Polarization of the Light of the Sky. 501 



Arago---,^ / \ ___--- Babinet 



Brewster. 



But the application of the formula to points out of the plane 

 of sun, zenith, and observer involves a pure assumption, viz. that 

 the neutral points are centres, or their radii vectores axes of the 

 polarization, so that D, D' may be applicable to distances from the 

 neutral points measured in any direction. For this assumption 

 there is no foundation whatever ; and it leads to the entire dis- 

 regard of the convention of sign above alluded to, and to the repre- 

 sentation of the polarization in the negative region as similar in 

 character, and, indeed, as continuous with, that in the positive 

 region. The adoption of this assumption by Brewster led to a 

 distribution of the polarization entirely inconsistent both with 

 his own observations and conclusions, and with those of all other 

 observers, as well as absurd in itself. In fact this is probably 

 the only case where geometers have for a considerable time been 

 content to acquiesce in the statement that the boundary between 

 two regions on the surface of a sphere is a point, or, as Bubenson 

 puts it, " Ces deux espaces du ciel, caracterises par leur polari- 

 sation contraire, sont separes Pun de Pautre par un intervalle 

 tres restreint, dont la lumiere ne montre pas la moindre trace de 

 polarisation, et que ?on appelle point neutre" (P. 3.) I have 

 to thank Prof. H. J. S. Smith for stating this point with remark- 

 able clearness at the meeting of the Ashmolean Society, at which 

 this paper was read. 



Brewster made this assumption — namely, that the above for- 

 mula was applicable in whatever direction D and D' were mea- 

 sured. Then in applying the case to the point in the horizon 

 at right angles to the sun, of which he had observations, he 

 found that the formula gave a polarization greater than that in 

 the zenith, whereas bis observations showed that it was less ; in 

 fact the formula was in no sense applicable to that point at all. 

 But to correct the discrepancy he introduced a term, —6° 34' 

 (sin z sin A) ; this reduced the value for the horizon maximum 

 to 27° very nearly, which is within the limits of the observations, 

 though still rather large, and did not affect the plane of sun, 

 zenith, observer, for which A = 0. (A = azimuth, z — zenith- 

 distance.) It was from this formula (R = 33|° sin D sin D' 



