242 Mr. J. F. W. Herschel on the aberrations of 
if the curvatures of the proposed system of surfaces be r , r 2 , 
r , &c., those of the equivalent system will be and r z , 
and r , &c. In this case we have 
L=(t*- -i )(Tj—r 2 ) ; L'= ( fx' — 1) (r -r 3 ) &c. 
and taking these as the values of L, L', See. the equation (0) 
will still hold good. 
Of the mode of correcting the aberrations of a compound lens ; and 
first, of the destruction of the spherical aberration in two lenses of 
the same medium placed close together , with a view to the im- 
provement of magnifiers , eye-glasses , and burning lenses. 
10. The value of A/ in a single lens, for parallel rays, is 
represented by ~ . [x 2 L A. If we put for A its value, and 
attempt to make this vanish by assigning a relation between 
r and r 2 , we shall find the roots of the equation imaginary, 
unless the refractive index exceed 4, a case which nature 
affords no approach to. If we would reduce it to its minimum 
value, we find 
Y 
z 2 — m — 4 m 1 
r, 2 + m 
In ordinary glass, we have ^ = 1.524, or nearly ~ whence 
we get m — a = + -L, « =— — , a =1, £ = + ^, 
13' = + 7 == -f" • In such glass therefore we have — = 
d-* or the lens must be double convex or double concave, 
having the radius of the posterior surface six times that of 
the anterior. 
* In strictness 0.1466, or little more than f ; but this part of the subject being of 
less moment, I have used \ for the value of to facilitate the calculations. 
