Intelligence and Miscellaneous Articles. 231 



axis of the crystal plate, either coincides with the plane of polariza- 

 tion of the rays studied or is perpendicular to it. 



This first determination having been effected, he produces the 

 physical phenomenon which will give rise to the rotation sought : 

 this will be either the interposition of a substance possessing a 

 natural rotatory power, or a magnetic influence, or some other phe- 

 nomenon. 



An equal rotation in the opposite direction to that which is really 

 produced is then observed through the crystal plate. Upon the 

 divided circle in the centre of which the analyzer is mounted, the 

 position of the plane of polarization thus observed is determined, 

 aud then the half-wave plate is withdrawn. The rays are then 

 received upon the analyzer polarized in the direction given them by 

 the experiment which was had in view ; and this direction is deter- 

 mined upon the divided circle. The angle of the two planes of 

 polarization, symmetrical with respect to their initial position, is 

 double the angle which would have been observed directly (without 

 making use of the lialf-ivave plate). 



In this second position the observer can replace the crystal plate 

 so that it does not give rise to any new deflection of the plane of 

 polarization ; and then he stops the phenomenon he is studying. 

 The plane of polarization of the rays which have passed through 

 the plate, instead of returning to its initial position, is thrown 

 symmetrically on the other side of the axis of the plate. The angle 

 between the extreme deflections obtained by the different operations 

 we have just indicated is treble that which would have been obtained 

 by a direct measurement. 



This method can be employed in a great number of circumstances. 

 It is peculiarly applicable to the system of two planes of polariza- 

 tion forming between them a constant angle, such as are obtained 

 with a penumbra-polarimeter, especially a cut Mcol. The deter- 

 minations are then made with great facility and precision. 



In an investigation in course of execution I have had occasion to 

 make use of the experimental arrangement I have just described ; 

 and it has given me the best results. 



An ordinary observation consists of two viewings, each suscep- 

 tible of an error. The method above explained admits of four 

 errors for the double deflection, and six for the triple deflection. 

 It is therefore necessary to determine whether the measurements 

 thus made possess greater precision than direct measurements. 



If the experimenter placed the axis of the half-wave plate every 

 time rigorously in coincidence with the plane of polarization of the 

 incident rays, or with the plane that bisects the system with pen- 

 unibrse, it is evident that the same precision of measurement applied 

 to angles twice or thrice as large would diminish in the same pro- 

 portion the probable errors. The precision of the method depends 

 therefore on the perfection of the preliminary determination. Now, 

 with the penumbra-polarimeter, for example, a small divergence 

 between the axis of the crystal plate and the plane of symmetry of 

 the polarizer gives rise to a variation of twice that amount in the 

 relative position of the two planes of polarization ; so that the sen- 



