710 
MR. G. F. FITZGERALD OR THE ELECTROMAGNETIC THEORY 
wave-propagation in a secondary degree— i.e., only to the extent to which ether motions 
are transformed into currents in or motions of the matter. The same applies to the 
opacity of the medium, which is similarly due to an exchange of energy between the 
ether and the matter. The function Professor Maxwell assumes to represent the 
effect of magnetisation on wave-propagation is an expression of the same hypothesis. 
In comparing my equations with Mr. Kerr’s results I shall consequently assume 
X =1 - 
Mr. Kerr’s most elaborate experiments have been made with the lines of magnetic 
force in the intersection of the surface of the medium and the plane of incidence,* and 
I shall confine my attention to this case. My equations give that the principal effect 
of reflection is to introduce a component perpendicular to the original plane of polari¬ 
sation whose amplitude is represented by the equation 
27 tv sin 2 i sin 2 i cos r 
T sin 2 (i + r). cos (i — r ) 
when the amplitude of the incident vibration is unity. 
The following table represents the values of the variable part of this for the several 
incidences mentioned by Mr. Kerr in his paper. This table is calculated on the 
assumption that 7 5° is the polarising angle for iron. 
i— 
0 
O 
O 
CO 
45° 
O 
O 
65° 
75° 
GO 
O 
o 
85° 
90° 
sin 2 i sin 2 i cos r 
sin 2 ('i + r ) .cos ( i—r ) 
0 
•6272 
•8646 
1-0007 
1-0058 
•9000 
•7554 
•4904 
0 
This table shows that the intensity of this introduced component vanishes for the 
two limiting incidences 0° and 90°, and attains a maximum value of P0067 at about 
63° 20b On comparing this with Mr. Kerr’s results there is a most striking corre¬ 
spondence. Summing up the results of his paper on reflection from a surface which is 
magnetised so that the lines of force are in the surface and the plane of incidence 
(‘Phil. Mag.,’ March, 1878, § 23), he says: “When the vibration reflected from the 
unmagnetised mirror is either parallel or perpendicular to the plane of reflection, the 
effect of magnetisation is to introduce a new and very small component vibration in a 
direction perpendicular to the primitive vibration.” This is what I have called c. He 
goes on to define its direction relatively to the Amperean currents which are supposed 
to produce the magnetic force; but as the sign of c depends on the sign of v, and thus 
on that of C, which cannot be certaiuly determined for iron otherwise than by these 
very experiments, any confirmation founded upon it such as I mentioned in my former 
paper is to a certain extent illusory ; but the same arguments as are there used would 
* ‘ Phil. Mag.,’ March, 1878. 
