162 Professor Forbes on the Refraction 



66. The table generally points to a coincidence, and that as 

 close as by the nature of the experiments we should perhaps be 

 warranted in expecting. If there be any excess in the second 

 column of results (which the observations with incandescent pla- 

 tinum might lead us to suspect), it is more than probable that it 

 arises from some imperfection in the apparatus employed, such 

 as the incomplete parallelism or perpendicularity of the mica plates 

 employed to polarize, a circumstance which was not minutely at- 

 tended to. 



67. The result, however, is highly satisfactory, as indicating 

 the almost exactly complementary nature of the ordinal*} and 

 extraordinary pencils, as in light. 



68. The somewhat complicated conditions of the variable 

 intensities of the ordinary and extraordinary images (which it is 

 to be recollected correspond to the Parallel and Perpendicular 

 positions of the analyzing plate) in the case of light, are easiest 

 kept in mind by Fresnel's formulae. 



o 2 



=F 2 ] 1 — sin 2 2 i sin 2 * (^^) 1 

 E 2 =F 2 J sin 2 2isin' * (~^) } 



where O 2 , E 2 , and F 2 , have the same signification as in (64), and i 

 represents the angle between the plane of polarization and the 

 principal plane of the crystal : — e is the difference of the retar- 

 dations of the ordinary and extraordinary rays within the crystal, 

 and x the length of an undulation. The sum of the two is al- 

 ways — F 2 . 



69. Now the quantity — e may always be known by refer- 

 ring to the retardation, which produces the corresponding tint 



* This corresponds to the formula -_ sin 2 2 <p -I 1 — cos v of Airy's 



Tract on the Undulatory Theory, Art. 172, Both are only restricted expressions of 

 more general theorems. 



