42 
PROFESSOR POWELI/S OBSERVATIONS ON CERTAIN CASES OF 
Incidence. 
Surface. 
Polarization. 
Centre. 
Direction of 
dislocation. 
O 
70 
Steel, plain 
Elliptic large 
O 
0 
Nobili’s films. 
A 
Elliptic, large 
90 
0 
1 
C yellow i 
First order. . < t „ 
bed.. 
Plane 
Dark. 
Elliptic, large 
Plane 
Bright. 
f green | 
Second order < 
[red .. | 4 
Elliptic, large 
90 
0 
Plane 
Elliptic, large 
Dark. 
Plane 
Bright. 
f green j \ 
Third order < > „ 
[red .. 
Elliptic, large 
90 
0 
Plane 
Elliptic, large 
Dark. 
Plane 
Bright. 
Fourth order { S r een 
[ red 
Elliptic, small ............ 
Dark. 
Dark. 
0 
0 
Elliptic, very small 
Black 
Elliptic, very small, or none 
Dark. 
0 
Analytical Investigation. 
Mr. Airy’s general formula is investigated as follows : — 
In the usual notation of the undulatory theory, we suppose a vibration in a plane 
P, represented by 
• 2 7T 
a sm — (v t — x ) 
incident on a metallic surface, so that P is inclined 45° to the plane of reflexion R. 
Then (the vibration perpendicular to R being accelerated in phase by g) the resolved 
parts are 
a . 2 7r 
— 7 = sin — (v t — x ) . . . . in R. 
V 2 A v ’ 
sin ~ (v t — x -f- §) • • perpendicular to R. 
Then for a plane Q in the crystallized plate inclined to R by an angle <p (omitting 
the constant coefficient) the vibration perpendicular to Q, giving the ordinary ray, O, 
will be 
sin (v t — x -f- g)') cos <p — sin ~ (v t — x) sin <p = O, 
and that in Q giving the extraordinary ray E will be 
sin (gjg {v t — x + £)) sin <p + sin —■ (v t — x) cos <p = E. 
But on emergence from the crystallized plate the latter is accelerated by 6 (depend- 
