236 Mr. A. W. Flux on the 



This vanishes when (x^+y 1 eos 2 0)/x vanishes. 

 Now 



2 (®*+f cos 2 6) ( z + z,) = x [(x*+f) sin + 2^] 

 — x [a 2 sin 6 + 2xz{]* 

 .'. \/B 2 + C 2 vanishes when 



a 2 sin 6 



and since ^ ,2 + z/ 2 = a 2 , this requires that x^>a, 



a sin 6 . 

 i.e. —^—<1, 



, 4^i 2 cos 6 

 \r sin 2 



. 4J 2 (/a 2 -l)*3in 2 0cos0 



Ar yU 6 COS 6 ^ 



For all rings of lower order than the limit so determined 

 there are two points quite distinctly visible, symmetrically 

 situated with regard to the plane xz, and on the side of thi 

 plane yz farthest from the incident light. 



To obtain the required criterion for bright rings it is only 

 necessary to write li + \ for h in the above. 



If the rings are examined by means of a microscope, the 

 breadth of the visual pencil is much greater than if the naked 

 eye were used. Thus much greater values of <f> are possible, 

 and the obscurity is consequently increased. 



For purposes of exact measurement, however, a microscope 

 is necessary, in spite of the consequent greater indistinctness 

 in the phenomena observed. 



Part II. — Newton's Rings in Transmitted Light. 



Section I. Calculation of the Relative Retardations. 



We now proceed to consider the case of transmitted light. 

 We shall take the axis of z in the opposite direction from that 

 before used in Part I., viz. drawn towards the side on which 

 the lens lies (fig. 6). 



