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VII. On the Equilibrium of Fluids, and the Figure of a Homogeneous Planet in 
a Fluid State. By James Ivory, A.M. F.R.S. Instit. Reg. Sc. Paris. Corresp. 
et Reg. Sc. Gottin. Corresp. 
Read January 13 and 20, 1831. 
I. Equilibrium of Fluids. 
1. XhE nature of the ultimate particles of a fluid, and the peculiar manner 
of their mutual connection, are entirely unknown to us. We conceive that 
they obey the same mechanical laws to which all matter is subject. Experience 
shows that the particles of a fluid move freely among one another, yielding to 
the least pressure in any direction ; and this is the most general property of 
such bodies that has yet been discovered. The perfect mobility of their par- 
ticles must therefore, in the present state of our knowledge, be considered as 
constituting the definition of fluid bodies, and as the foundation of all our rea- 
soning concerning them. We here confine our attention to a fluid in equili- 
brium, or at rest, in which state every particle is pressed equally on all sides. 
It is evident that the mobility of the particles among one another, and their 
readiness to obey any new impulse, is nowise impeded by the magnitude of 
their mutual pressure, since this acts at every point with the same intensity in 
all directions. 
If we set aside the effect of gravity, and of all accelerating forces, it follows, 
from the definition, that the pressure will be equal in all parts of a continuous 
fluid at rest. In this state we must conceive that the particles are equally 
distant, and arranged similarly about every interior point. Their mutual 
distance, it is natural to think, must be connected with the magnitude of 
pressure ; so that when they are more pressed, they will approach one another, 
and the volume will be diminished ; and, when they are less pressed, they will 
recede from one another, and the volume will be enlarged. Accordingly it is 
found that no fluid is perfectly incompressible. But in some, such as water 
