CHAP. L, 2.] 



MATHEMATICS PHYSICS MECHANICAL ARTS. 



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 



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. 1 



2. On the relations between Mathematics and Natural Philosophy, and between the latter and 



the Mechanical Arts. 



(24.) The object of this Dissertation has little in corn- 

 Connection mon w ith an attempt formally to subdivide human 

 ofMathe- jj now i e ^or e j n t o compartments, and to assign their 

 matics, , p . - .-I-! TJ. I.* .a 



physics.and boundaries with metaphysical exactness. It is chiefly 



mechanical in their practical bearing on one another that they 

 must be considered. If one science, like Mathe- 

 matics, furnish the only sure step towards the un- 

 derstanding or the enlargement of another, as Astro- 

 nomy or Optics, a practical link is constructed be- 

 tween them, which renders the progress of the one 

 not independent of the progress of the other. The 

 intimate and reciprocal connection thus subsisting 

 between Mathematics and Physics is to be found in 

 almost an equal degree between Pure Physics and the 

 Mechanical Arts, of which we take Civil Engineer- 

 ing to represent the department most cognate to 

 that of Natural Philosophy, of which this Disserta- 

 tion more especially treats. 

 (25.) The history of the last seventy or eighty years 



Boundaries enforces this conclusion. The boundaries of Science 



and S Art n un- and Art are a3 undefinable as those of " fact " and 

 defined. " theory," or those which separate the kingdoms of 

 nature from one another. There are arts which can 

 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 



(26.) 



rightly without teaching its applications; and that 

 the limit to which we are to do so is a limit depend- 

 ing solely on the judgment of the teacher, and on 

 the special purpose of the lesson. But the progress 

 of science is a lesson learnt from the great book of 

 experience; and if we are to feel the force of its 

 teachings, we must consult, not one, but many of its 

 pages. Looking to the history of science since 1750, 

 but especially during the present century, it is quite 

 impossible not to admit how large a share the sciences 

 of application have had in moulding the direction of 

 men's thoughts and speculations, and in enabling, 

 nay, compelling them to realize certain abstract no- 

 tions far from easy of conception. Instances of this 

 are to be found in the force of percussion, the co- 

 existence of vibrations in air and other substances, 

 and such notions of body as we derive from practical 

 efforts of continually-increasing boldness to extend 

 the scale of our constructions. 



The analogy of the relation between Mathematics 

 and Physics, and of the latter to civil Engineering, is 

 so close that the three subjects might almost be re- O f the last 

 presented as three terms of a continued proportion. 100 years. 

 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 



(27.) 



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 consulted 

 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 Eepertorium, and that of Dove, afford a vast amount of historical infor- 

 mation. The Transactions and Proceedings of the various societies, British and Foreign, have of course furnished a great part 

 of my information. Such strictly biographical details as I have made use of, have in general been very carefully taken from 

 the best accessible authority. 



