134 Prof. E. C. Pickering on the Polarization of 



This method, though elegant theoretically, does not appear very 

 accurate practically, as the plane is more accurately determined 

 by covering the end of the polarimeter with a cap containing a 

 plate of selenite, thus converting it into an Arago's polariscope. 

 Then turn the tube until the two images have precisely the same 

 colour, when their line of junction will be inclined 45° to the 

 plane of polarization. The plane may also be determined, more 

 easily but less accurately, by removing the NicoFs prism, and 

 turning the tube until the two images are equally bright, and 

 adding 45° to the reading. 



We next wish to determine the delicacy of this instrument in 

 different parts of its scale. If the NicoFs prism be set at an 

 angle v', differing slightly from its true value v, the brightness 

 of the two images will be A sin 2 v' and B cos 2 v' respectively. 

 Now it is commonly assumed that the difference in two such 

 images will be perceptible when the difference in brightness, di- 

 vided by the brightness of either, equals a certain fraction -, in 



which a equals about 80. By differentiation it may be proved 



that the error in p or dp corresponding to any value of a is given 



1— » 2 

 by the formula dp = , from which the error in the result 



for any unobserved difference in brightness of the two images is 

 readily determined. 



If p=0, dp— —j its greatest value, which diminishes as the 



polarization increases, becoming zero when^ = 0. Hence the 

 greater the polarization the more accurately it can be measured. 

 If « = 80, dp = j^q for its greatest value ; hence the instrument 

 should always give results within two thirds of 1 per cent. Ob- 

 servation, however, shows that the error is much greater, a dif- 

 ference in brightness of j^ being by no means perceptible. 



The first series of observations were made on the light of the 

 sky. The instrument was screwed into a post and levelled, the 

 altitude and azimuth of the sun taken, and the instrument then 

 directed towards the points to be observed. Most of these were 

 in the same vertical plane with the sun, so that it was only ne- 

 cessary to determine their altitudes. The line of junction was 

 then brought parallel to the plane of polarization — that is, 

 turned until it was vertical, since it then lay in the plane passing 

 through the sun. The four positions of the NicoFs prism, in 

 which the two images were equally bright, were then observed, 

 reading the angles to tenths of a degree, and taking the mean. 

 The percentage of polarization was finally obtained as described 

 above. Eleven series of observations were taken : — nine at Water- 



