compound lenses and object-glasses. 263 
extent of the table, i. e. as far as 17=070, (beyond which it 
is very unlikely it should ever extend in practice). In fact, 
these values have, the one a maximum and the other a mini- 
mum between ■ar=o , 55 and w=o-6o. The principal variation 
takes place on the values of r z and r , which change rapidly 
as sr increases, the whole stress of the adjustment by which 
the aberration is corrected being laid on these surfaces. We 
may take advantage of this fortunate and very remarkable 
circumstance, and assigning to r j and r ^ constant values, such 
as to give the least average error, employ them to complete 
the interior curvatures : thus we may announce it as a prac- 
tical theorem, which in all probability will be found suffi- 
ciently exact for use, that a double object-glass will be free from 
aberration , provided the radius of the exterior surface of the crown 
lens be 6720, and of the flint 3 4/20, the focal length of the com- 
bination being 10x00, and the radii of the mterior surfaces being 
computed from these data , by the formula given in all elementary 
works on optics , so as to make the focal lengths of the two glasses 
in the direct ratio of their dispersive powers. 
27. It remains to examine the effect of a change of the 
values of p, and p/ on the curvatures. Now the variations to 
which these quantities are subject being very trifling, we may 
neglect their squares and products, and we shall have 
where ~ and are constant co-efficients, which are most 
dp dp' 
readily computed by repeating the preceding calculations for 
values of p, and p/ a little differing from those before assumed. 
And first, with respect to if we take p, = 1504, and 
