112 Professor Airy on the 



This is exactly the same series as that for the original direction of the 

 radius vector: and therefore the values of 6 are exactly the same for 

 any radius vector as for that opposite. But the curve (as we have seen 

 above) is spiral. These two conditions require that the form of the dark 

 line be two similar spirals mutually inwrapping each other, their positions 

 differing by 180". But no other alteration of will give the same values 

 of 6 in the dark rings. Consequently the form of the dark rings is two 

 spirals, and only two, turning in the same direction, and in opposite 

 positions. This remarkable conclusion is supported by fact. 



5 th . When 20 is between and 90°, x * s greater than 20: when 

 20 is between 90 and 180°, % i s less than 20: and so for successive 

 quadrants. That is, when is between and 45°, ^ is too great, or 

 <-) too small, for a spiral of uniform approach to the center : when is 

 between 45° and 90°, is too great. This shews that the spiral will have 

 a square appearance, the right-hand angles being higher than the center. 

 This is precisely the form really presented to the eye. 



6 th . The expression for the brightness of the center (where k = l) is 



simply — . As this is independent of X, it shews that there is the same 



mixture of colours at the center as in the light which we use : and 

 that therefore with common light the center is white. 



I should only take up the reader's time unnecessarily by 

 going through the investigation with the rhomb in position 135°. 



VIII. We have found (in the investigation of IV.) that put- 

 ting £ for — (vt-x), the expressions for the vibrations when light, 

 at first plane-polarized, has passed through a plate of right- 

 handed quartz, are (omitting the common multiplier jt^) : 



