134 THIRD REPORT — 1833. 



a proof of the law of equal pressure, are given at the beginning 

 of the Elements of Hydrostatics and Hydrodynamics of Pro- 

 fessor Miller *. Several advantages attend this mode of com- 

 mencing the mathematical treatment of fluids. The principle 

 is one which perfectly characterizes fluids, as distinguished in 

 the internal arrangement of their particles from solids. It may 

 be rendered familiar to the senses. It is, I think, necessary for 

 the solutions of some hydrostatical and hydrodynamical pro- 

 blems, particularly those of reflection f. Lastly, in reference 

 to the department of science proposed to be called Physical 

 Mathematics, the propositions of the common theory ought to 

 be placed on the simplest possible basis, because the questions 

 of most interest in that department are those which have in 

 view the explanation of the phasnomena that are the founda- 

 tions of the reasoning in the other kind. The solution of one 

 such question is a great step in scientific generalization. It is 

 plainly, therefore, of importance that the fact proposed for ex- 

 planation should be the simplest that direct observation can 

 come at. 



The analytical theory of hydrodynamics is of a much more 

 difficult nature than that of hydrostatics. The assumptions it is 

 necessary to make to obtain even approximate solutions of the 

 simplest problems of fluid motion betray the difficulty and im- 

 perfection of this part of science. There are cases, however, of 

 steady motion, that is, of motion which has arrived at a pei'ma- 

 nent state, so that the velocity is constantly the same in quantity 

 and direction at the same point, which require a much more 

 simple analysis than those which do not satisfy this condition. It 

 does not appear that the equations applicable to this kind of mo- 

 tion were obtained in any general manner till they were given in 

 an Elementary Treatise on Hydrostatics and Hydrodynaynics 

 by Mr. Moseley %, who has derived them from a principle of so 

 simple a nature, that, as it can be stated in a few words, it may 

 be mentioned here. When the motion is steady, each particle 

 in passing from one point to another, passes successively through 

 the states of motion of all the particles which at any instant lie 

 on its path. This principle is valuable for its generality : it is 

 equally applicable to all kinds of fluids, and will be true, whe- 

 ther or not the efl^ect of heat be taken into accoimt, if only the 

 condition of steadiness remains. The equations of motion are 

 readily derived from it, because it enables us to consider the 



.* Cambridge 183 J. 

 t Dr. Young employed an equivalent principle to determine the manner of 

 the reflection of waves of water. See his Natural Philosophy, vol. ii. p. 64. 

 t Cambridge 1830. 



