iv PREFACE. 



placed in a decidedly new light, it may be proper to 

 point out the extreme simplicity which is given, at 

 the end of the book, to the theory of waves and of 

 sounds, and the still greater novelty of that of the 

 cohesion of fluids, which, it is presumed, will be 

 allowed to be deduced in a most unexceptionable 

 manner from the general principle of virtual veloci- 

 ties. There are, also, some remarks on the applica- 

 tion of Taylor's theorem, which may be found of 

 considerable utility in computing the forms of the 

 surfaces of fluids, and which are still more im- 

 portant on account of the great assistance, which 

 may be derived from them, in calculations respecting 

 the figure of the earth, as connected with its 

 compressibility. 



It is almost superfluous to add, that any correc- 

 tions, which may occur to the mathematical reader, 

 whether of errors of the press, or of more serious 

 mistakes, will be gratefully received, and candidly 

 acknowledged, by the author of these illustrations. 



London, 28 Feb, 1821. 



