and its application to the observation of the Sky. 25 



gives no bands where the polarization is inclined 45° to the 

 direction of the bands. Now when the neutral point is re- 

 garded with the Savart under favourable conditions, a neutral 

 line is seen to extend across the bands, if they are vertical or 

 horizontal, in a shape somewhat resembling an hyperbola, with 

 the vertex at the neutral point, and the convexity turned 

 downwards ; but there is always a portion at the vertex which 

 looks like a horizontal neutral line, presenting the appearance 

 figured in Brewster's paper (Edinb. Trans. 1861, p. 213). In 

 particular the neutral line is horizontal, or nearly so, where 

 the part of it due to the property of the Savart joins the true 

 neutral point. Under these circumstances I am able to say 

 with certainty that the polarization in the region immediately 

 adjoining the neutral point at its side is always in a plane in- 

 clined 45° to the vertical nearly. I then employed both 

 polariscopes to find out what the actual directions were ; the 

 results are expressed in the following sketch, which also em- 

 bodies the general distribution throughout the region in 

 question, as derived from a considerable number of observa- 

 tions of Arago's and Babinet's points. The distribution about 

 Arago's point and the antisolar point is similar to that about 

 Babinet's point and the sun, as Brewster made it. I have 

 not attempted to observe Brewster's point for this purpose, as 

 the observations are trying to the eyes when the sun is high 

 enough to see it. The continuous lines in the figure give 

 approximately the positions of the plane of polarization. The 

 hyperbolic dotted line represents the neutral curve seen with 

 a Savart with bars vertical or horizontal ; it is the locus of 

 points where the direction-lines are inclined 45° to the ver- 

 tical. The neutral point is in the middle, the sun or anti- 

 solar point is represented by the dot below. 



It is a matter of some interest to inquire what is the figure 

 of the tract which separates the positive and negative regions. 

 We may for this purpose draw the locus of points at which 

 the directions of polarization make an angle of 45° with the 

 radius vector to sun or antisolar point ; the resulting locus 

 may be regarded as a sort of diameter of the tract in question, 

 which extends on both sides of it. It forms a curve like a 

 loop of a lemniscate, having its centre at the sun or antisolar 

 point, and tc iching the vertex of the Savart hyperbola with 

 the flat end of the loop, if we imagine the two curves con- 

 tinued through the neutral point, of which their common 

 vertex is the centre. It is drawn in dots in the lower part of 

 the figure. 



