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XVII. On the aberrations of compound lenses and object-glasses. 
By J. F. W. Herschel, Esq. F. R. S. &c. 
Read March 22, 1821. 
It has not unfrequently of late been made a subject of re- 
proach to mathematicians who have occupied themselves with 
the theory of the refracting telescope, that the practical be- 
nefit derived from their speculations has been by no means 
commensurate to the expenditure of analytical skill and 
labour they have called for, and that from all the abstruse 
researches of Clairaut, Euler, D’Alembert, and other 
celebrated geometers, nothing hitherto has resulted beyond a 
mass of complicated formulae, which, though confessedly 
exact in theory, have never yet been made the basis of con- 
struction for a single good instrument, and remain therefore 
totally inapplicable, or at least unapplied, in practice. The 
simplest considerations, indeed, suffice for the correction of 
that part of the aberration which arises from the different 
refrangibility of the differently coloured rays ; and accord- 
ingly, this part of the mathematical theory of refracting 
telescopes was soon brought to perfection, and has received 
no important accession since the original invention of the 
achromatic object-glass. Indeed the theoretical considera- 
tions advanced on this part of the subject by Euler and 
D’Alembert have even had a tendency to retard its advance- 
ment, by appearing to establish relations among the relative 
