io 6 Mr. Ivory on the figure requisite to maintain the equilibrium 
homogeneous fluid body, the particles of which attract one 
another, that the resultant of the forces X, Y, Z, be directed 
inward, and that X d x + Y dy + Zdzhe an exact differen- 
tial : to these conditions it is necessary to add that, every 
particle placed within a stratum bounded by two level sur- 
faces, be in equilibrio by the attraction of the stratum. 
The conclusion we have arrived at does not coincide with 
the usual determination of the equilibrium of a fluid mass, in 
which no distinction is made between the two cases when the 
particles attract one another, and when they possess no such 
powers. The difference arises from this, that no notice is 
commonly taken of the attraction which the thin level stra- 
tum exerts upon the fluid body to which it is added. Every 
difficulty respecting this point will be removed, if it be im- 
pressed on the mind that the gravity at any level surface, 
and the pressure caused by it, are forces distinct from, and 
independent of, the attraction of the exterior matter. In 
estimating the pressure, the exterior fluid is unavoidably re- 
garded merely as inert matter subjected to external force ; 
and when there are active powers inherent in it, the effect of 
these must be separately investigated. It is said that nothing 
more is requisite to the equilibrium of a homogeneous fluid, 
than that the pressure be equable over all the outer surface^ 
For, it is argued, since there is no distinction of density in 
the interior, it is always possible to trace curves that shall 
cut at right angles the resultants of all the forces urging the 
particles ; which curves will therefore be level surfaces. But 
the defectiveness of this reasoning will appear if it be 
observed that, as every particle of the fluid is attracted by 
the whole mass, the curve surfaces traced in the manner 
