162 Professor Forses 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 ordinary 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 Fresnet’s formule. 
O?= cae | 1 — sin? 27 sin? x (=) 
o—e 
=F? sin? 27 sin*® + (= \ 
where O°, E’, and F’, have the same signification as in (64), and z 
represents the angle between the plane of polarization and the 
principal plane of the crystal : 0 — e is the difference of the retar- 
dations of the ordinary and extraordinary rays within the crystal, 
and 4 the length of an undulation. The sum of the two is al- 
ways = F’. 
69. Now the quantity o—e may always be known by refer- 
ring to the retardation, which produces the corresponding tint 
el ee pe 2 = 
* This corresponds to the formula “sin? 20 fa — cos aa of Airy’s 
Tract on the Undulatory Theory, Art. 172. Both are only restricted expressions of 
more general theorems. 
