JAMIN ON METALLIC REFLEXION. 89 



may be given to the experiments. It is clear that in every case 

 where the ellipse is not sensibly a straight line, the difference 

 between the maximum and minimum will not be very sensible, 

 and^therefore the direction of the axes will be difficult to find. 

 But we may replace this determination by another, by calling to 

 mind^that the analyser being inclined at 45° to the direction of 

 the axes, the two images are equal : we shall then determine 

 this latter direction ; and by increasing or diminishing the angle 

 found by 45°, we shall have the position of the two axes. 



But,' in order to obtain certain results, it is absolutely neces- 

 sary to operate with a light rendered homogeneous by a red glass 

 well chosen ; otherwise the two images would always have dif- 

 ferent tints, and the process would lose all its accuracy. Let it 

 be observed also that there are four directions inclined at 45° to 

 the axes, and that for each incidence we may determine the azi- 

 muths of equal tints (w), 90° + «, ] 80° + w, 270° + w. These 

 directions being once known, those of the axes will be found by 

 increasing or diminishing them by 45°. 



In the following tables we have always indicated the azimuth 

 for which the extraordinary image is a minimum, which is that 

 of the minor axis of the ellipse : this would be the azimuth of 

 the plane of polarization if the ellipse degenerated into a straight 

 line. 



On the other hand, the direction of the axes of the ellipse is 

 given theoretically by the formula 



tan 2 oj = tan 2 a cos 5, 



calling to mind the equation of condition 



tan a = J tan a. 



These two formulae allow of the angle (cu) being calculated as a 

 function of a, I, I and J, for each particular incidence, and ex- 

 periment may be compared with calculation. 



I have made three series of observations on mirror-metal in 

 polarizing light in the azimuths 20° 15', 46° and 71° 25'. The 

 observations repeated several times have always given numbers 

 agreeing with each other, and the mean results are completely 

 in accordance with the theory, as the following tables show. 



