Lord Ravleigh's Investigations in Optics. 485 



f " P ' k (9) 



?;= —2yp\ry.J 



If y = 0. the secondary focal line is formed without aberration, 

 but not otherwise. In general the curve traced out by the 

 rays for which ;r -\- y 2 = r , is 



f? I (p-p>V : 



p-p'J * ' 4/fffPp ' 



(10) 



in the form of a figure of eight symmetrical with respect to 

 both the axes. The rays starring either in the primary or in 

 the secondary plane pass through the axis of f*, the thickness 

 of the image being due to the rays for which a?=jy=r-r- v 2*. 



This subject can be illustrated without difficulty by experi- 

 ment. A radiant point is obtained by admitting sunlight into 

 a darkened room through a lens of short focus placed in the 

 window-shutter. A real image of the radiant is received upon 

 apiece of ground glass and examined from behind. To render 

 the light approximately homogeneous, a piece of red glass is 

 employed. The following results relate to an equiconvex 

 lens of 6 inches aperture and about 3 feet focus, on which the 

 light falls obliquely. 



As the screen is moved gradually back from the lens, the 

 illuminated area diminishes. At a certain point it begins to 

 double back upon itself, until at the primary focus the whole 

 area is double. The light is seen to be very unequally distri- 

 buted. At the edges corresponding to the boundary of the 

 lens the illumination is feeble, while at the folded edge, cor- 

 responding to the central vertical line of the lens, a caustic is 

 formed. On this account it would seem that curvature of the 

 primary focal line is a worse fault than thickness for the pur- 

 poses of the spectroscope. 



The accompanying figures show the general character of 

 the image at the primary focus under various circumstances. 

 The thick line represents the folded and highly illuminated 

 edge, the thin line the double edge corresponding to the mar- 

 gin of the lens. The quantities u. i\. v 2 are the distances 



* I have lately fuund that the aberration of un symmetrical pencils was 

 very generally treated by Sir W. Hamilton in his work on Systems of 

 Rays. Even if I could have supposed Hamilton's results to be known to 

 the reader, the investigation in the text would still be necessary, as my 

 purp3>se is very different from his. In the general theory ('with 3 and 6 

 nnite ) there is no distinction between the primary and secondary images. 



