410 Transactions of the Society. 



Now adopting the second of these expressions and assuming every- 

 thing but r to be constant, we may write (5ft) thus : 



p = Cr. ....... (6) 



It follows from this that no diffraction can arise in a focal 

 plane where the radius of curvature of the wave-fronts = 0. It 

 follows again that any disturbance caused by diffraction arising on 

 the stage of the Microscope, can always be avoided by focussing 

 the source of light upon the stage. Hence the value, for exact 

 work, of what is known as critical illumination, and of condensers 

 capable of accurate focussing.* 



(4) Finally, the phase remaining constant, if we change the 



wave-length and the divergence angle, we obtain an antipoint 



according to the law 



\« , a constant 

 p e = <£ = — _ 



2 sin v ( T n f sin u e 



P* n v sin u v 



, and 



p-n n e sin u f 



n e sin u<: p e = n v sin u v p v (7) 



Comparing this equation with equation (4) (see above, p. 396), we 

 see that antipoints are conjugate images of each other, and are 

 formed and proportioned according to the sine law of image 

 formation. This may fairly be described as the great result of 

 Helmholtz' investigation. 



Diffraction in the Microscope. 



We are now in a position to renew the consideration of Helm- 

 holtz' proposition (p. 402), that the loss of resolution due to diffrac- 

 tion in the instrument is the same that would arise from viewing 

 the image formed in the instrument through an aperture equal to 

 that of the Eamsclen circle. The question which we left over at 

 p. 403 was whether diffraction arising in any other part of the 

 instrument would make matters worse than this. 



A reference to fig. 89 above, p. 401, in which the course of an 

 axial and of an oblique beam are traced through an ordinary com- 

 pound Microscope, will assist the enquiry. If we now consider 

 first the axial beam it will appear that there is no mischievous 

 diffraction beyond what is traceable to the Eamsden circle. For 

 the beam which comes from the objective has the same numerical 

 aperture as that which enters the eye-lens and, therefore, by 

 equation (7) (see above), the antipoint produced by the objective 



* See Appendix, Note III. 



