Mr. Ivory on the Equilibrium of Fluids. 37 



application of the condenser the same reduction miglit take 

 place. This expectation is fully justified by an effect already 

 observed and described (1229.). 



1316. In that case the application of the instrument to very 

 extensive research is evident. Comparatively small masses 

 of dielectrics could be examined, as diamonds and crystals. 

 An expectation, that the specific inductive capacity of cry- 

 stals will vary in different directions, according as the lines 

 of inductive force (ISO-i.) are parallel to, or in other positions 

 in relation to the axes of the crystals, can be tested : I pur- 

 pose that these and many other thoughts which arise respect- 

 ing specific inductive action and the polarity of the particles 

 of dielectric matter, shall be put to the proof as soon as 1 can 

 find time. 



1317. Hoping that this apparatus will form an instrument 

 of considerable use, I beg to propose for it (at the suggestion 

 of a friend) the name of Differential Inductometer. 



Royal Institution, March 29, 1838. 



VIII. On the Equilibriimi of Fluids, occasio7ied by an Ar- 

 ticle of Professor Sylvester on Fluids, 'published in this 

 Journal for December 1838. By J. Ivory, K.U., F.R.S.* 



|3ROFESSOR Sylvester has deduced the usual laws of the 

 ■*- equilibrium of incompressible fluids from a principle 

 proposed by the eminent mathematician and philosopher 

 Gauss. Not to speak of the motion of fluids, the theory of 

 which is pressed by so many difficulties, the results respecting 

 equilibrium obtained by the Professor coincide entirely with 

 what has been investigated from principles, seemingly difl^erent, 

 by Clairaut, Euler, Lagrange, Laplace, and Poisson, this 

 last having extended his views to the molecular forces that 

 act upon the particles. Such a concurrence in the conclu- 

 sions arrived at, begets a suspicion that in reality all the pro- 

 cesses are guided by one invariable principle, which, although 

 hidden under algebraic operations, necessarily conducts the 

 analyst to the same landing-place. To prove that this is ac- 

 tually the case is the intention of what follows. 



The general laws of equilibrium in question are deducible 

 from the following theorem, which is grounded on the most 

 general conception of fluidity that can be formed. In a fuid 

 at rest, the -particles of which arc urged by accelerating forces, 

 the pressure at the several 2>oints of the mass, can be mathema- 

 tically expressed onlij bij a function of the coordinates that 



• Communicated by tlic Author. 



