ABE 



is an equation to the circle \vhen the centre of the polar coordinates 

 i* in the circumference (see Circle Equation to}, .-. the aberratic curve is a 



circle, whose rad. is -= . 

 LI 



b z 11 

 2. Let the orbit be an ellipse, whose equation is p% - - - ; Then 



, 



P 



that the aberratic curve (-see Circle Equation to) is a circle, whose ra- 

 dius is -^J-, and the distance of whose centre from the centre of coor- 

 dinates is ~ V a 2 2. 

 3. Let the orbit be the log. spiral, whose equation is p = m y, then y' 



= -^-^ = -^ = ?', .". p' \ .'. the aberratic curve is also 

 P y c_ m' 



P' 

 a log. spiral. 



ABERRATION in Optics. (Coddington.) 

 I. Aberration in reflection at spherical surfaces. 

 Let E Q = 7, E 7 = ?', 



E F = /, A N = v 

 and the point v> in the figure being 

 the actual intersection of the re- 

 flected ray and axis, let E v j\ 



Q 



(9 -I-/) 3 



&c. 



This in geometrical terms is equivalent to 

 OE 2 AN QE3 A Ng 



HF2"' T" " h Q F3 ' 4 E F "*" 



& .'. 9 X . ? ', or aberration in longitude, is 



- &c. or, because v is small, is 



1 E F 



QE8 AN 



