a td 
Cuar. I., § 2.] 
instances, however, it has been necessary to introduce 
the same individual into two or three different sec- 
tions, and even into different chapters, when his pur- 
suits have been in very various branches of science. 
This has been avoided, however, as much as possible, 
and a sacrifice has occasionally been made of the 
methodical order of the subjects, so as to combine in 
one view all that has made an eminent philosopher 
illustrious. Such little sacrifices of arrangement are 
MATHEMATICS—PHYSICS—-MECHANICAL ARTS. 
805 
incidental to the way of treating the whole subject ; 
and it may be hoped that its practical advantages, 
in the eye of the general reader, will be found to 
compensate for its defects as they may appear to the 
more rigorous student. For the sake of the latter 
especially, a short but comprehensive index of Names 
and Terms is prefixed, by which, I believe, it will be 
easy to trace all that is said of any one person or 
subject in any of the chapters.' 
§ 2. On the relations between Mathematics and Natural Philosophy, and between the latter and 
the Mechanical Arts. 
(24.) The object. of this Dissertation has littleincom- rightly without teaching its applications; and that 
Connection mon with an attempt formally to subdivide human the limit to which we are to do so is a limit depend- 
aaa knowledge into compartments, and to assign their ing solely on the judgment of the teacher, and on 
physics,and boundaries with metaphysical exactness. Itis chiefly the special purpose of the lesson, But the progress 
mechanical in their practical bearing on one another that they of science is a lesson learnt from the great book of 
— must be considered. If one science, like Mathe- experience; and if we are to feel the force of its 
matics, furnish the only sure step towards the un- teachings, we must consult, not one, but many of its 
derstanding or the enlargement of another, as Astro- pages. Looking to the history of science since 1750, 
nomy or Optics, a practical link is constructed be- but especially during the present century, it is quite 
tween them, which renders the progress of the one impossible not to admit how large a share the sciences 
not independent of the progress of the other. The of application have had in moulding the direction of 
intimate and reciprocal connection thus subsisting men’s thoughts and speculations, and in enabling, 
between Mathematics and Physics is to be found in nay, compelling them to realize certain abstract no- 
almost an equal degree between Pure Physics and the tions far from easy of conception. Instances of this 
Mechanical Arts, of which we take Civil Engineer- are to be found in the force of percussion, the co- 
ing to represent the department most cognate to existence of vibrations in air and other substances, 
that of Natural Philosophy, of which this Disserta- and such notions of body as we derive from practical 
tion more especially treats. efforts of continually-increasing boldness to extend 
(25.) The history of the last seventy or eighty years the scale of our constructions. 
op credo enforces this conclusion. The boundaries of Science The analogy of the relation between Mathematics Fah 
tica 
and Art are as undefinable as those of ‘ fact”’ and 
“theory,” or those which separate the kingdoms of 
nature from one another. There are arts which can 
and Physies, and of the latter to civil Engineering, is aresredh 
so close that the three subjects might almost be re- of the last 
presented as three terms of a continued proportion, 100 years. 
and Art un- 
defined. 
(26.) 
hardly be called scientific, and there are others which 
have contributed more to the original stock of know- 
ledge than they ever drew from it. These last are 
like the shoots of those tropical plants which at first 
are mere buds upon the trunk, and are nourished 
solely by its juices, but which, when they reach the 
ground, plant themselves there, and become not only 
the props and stays of the parent stem, but supply it 
from an ever-increasing area with the sap which they 
originally borrowed, 
The more closely we examine the subject, the more 
are we satisfied that it is impossible to teach science 
What the second is to the first may be affirmed of 
the third relatively to the second. Physics may 
exist, at least to a limited extent, without a mathe- 
matical basis, as the art of construction long preceded 
a knowledge of the principles on which it is founded, 
But as knowledge advances it extends in both 
directions towards speculation and towards practical 
applications, but most towards the applications. This 
Bacon well understood, and he has consistently main- 
tained, that knowledge, to be profitable to its cultiva- 
tors, must also be fruitful to mankind. And all the 
history of science since Bacon’s day has read this 
1 I have borrowed but sparingly, in the following pages, from the existing compilations on the history of science. Indeed, 
a writer who intends to make a subject his own by a well-considered, fundamental plan of treating it, will use such works prin- 
cipally as a guide to his own further inquiries, and to assist him in selecting the topics worthy of fullest discussion. 
In this 
respect Dr Whewell’s excellent writings, already cited, have been of great use to me; and in the particular department of 
Astronomy, I have often referred to Mr Grant’s valuable History of that science, as well as to the writings of Delambre, and 
the very elaborate Historical Essay by M. Gautier, on the problem of the Three Bodies, which is not, I think, noticed by 
Mr Grant, but which contains a most elaborate history of the researches of Lagrange and Laplace. In optics, I have lted 
the systematic treatises of Dr Young, Sir D. Brewster, Sir J. Herschel, Dr Lloyd, M. Moigno, and M. Radicke ; and so of other 
subjects. Gehler’s Physikalisches Worterbuch, Fechner’s Repertorium, and that of Dove, afford a vast amount of historical infor- 
mation. The T'ra tions and Proceedings of the various societies, British and Foreign, have of course furnished a great part 
of my information. Suclr strictly biographical details as I have made use of, have in general been very carefully taken from 
the best accessible authority. : 
