* The same formula and tlie same explanation of it is given by Professor 

 Abbe, in H xix. of his essay (page 244 this vol.), namely, that it expresses the 

 extreme limit of separable objects — so far as seeing is concerned. But this 

 theoretically possible " resolution'' becomes an actual one, only when the 

 essential conditions of definition — accurate focussing function^ and '; regu- 

 lated angle of illuminating pencils — are also properly fulfilled. 



