Mr. J. F. W. Herschel on the aberrations , &c. 223 
refractive powers of media on rays of different colours which 
later experimental researches have exploded. 
In the more abstruse and difficult part of the theory of 
optical instruments which relates to the correction of the 
spherical aberration, the necessity of an appeal to the powers 
of algebraic investigation has been all along acknowledged ; 
and as the subject is confessedly within its reach, and pre- 
sents none of those difficulties which obstruct our progress 
in the transcendental analysis, but merely such as arise from 
the involved nature of the equations, and the number of 
symbols which enter into them, it might have been expected 
that the appeal would, long ere this, have been successful, 
the artist have bowed to the dictates, however oracular, of a 
theory which he was satisfied had its foundation in unerring 
truth, and the result of their combined labours have been the 
attainment of all the perfection the telescope is susceptible of. 
Unhappily, however, this is far from being the case. Investiga- 
tionsritis true, have been accumulated on each other; formulae 
have been deduced, and even tables computed from them ; but 
the investigations, from their dry and laborious nature, and 
the almost total want of that symmetry which is especially 
necessary in so complicated a subject, have been studied by 
few ; the formulae, requiring a more extensive share of 
algebraical knowledge than can be expected in a practical 
optician, are thrown aside by him in despair, and the tables 
hitherto constructed from theory, being founded on data 
which may never again occur, are worse than useless, serving 
only to mislead. In consequence, the best and most success- 
ful artists are content to w f ork their glasses by trial, or by 
empirical rules, embodying the result of numerous preceding 
