ratio rif the focal lpiijrth-> of two louses formed of these substances, which, 

 when united, will produce images nearly free from colour. 



Let | and $' be the focal lengths of the lenses, 1 + r and 1 -f v the ra- 

 tio of refraction belonging to the red and violet rays respectively in the 

 1st lens, and 1 4. /' and 1 -f v = ditto of the other ; then 



Hence it appears that p' and must be of dilfererit signs, or one lens 

 concave and the other convex ; and that they are as the respective dis- 

 persive powers of the substances of which the lenses are made. 



The common practice of opticians, is to use flint glass and crown glass, 

 the dispersive powers of which are in the ratio of 50 to 33 ; and .". a 

 compound lens, in which the separate focal lengths for the same kind of 

 homogeneous light, are as 50 I 33 will make the red and violet rays, con- 

 verge accurately to one point. 



9. Having given the aperture of any lens, and the foci to which rays 

 of different colours, belonging to the same pencil, converge ; to find the 

 least circle of aberration through which these rays pass. 



Let D diameter of the least circle of aberration, , aperture of the 

 lens, the rest as before ; then 



D = 



r + r 



Suppose, for instance, the lens be of crown glass, v = .56, r = .54 ; 



.'. r^r ; D .". is of the aperture. 



0*4. r 5a ' 5 ) 



Light, aberration ofsec Aberration. 



For a concise account of other physical properties of light, such as the 

 phaenomena of coloured rings, double refraction, polarization of light, 

 &c. see Coddington's Optics ; these subjects, as requiring diffuse expla* 

 nations, cannot here be entered upon. 



LINE right. 



Equations and Problems relating to, the co-ordinates being supposed 

 rectangular. (Hamilton. ) 



1. The equation to a straight line is y 

 ax + b, where a is the tangent of the 

 angle which the line makes with the axis 

 X A x t and b is the distance from A at 

 which it intersects the axis Ay, 



