of the Atmosphere. 451 



it is compensated or neutralized by a fixed number of thin 

 glass plates, or the varying number of refracting surfaces, by 

 which the same effect may be produced at a fixed angle, ca- 

 pable also of being changed*. 



With apolarimeter thus constructed, I have determined that 

 the maximum polarization of a clear blue sky is equivalent to 

 a rotation in the plane of a polarized ray of 30^ ; and that this 

 maximum takes place at a distance of from 88° to 92° from 

 the sun, and in the plane passing through the sun and the 

 zenith. This maximum is of course dependent on the state of 

 the atmosphere, both with respect to its magnitude and posi- 

 tion; but we shall assume 30° as its amount, and 90° from the 

 sun as its position in a normal state of the atmosphere, and 

 when the sun is in the horizon. 



VI. On the Form of the Lines of equal Polarization in the 

 Atmosphere. 



It is obvious, from the phsenomena already described, that 

 the polarization of the atmosphere, produced by the reflexion 

 of the sun's light from the matter which composes the atmo- 

 sphere, in planes passing through the sun, the point of re- 

 flexion, and the eye of the observer, would have been equal in 

 circles of which the sun and the antisolar point are the centre, 

 had there been no disturbing causes, or had the atmosphere 

 been a perfectly transparent medium. In this case the pola- 

 rization would have been complete, or 45° ; and this maximum 

 would have occurred at a distance from the sun, the half of 

 which was the polarizing angle of the medium. There is ob- 

 viously, however, a cause depending on the zenith distance of 

 the polarizing point of the sky, which acts in opposition to the 

 polarization produced by reflexion, and compensates it at the 

 neutral point already described. When the sun, therefore, is 

 in the horizon, these two actions are rectangular, as in biaxal 

 crystals ; and we must therefore determine the form of the 

 lines of equal polarization when the sun is in the horizon, and 

 when the atmosphere is perfectly pure. When viewed, con- 

 sequently, in their general aspect, the phasnomena of atmo- 

 spherical polarization may be represented by the formula 



R=30°(sinDsinD'),; 



where R = rotation, or degree of polarization, and 



D and D' = the distances of the point whose polarization is 



required from the tvoo neutral points. 



This formula would make the lines of equal polarization 



* See the Transactions of the Royal Irish Academy, vol. xix. part S. 



2 G2 



