386 ON LIGHT. 



zero, but from half an undulation. Of the two partial 

 systems of waves that interfere, in the case considered, 

 that which belonged to the ordinary pencil in the crys- 

 tal passes, as an extraordinary one, through the analyz- 

 ing plate. Now it is a law, susceptible of demonstra- 

 tion, but which it would lead us too far aside at present 

 to demonstrate that in the transition from an ordinary 

 to an extraordinary refraction, half an undulation is 

 gained. With the other portion of the interfering pencil, 

 no such transition takes place. Half an undulation then 

 has to be reckoned in addition to the phase-difference 

 due to the simple passage of the two rays through the 

 crystal just as is the case in the Newtonian reflected 

 rings, and with the same result. 



(162.) If we follow out the same chain of reasoning 

 in the case when the analyzing plate is parallel to the 

 polarizing one, the conclusions will be identical up to 

 this last step. But here the cases differ. Neither of 

 the interfering pencils here at its entry into the second 

 tourmaline undergoes extraordinary refraction, and there 

 is accordingly no semi-undulation to be added to the 

 phase-difference. The rings, therefore, will have the 

 characters of the transmitted series of Newton's colours. 



(163.) In the generality of uniaxal crystals, the tints 

 of the rings, when the crystal itself is colourless (or as 

 nearly as its colours will allow), follow a succession identi- 

 cal with that of the Newtonian colours of their plates. 

 I have elsewhere called attention, however, to several 

 instances of deviation from this rule, some of which are 

 of so remarkable a nature as to deserve special mention. 



