MECHANICAL PRINCIPLES OF FLUIDS. 351 



is very great: but these calculations are performed by means of 

 empirical formulae, which do not connect the facts with their causes, 

 and still leave a wide space to be traversed, in order to complete the 

 science. 



In the mean time, all the other portions of Mechanics were reduced 

 to general laws, and analytical processes ; and means were found of 

 including Hydrodynamics, notwithstanding the difficulties which attend 

 its special problems, in this common improvement of form. This pro- 

 gress we must relate. 



[2d Ed.] [The hydrodynamical problems referred to above are, the 

 laws of a fluid issuing from a vessel, the laws of the motion of water 

 in pipes, canals, and rivers, and the laws of the resistance of fluids. 

 To these may be added, as an hydrodynamical problem important in 

 theory, in experiment, and in the comparison of the two, the laws of 

 waves. Newton gave, in the Principia, an explanation of the waves 

 of water (Lib. ii. Prop. 44), which appears to proceed upon an erro- 

 neous view of the nature of the motion of the fluid : but in his solution 

 of the problem of sound, appeared, for the first time, a correct view of 

 the propagation of an undulation in a fluid. The history of this sub- 

 ject, as bearing upon the theory of sound, is given in Book viii. : but 

 I may here remark, that the laws of the motion of waves have been 

 pursued experimentally by various persons, as Bremontier (Recherches 

 sur le Mouvement des Ondes, 1809), Emy (Du Mouvement des Ondes, 

 1831), the Webers (Vfellenlehre, 1825); and by Mr. Scott Russell 

 (Reports of the British Association, 1844). The analytical theory has 

 been carried on by Poisson, Cauchy, and, among ourselves, by Prof. 

 Kelland (Edin. Trans.), and Mr. Airy (in the article Tides, in the 

 Encyclopaedia Metropolitana). And though theory and experiment 

 have not yet been brought into complete accordance, great progress 

 has been made in that work, and the remaining chasm between the 

 two is manifestly due only to the incompleteness of both.] 



Perhaps the most remarkable case of fluid motion recently discussed, 

 is one which Mr. Scott Russell has presented experimentally; and 

 which, though novel, is easily seen to follow from known principles ; 

 namely, the Great Solitary Wave. A wave may be produced, which 

 shall move along a canal unaccompanied by any other wave : and the 

 simplicity of this case makes the mathematical conditions and conse- 

 quences more simple than they are in most other problems of Hydro- 

 dynamics. 



