144 



THE APPARENT POSITION OF THE ZODIACAL LIGHT. 



If these results are laid down as points determined by rectangular co-ordinates, 

 the abscissas representing the variations of absorption, expressed in tenths of a 

 magnitude, and the ordinates representing variations in latitude, expressed upon 

 the same scale in degrees, a curve passing through the origin and nearly through 

 the projected points may be drawn with some confidence ; but beyond the ex- 

 treme point its course would be doubtful. Hence it seemed best to employ a 

 curve of some simple theoretical form suggested by the graphical result. The 

 curve selected was a parabola passing through the origin, with its axis parallel to 

 the axis of abscissas. Upon this assumption, the mean values just obtained for the 

 corresponding variations in absorption and in latitude Avill fiu'nish four equations of 

 condition, of the form p z -\- hy =: hy^, if we denote by 2p the parameter of the 

 parabola, and by — b the ordinate of the vertex. The solution of these equa- 

 tions by the method of least squares results in the values 2p = 4.77 and b = 

 1.70. Hence the abscissa of the vertex is — 0.61, and the equation of the para- 

 bola is (y -\- 1.70f = 4.77 {x -\- 0.61), from which values of y in degrees may be 

 obtained for values of x given in tenths of a magnitude. This parabola was 

 charted, and the corrected latitudes, entered in the two columns of Table H. 

 next to the last, were mostly found from the chart. 



Results previously reached by other methods for the relation between absorp- 

 tion and latitude did not materially differ from those just given. The method 

 here adopted has the advantage of leaving comparatively little to be arbitrarily 

 determined. 



The experiment was afterwards made of grouping the remainders derived from 

 the inclination of the ecliptic and from the latitude of the axis in Table IV., the 

 form of which resembles that of Table III. 



