ioo Mr. Ivory on the figure requisite to maintain the equilibrium 
equal pressure upon every part of the upper surface of a level 
stratum, being propagated through the interior fluid, will 
act with equal force in an opposite direction upon every part 
of the lower surface ; and hence, every molecule of the 
stratum will be equally pressed in all opposite directions. 
When the fluid mass is homogeneous, the distinction of the 
level strata arising from the difference of their densities is 
lost ; but the possibility of dividing it into any number of 
strata separated by level surfaces, is still a necessary con- 
dition of the equilibrium. 
The condition, that every level surface must be a continu- 
ous curve stretching through the whole fluid mass, imposes 
a limitation on the forces with which the equilibrium is pos- 
sible. All these curve surfaces are defined by a common 
equation between three independent co-ordinates ; and as 
this equation is to be found by integrating an expression con- 
taining the co-ordinates and their fluxions, the operation 
must be practicable, without supposing any relation between 
the three variable quantities. Hence, the forces acting on 
the particles of the fluid must be such, that the three diffe- 
rential coefficients shall fulfil what is called the criterion of 
integrability ; otherwise the equilibrium will be impossible. 
In determining the equilibrium of the fluid placed on the sur- 
faces of the planets, the nature of the forces brought into 
action is such, that the problem is always free from contra- 
dictory conditions. 
To come now to the main object we have in view,* con- 
ceive that H K I is a body of homogeneous fluid in equilibrio 
* Theorie de la Figure de la Terre par Clairaut. Premiere Partie* cap. V. 
4 XXI. 
