Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

458 REASONING AND DEDUCTIVE EVIDENCE.
be confidently affirmed to belong to this diagram. As the thing,
however, here supposed, is rendered impossible by the imperfection of our senses, the truths of geometry can never, in their
practical apptications, possess demonstrative evidence; but only
that kind of evidence which our organs of perception enable us
to obtain.
But although, in the practical applications of mathematics, the
evidence of our conclusions differs essentially from that which
belongs to the truths investigated in the theory, it does not
therefore follow that these conclusions are the less important.
In proportion to the accuracy of our data will be that of all our
subsequent deductions; and it fortunately happens, that the same
imperfections of sense which limit what is physically attainable
in the former, limit also, to the very same extent, what is practically useful in the latter. The astonishing precision which
the mechanical ingenuity of modern times has given to mathematical instruments, has, in fact, communicated a nicety to the
results of practical geometry, beyond the ordinary demands of
human life, and far beyond the most sanguine anticipations of
our forefathers.*
* See a very interesting and able article, in the fifth volume of the
Edinburgh Review, on Colonel Mudge's account of the operations carried on for accomplishing a trigonometrical survey'of England and Wales.
I cannot deny myself the pleasure of quoting a few sentences.
"In two distances that were deduced from sets of triangles, the one
measured by General Roy in 1787, the, other by Major Mudge in 1794,
one of 24,133 miles, and the other of 38,688, the two measures agreed
within a foot as to the first distance, and sixteen inches as to the second.
Such an agreement, where the observers and the instruments were both
different, where the lines measured were of such extent, and deduced
firom such a variety of data, is probably without any other example.
Coincidences of this sort are fiequent in the trigonometrical survey, and
prove how much more good instruments, used by skilful and attentive
observers, are capable of performing, than the most sanguine theorist
could have ever ventured to foretell.
" It is curious to compare the early essays of practical geometry with
the perfections to which its operations have now reached, and to consider
that, while the artist had made so little progress, the theorist had reached