viii AUTHOR'S PREFACE. 



With the addition of the materials acquired in making this com- 

 pilation, and of the results of many original investigations, to which 

 they had given rise, it hecame almost indispensable to copy the whole of 

 the lectures once more, and to exchange some of them for others, which 

 were wholly new ; at the same time all possible pains were taken to dis- 

 cover and to correct every obscurity of expression or of argument. 



Drawings were also to be made, for representing to the reader the appa- 

 ratus and experiments exhibited at the time of delivering the lectures, for 

 showing the construction of a variety of machines and instruments con- 

 nected with the different subjects to be explained, and for illustrating them 

 in many other ways. These figures have been extended to more than 

 forty plates, very closely engraved, and the execution of the engravings has 

 been minutely superintended. But the text of the lectures has been made 

 so independent of the figures, that the reader is never interrupted in the 

 middle of a chain of reasoning, but is referred, at the end of a paragraph, 

 to a plate, which has always a sufficient explanation on the opposite page. 



The bulk of this work is not so great as to require, for its entire perusal, 

 any unreasonable portion of time or of labour. There may, however, be 

 some persons who would be satisfied with attending to those parts in which 

 it differs most from former publications, without having leisure or inclina- 

 tion to study the whole. To such it may be desirable to have those sub- 

 jects pointed out which appear to the author to be the most deserving of 

 their notice. 



I The fundamental doctrines of motion have, in the first place, been more 



II immediately referred to axioms simply mathematical than has hitherto been 

 1 usual ; and the application of these doctrines to practical purposes has 



perhaps in some instances been facilitated. The passive strength of 

 materials of all kinds has been very fully investigated, and many new 

 conclusions have been formed respecting it, which are of immediate 

 ' importance to the architect and to the engineer, and which appear to con- 

 tradict the results of some very elaborate calculations. 



The theory of waves has been much simplified, and somewhat extended, 

 and their motions have been illustrated by experiments of a peculiar nature. 

 A similar method of reasoning has been applied to the circulation of the 

 blood, to the propagation of sound, either in fluids or in solids, and to the 

 vibrations of musical chords ; the general principle of a velocity corre- 

 sponding to half the height of a certain modulus being shown to be appli- 

 cable to all these cases, and a connexion has been established between the 

 sound to be obtained from a given solid, and its strength in resisting a 

 flexure of any kind ; or, in the case of ice and water, between the sound 

 in a solid and the compressibility in a fluid state. 



The doctrine of sound, and of sounding bodies in general, has also 

 received some new illustrations, and the theory of music and of musical 

 intervals has been particularly discussed. 



With respect to the mathematical part of optics, the curvature of the 

 images formed by lenses and mirrors, has been correctly investigated, and 

 the inaccuracy of some former estimations has been demonstrated. . 



In the department of physical optics, the phenomena of halos and 



