13 
of Achromatic Object-Glasses. 
Log of index B =1.601 = 0.2043913 
Log of decimal of index A = .528 = 1.7226339 
Second sum, 1.9270252 
From 1.7615035 
Take 1.9270252 
Nat. n° .68309 = 1.8344783 
Whence the ratio of the dispersive powers of the two glasses is 
1 : .68309 ; or .68309, according to the common mode of expres- 
sion. 
We have thus obtained the requisite data for determining the 
radii of curvature to be given to our plate and flint lenses, in or- 
der to produce an achromatic object-glass. 
13. Computation Tables , Sfc.for finding the Radii of Curvature; 
the refractive index of each glass , and their dispersive ra- 
tio, being given. 
If we were now merely required to correct the object-glass 
for colour or dispersion, all that would be necessary, would be 
to make the focal lengths of our two lenses in the direct ratio of 
their dispersive powers ; and, therefore, with three of the sur- 
faces formed at pleasure (at least within certain limits), the 
fourth might still be so determined as to produce a correction 
of colour; and this is probably still practised by some opticians : 
but the correction of colour is by no means all that is to be con- 
sidered in working an object-glass for a good telescope ; for if, 
also, we have not regard to the spherical aberration, the image, 
although free from colour, will be seen in a cloudy or smoky 
field of vision, which will render it very imperfect and indis- 
tinct. 
With a view to this latter correction Mr Herschel has given 
a very elaborate and valuable paper in the Philosophical Tran- 
sactions of the Royal Society, Part ii. for 1821, with Tables, 
&c., so as to reduce very considerably the labours of computa- 
tion ; and, by extending these tables to a greater length, it is 
presumed that we have added our mite towards the simplifying 
this important but otherwise laborious and intricate calculation. 
However, before entering upon an explanation of this process, 
