PREFACE. VH 



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 inclination to study the whole. To such it may be 

 desirable to have those subjects pointed out, which appear to the au- 

 thor to be the most deserving of their notice. 



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

 more immediately referred to axioms simply mathematical, than has 

 hitherto been usual; and the apphcation 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 

 inunediate importance to the architect and to the engineer, and which 

 appear to contradict the results of some very elaborate calculations. 



The theory of waves has been much simplified, and somewhat ex- 

 tended, 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 prin- 

 ciple of a velocity, corresponding to half the height of a certain modu- 

 lus, being shown to be applicable 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 gene- 

 ral 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 



