Double Refraction of Quartz. 93 



least when it = 0, = 2tt, &c. : and the same holds if we increase all these 

 angles by 90°. Thus there is in fig. 3. a mixture of parts of the two 

 systems of rings in figs 1. and 2. 



II. Now let a FresneFs rhomb be interposed, and let RAr, 

 fig. 16. represent the plane perpendicular to the plane of internal 

 reflection, and making the angle /3 with the plane of original 



polarization; the rest as before. The vibration c.sin — (vt — x) 

 perpendicular to P t A may be resolved into 



2tt 



c.sin — (vt— a;). sin /3 parallel to Ar, 



27T 



and c.sin-— (vt—x). cos /3 perpendicular to Ar 



A 



Of these the former, by Fresnel's theory, is retarded one quarter 

 of an undulation, or the latter is accelerated as much. Adopting 

 the latter supposition, we must suppose that after the emersion 

 from the rhomb, the vibrations are 



c. sin — - {vt— x) . sin /3 parallel to Ar, 



and c.sin — - (vt— x) + 90°. cos /3, or c. cos — (»£— x). cos/3 



perpendicular to Ar. These will furnish for the ordinary ray of 

 the crystal 



27T . 2„- 



c -sm — - (vt-x).sm fi.sin fi-i-a + <p + c. cos — (vt—x).cos /3 . cos fi + a + <p 



" A 



and for the extraordinary ray 



. 2 



— c.sin — (ot-x). sin /3. cos/3 + a + + c.cos : ^—(y/— a;), cos /3.sin/3 + a + <p. 



