2(>3 
Mr. J. F. W. Herschel on the aberrations of 
putting together of the lenses, it will be observed that for the 
lower values of •sr, or the more dispersive varieties of flint- 
glass, the curvature of the third surface is a very little greater 
than that of the second, so that the glasses when laid together 
in their proper position will have a minute interval between 
them. At a certain value of nr between 0-55 and 0 60 
(^•=0*58 nearly) this interval vanishes, and the glasses are 
in contact over their whole surface. For higher dispersive 
ratios, if laid close together, they would touch in the vertex. 
This is regarded as an objection in practice, and justly, (espe- 
cially when the curvatures of the surfaces in contact differ 
considerably) as their pressure on each other at the centre 
must tend to distort their figures, and disturb the uniformity 
of their density, not to speak of the production of the colours 
of thin plates, whose effect on vision is more problematic. 
But in fact, the difference of the curvatures in this construc- 
tion is so very trifling,as to fall within the limits of practical 
errors, and therefore, if the separation of the two glasses by 
a ring of metal (which in a 10 feet object-glass, of 5 inches 
aperture, even in the very unfavourable case of to=o‘7o need 
not exceed i-4,ooth of an inch in thickness) be deemed un- 
advisable, it may be neglected, and the glasses ground to 
the same radius, provided only the necessary alterations are 
made in the other surfaces to preserve the proper proportion 
of their focal lengths. 
2 6. With regard to the interpolation of the tables above 
given for intermediate values of if we cast our eyes down 
the second and 5th columns, we cannot but be struck by the 
very small alteration in the values of r x and r , the curvatures 
of the first and last surfaces throughout the whole useful 
