618 
MB. B. T. GXAZEBBOOK ON THE REFRACTION OF PLANE 
wrong in so doing. The table, however, shows us conclusively that we cannot so 
determine this constant as to bring theory and experiment into exact agreement. 
The last two columns in each table enable us to compare these results with those of 
our former experiments. 
The one gives us the rotation of the plane of polarization when only one wave 
traversed the crystal according to the electro-magnetic theory, the other the measured 
value of the same rotation. 
Consider Table IY. first. At high angles of incidence the theoretical value of rotation 
is greater than the experimental. As the angle of incidence decreases the two become 
more nearly equal and agree within the limits of the error of experiment between 
angles of incidence ranging from 55° to 45°. As the angle of incidence still further 
decreases the theoretical value of the rotation becomes decidedly less than the 
experimental. 
In the main this agrees with Table II. At high angles of incidence the rotation 
given by theory is greatly in excess of that given by experiment, the two agree 
between 55° and 40°, but for the lower angles of incidence Table II. shows a slight 
increase in the theoretical value as compared with the experimental. 
Turning now to the last two columns in Table V., we see that the theoretical 
rotation is at high angles of incidence less than the experimental, that as the angle 
of incidence decreases the two tend to become equal and agree very closely for angles 
of incidence between 55° and 45°, while from that point onwards the theoretical rotation 
is bigger than the experimental. The change in the relative values of the two is very 
regular, while the actual change of sign in their difference occurs between the values 
49° 5' 40" and 43° 46' 45" of the angle of incidence. 
Referring to Table III. we see that this is exactly the state of affairs there indicated. 
The theoretical rotation is at first less than the experimental and increases gradually 
as the angle of incidence decreases, becoming the greater between the values 50° 27' 30" 
and 45° 1 5', almost the same limits as above, of the angle of incidence, and continuing 
so throughout the rest of the arc examined. 
With the exception then of one or two observations recorded at the end of Table II., 
the results of the two series of experiments, the one made during the autumn of 1880, 
the other during the summer of 1881, agree and lead us to the conclusion that the 
laws arrived at by the electro-magnetic theory connecting the planes of polarization of 
the incident and refracted rays in the case of refraction at the surface of a uniaxal 
crystal are not exact but are probably close approximations to the truth. 
These same laws have been arrived at by Neumann, 4 ' MacCullagh,! Kirchkoff J 
and others on various assumptions as to the nature of the ether; and in the case of an 
* Abhand. der Akad. der Berlin, 1835. 
f Irish Trans., 1837. 
\ Abband. der Akad. der Berlin, 1870. 
