14 



PROCEEDINGS OF THE AMERICAN ACADEMY 



TABLE IX.,— continued. 

 Table for Polarimeter : p = cos 2a X 100. 



cos2 w -i- B sin''^ w} -+• (A sin''^ iv -\- B cos''^ w) 

 cos 2 IV = p cos 2 w. Hence, if the line of junction is not 



Evidently when the light is unjiolarized, the angle will be 45° ; when 

 totally polarized, 0°. We must now determine the effect when the 

 line of junction is not parallel to the plane of polarization, but inclined 

 at an angle w. The two images will in this case have a brightness 

 (A cos^ to -\- JB sin^ w), and {A sin^ w -\- B cos^ w). Hence the ap- 



, . ,. , (A cos^ w -h B sin2 iv) — (A sin^ w + B cos'-^ w) 

 parent polarization p' =l j-^ ^ 



_ A — B 



A + B 



parallel to the plane of polarization, the observations must be reduced 



by dividing by cos 2 w. Evidently if w ^ 45°, the light appears to 



be uni->olarized. The above discussion suggests a means of determining 



the direction of the plane of polarization. IMake two observations of 



the amount of polarization, turning the polarimeter 45°. Then call 



p, p', p", the true and the observed polarization in the two cases, and 



w the unknown angle between the line of junction in its first position 



and the plane of polarization. Having given p' and p", we wish to 



determine p and w. Evidently p' = p cos 2 to, and p" = p cos 2 



p" 

 (45° — w) = jo sin 2 w. Taking their quotient gives tang 2 w = — , 



and the sum of their squares gives p = V/>' ^ -)- p^\ 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 color, when their line of junction will be inclined 



