120 Professor Airy on the 



where 9' is the value of 9 corresponding to 6 — 0, 

 Consequently, 



or 9 = - — . 



A7T 



eT eT 



e T 



But — j- is the angle through which the analyzing plate must be turned 



to the left to see the dark spot with the right-handed plate alone. Con- 

 sequently the dark cross in which the spirals originate is inclined, (the 

 upper part to the right), by an angle half as great as the angle through 

 which the analyzing plate must be turned (the upper part to the left) 

 to see the dark spot with the right-handed plate only. This appears to 

 agree with experiment. 



7. In the whole of this we have supposed the right-handed plate 

 to be nearest to the polarizing plate. If the combination be turned, with 

 the left-handed plate nearest to the polarizing plate, we must change the 

 sign of k. This changes the sign of x (that of <p being supposed the 

 same); and it will very easily be seen that in consequence of this change, 

 the direction and position of the spirals will be exactly inverted. This is 

 found to be true. 



8. When k is small, the expression for the brightness becomes small 

 if sin" 2 <f> = 0, that is, if (j> = 0, or = 90", &c. This accounts for the dark 

 blushes seen parallel and perpendicular to the plane of reflexion at a great 

 distance from the center. 



9- When <j> is > o < 45°, x is > 2<£: when <p is > 45° < 90°, x 1S 

 < 2(p. Observing that the spirals intersect the circles when $> = 0, =90", &c, 

 it is easily seen from this that they cut them at an angle rather 

 greater than the angle at which a uniform spiral would cut them. This 

 seems to be observable in the experiment. 



