AND THE FIGURE OF A HOMOGENEOUS PLANET. 
131 
urging the particles contained in them, as will readily be proved by differen- 
tiating equation (3), making p constant. 
In order to place what has been said in the clearest light, let A B C repre- 
sent the mass of fluid, the surface being determined by the equation, 
C = V (R) + 4 (y 2 + * 2 ) ; 
and suppose that a b c is an interior surface, obtained by making p constant in 
the equation, 
p = V (r) + y ( y 2 + s 2 ) - C : 
then, if the narrow canal A a m M 
stand upon the molecule am of the 
interior surface, and extend to the 
upper surface of the fluid, the in- 
tensity of pressure upon a m, or the 
given quantity p, will be equal to 
the sum of all the impulses caused 
by the action of the principal forces 
upon the molecules contained in 
the canal, every impulse being re- 
duced to the direction of the canal 
and to the unit of surface. The 
same thing is true of any other mo- 
lecule in the same surface upon which there stands a similar canal B&hN. 
If we attend to the conditions of equilibrium required by the general theory, 
it will readily appear that the equilibrium of the mass ABC will be impossi- 
ble, if at any point, as a m , of the interior surface a be, any other pressure exist 
besides that represented by p, or any other forces be in action besides those 
expressed by the coefficients of the variations in equation (2). For, at the 
upper surface, there are no forces in action but the principal forces, and the 
equilibrium will be impossible if other forces prevail in the interior parts be- 
sides the principal forces. On the other hand, the matter contained in the 
stratum between the two surfaces will attract every particle, as a m, situated 
in the interior surface. The attraction of the stratum is an indelible force not 
