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of Edinburgh , Session 1871 - 72 . 
power and originality, as well as elegance. In all these respects it 
far surpasses his subsequent mathematical writings, excellent as are 
many of them ; for instance his celebrated treatises on * Light ’ and 
on 1 Sound’ in the ‘ Encyclopaedia Metropolitana.’ The appendix 
to Lacroix which was written by Babbage, was devoted to the 
‘ calculus of functions,’ a strangely weird branch of analysis, which 
remains even now much as Babbage left it. That in this direction 
there is a splendid field open for the inquirer, is evident to any one 
who consults Babbage’s papers on it; and it is wonderful that it 
has not been greatly developed of late years, when so many mathe¬ 
maticians, especially at home, have been found to apply themselves 
almost exclusively to those branches of the science which seem the 
least likely ever to have useful applications. 
“In their after-life the careers of these great workers and 
thinkers led them widely apart. Herschel devoted himself mainly 
to astronomy, but also to chemistry, photography, and occasionally 
to mathematics. His astronomical work is all of the very highest 
class, whether it consisted in his seclusion, for several of the 
best years of his life, at the Cape of G-ood Hope in the close observa¬ 
tion of the stars and nebulse of the Southern Hemisphere; or in 
first writing, and then, as edition after edition was called for, 
extending and improving his splendid semi-popular work, the ‘ Out¬ 
lines of Astronomy,’ which none, even of men of science, can read 
without deriving from it at once pleasure and profit. 
“ Babbage, on the other hand, applied himself mainly to machin¬ 
ery and manufactures. His so-called ‘ Ninth Bridgewater Treatise’ 
was pre-eminent even among the best of that singular series; his 
‘ Economy of Machines and Manufactures ’ is still a wonder¬ 
fully suggestive work; and his ‘Mechanical Notation’ supplies 
us with an insight into the kinematics of all possible combinations 
of machinery, which none can have any conception of without 
making it a special subject of study. He was led to its invention 
by his celebrated attempts to achieve the construction of a differ¬ 
ence-engine, and even of an analytical engine—machines totally 
unintelligible, in their conception, to the majority even of those 
who are capable of understanding the nature of the work for which 
they were designed. Enough was constructed, though it was a 
very small part, of the first of these engines to show not only that 
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VOL. VII. 
