234 Mr. A. W. Flux on the 



just written, the bright ring of order k lies partly below the 

 glass plate. 



If we denote the line (iii.) of the last section, viz.: 



a? sin 0-22=0") 



the principal line, and the plane 



x sin 0—2^=0, 

 the principal plane. 



The rings lie wholly below the principal plane so long as 



x sin 



The greatest value of z determined from equations (i.) and 



x sm 

 (ii.) of the last section is less than — -^ — so long as 



0^-l)cos^. 

 < a ft 6 sin 2 cos 6 6, ' 



±d* f^-l) cos-^fl 

 *"'" < \r fi 6 sin 2 cos 6 0/ 



It will be observed that this value of h and the first two of 

 those just given is greater as is smaller and decreases as 

 increases. 



It is otherwise with the number determining the order of 

 ring lying below the lower surface of the glass plate. 



It was found that the axis of z lies entirely in the surface 

 between z = and z=—z v 



Thus there arises a certain degree of indeterminateness 

 with regard to the central black spot, any point between these 

 limits being seen with equal clearness. This difficulty is 

 actually found in the course of the experiments undertaken in 

 connexion with this more exact theory of Newton's Rings. 



Section VI. Relative Distinctness of Different Portions of 

 the Ring -system. 



We shall now consider where and under what conditions 

 the rings are formed most distinctly. 



In Sect. III. (ix.) the expression found for the retardation 

 was 



A/ = A + B <f) cos i/r + C c/> sin ty, 



Q 



=A+ VB 2 + C 2 <\> cos (<*/r- «), where tan a = ^« 



When B 2 -f C 2 is a minimum, 



A = ^cos 0(.i' 2 + /). 





