J. J. FIELD ON THE RATIO-MICRO-POLARISCOPE. 217 



ated by what I may term a /a^cra/ displacement; but the extraordinary 

 ray being retarded in its oblique passage through the depolarizing 

 film, emerges (except under certain exceptional conditions) in a 

 different phase of vibration from that of the ordinary ray ; in 

 other words, supposing the undulations of the two rays could be 

 made visible, moving side by side, it would be seen that the crests 

 and hollows of the one wave were not coincident with those of the 

 other. 



Now a little reflection will suffice to show, that if this difference 

 of phase amounted exactly to a semi-undulation, the effect of 

 bringing the two beams into collision would be to cause their 

 mutual extinction ; inasmuch as that equal forces would thus meet 

 in antagonism at points where they would possess equal advantages, 

 and thus the power of each would be neutralised and destroyed. 

 On the other hand, if, when the two rays emerged, there existed 

 an exact correspondence between their undulations (which could 

 only occur when the thickness of the doubly refracting struc- 

 ture was sufficient to make the phase-displacement equal to a full 

 undulation), they would, if brought together as before, double each 

 other's intensity; in other words, we should simply have the 

 polarized beam in its original form once more. 



Now, since it can only occur as an exceptional chance, that any 

 doubly-refracting structure we may wish to view, should possess 

 either the precise thickness necessary to separate the extraordinary 

 from the ordinary ray by an exact se?ra2-undulation ; or, on the other 

 hand, by an exact entire undulation ; and as any thickness interme- 

 diate between these two extremes must result in an interference 

 between rays only of a certain degree of refrangibility (the par- 

 ticular rays in every given case depending vipon the amount of 

 phase-displacement), we might, at first, suppose that all doubly 

 refracting structures, when viewed by polarized light, would yield 

 chromatic eff'ects, except in those portions of the structure which 

 (if any) might chance to possess the exceptional thickness named 

 before. 



In practice, however, this is far from being the case ; for very 

 many structures, and parts of stractures, which can be proved not 

 to have the exact thickness needed to produce either total suppres- 

 sion or doubled force of the beam, nevertheless, do not, when viewed 

 simply between two polarizing prisms, exhibit any chromatic eff'ects 

 whatever. Yet we all know that many of the structures I now 



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