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times the thickness of tlie lens at the centre. The smallest 
aberration takes place when the lens used is a doable convex 
one, the radii of the spherical surfaces being as one to six, and 
the more convex surface being exposed to the parallel rays, in 
which case the distance//' amounts to one and one-fourteenth 
of the thickness of the lens. The spherical aberration can 
likewise be corrected by making use of elliptical and other 
curves instead of spherical, but the latter from their simplicity 
are now always preferred. 
The greatest objection to the use of the refracting telescopo 
with one lens was, however, the fringe of extraneous colour 
which surrounded all the objects. In a homogeneous convex lens 
of glass the 
violet rays are 
bent much 
more than the 
red, so that the 
— - focus of the 
former Y (fig. 
2) is situated 
nearer to the 
object-glass 
than the latter 
R, and the 
other coloured rays have their foci between those two points. 
It has been calculated that in a lens with a focus of twenty- 
seven feet, the distance between the foci of those two points 
amounts to one foot. The confusion of the coloured images 
resulted, and which even Newton regarded it hopeless to think 
of correcting-, was at length got rid of by Dollond (though it 
had previously been found out by Hall), and is considered to 
be the greatest optical discovery of the eighteenth' century. By 
making use of prisms of different liquid or solid transparent 
substances, it was found that the separation of the ray 
of white light into a coloured ribbon was not always of 
the same length, nor had it the same position in respect 
to the incident ray. From this Dollond hit upon the happy 
idea that it might be possible, by combining two trans- 
parent media of different dispersive powers (as these changes 
were called), to bend a ray of white light out of its original 
path without separating it into colom’ed rays. He found that 
by placing a prism of crown-glass with an angle of thirty 
degrees in front of another of flint-glass with an angle of 
nineteen degrees (the angles being opposed), that this result 
was completely attained ; and as a lens may be considered as 
a series of prisms, it followed that if a convex lens of crown- 
glass A B, (fig. 2) were placed in front of a concave lens 
