196 LECTURE XXI. 



first subdivision which we shall consider, will relate to the laws of the 

 equilibrium of fluids, or of the opposition of forces acting on them without | 

 producing actual motion, comprehending hydrostatics, or the doctrine of ' 

 the equilibrium of liquids, either within themselves or with moveable bodies ; 

 and pneumatostatics, or the equilibrium of elastic fluids. The actual 

 motions of fluids will be considered in the second subdivision : and the 

 third will relate to the instruments and machines in which the principles 

 of hydrostatics, hydraulics, and pneumatics, are applied to the purposes of 

 the arts or of domestic convenience. The science of hydraulics must be 

 allowed to be of as great importance to civil life, and especially to a mari- 

 time nation, as any department of practical mechanics. Let us only reflect 

 for a moment to what the metropolis of England would be reduced, if 

 deprived of pipes for the conveyance of water, of pumps, and of fire 

 engines ; and how much the commerce of the whole kingdom has been 

 facilitated by the formation of navigable canals, and we shall soon be con- 

 vinced of the obligations that we owe to the art of modifying the motion 

 of water, and to the principles of hydraulics on which that art depends. 



The facts concerned in acustics and harmonics, or the doctrine of sound 

 and the science of music, are not exclusively dependent on the characteristic 

 properties of fluids. In these departments, although we can by no means 

 explain with precision the manner in which every appearance is produced, 

 we shall still find a variety of very beautiful phenomena, which have 

 indeed been too generally neglected, and supposed to be of the most 

 abstruse and unintelligible nature ; but which, when carefully examined, 

 will appear to be much more within the reach of calculation, than the 

 simplest doctrines of hydraulics. We may also apply some of these 

 phenomena to a very complete explanation of an extensive class of facts 

 in optics, which, in whatever other way they are considered, are inextri- 

 cably obscure. Whether this explanation may or may not be admitted as 

 satisfactory, it deserves at least a fair examination; it would, therefore, 

 be impossible to assign to the science of optics an earlier place in the order 

 of the system, even if we agree with those who imagine that all the pheno- 

 mena of light depend on causes wholly deducible from the mechanics of 

 solid bodies. 



We must commence the subject of hydrostatics, or the doctrine of the 

 equilibrium of liquids, with a definition of the essential characteristics of a 

 fluid substance. The most eligible definition appears to be, that a fluid is 

 a collection of material particles, which may be considered as infinitely 

 small, and as moving freely on each other in every direction, without 

 friction. Some have defined a fluid as a substance which communicates 

 pressure equally in all directions ; but this appears to be a description of a 

 property derivable from the former assumption, which is certainly more 

 simple ; and although it may be somewhat difficult to deduce it mathe- 

 matically, in a manner strictly demonstrative, yet we may obtain from 

 mathematical considerations a sufficient conviction of its truth, without 

 assuming it as a fundamental or axiomatic character.* A fluid which has 



* See Miller's Hydrostatics, Camb. 1831. Challis's Report on Hydrostatics and 

 Hydrodynamics, Brit. Assoc. 1833, p. 134. 



