THE 



LONDON AND EDINBURGH 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



NOVEMBER 1838. 



XLII. On a Principle laid down by Clairaiitybr determining 

 the Figure of Equilibrium of a Fluids the Particles of 'which 

 are urged by accelerating forces. (Theorie dela Figure dela 

 Terre, premiere partie, chap. 5'"^) ^j/ James Ivory, i^./f., 

 F,n.S., c^c* 



/^LAIRAUT's principle alluded to, has all the precision 

 ^^ and elegance which are admired in the applications of 

 the ancient geometry, such as are found in the writings of 

 Aixhimedes. It might not be useless to inquire how it hap- 

 pens that geometers, neglecting the elegant method of Clair- 

 aut, have so generally agreed in giving the preference to the 

 theory of Euler, grounded on the equality of pressure which 

 necessarily takes place in every fluid at rest, whatever be the 

 causes by which such a state is induced. It would, no doubt, 

 be found that this is owing to the great generality of the 

 equations of Euler's method, which are easily obtained, and 

 seem to embrace every proposed problem and to reduce it 

 immediately to a question of abstract mathematics. 



Clairaut begins with supposing a mass of fluid in equili- 

 brium, thus laying a sound foundation for his reasoning. The 

 forces at the several points of the supposed mass, which may 

 be called A, being expressed in numbers, he next spreads 

 over the surface of A, a thin stratum 8 A, so as to fulfil the 

 condition, that the force at any point of the surface of A mul- 

 tiplied by the thickness of S A at the same point, shall con- 

 stantly make the same product. This being done, when the 

 quantities of the matter of the stratum on which the forces 

 act are taken into account, it follows that every infinitesimal 

 portion of the surface of A, will sustain a proportional press- 

 ure ; so that the intensity of pressure, estimated on a given 



* Communicated by the Author. 

 Phil. Mag. S. 3. Vol. 13. No. 83. Nov. 1838. Y 



