112 Mr. Ivory on the figure requisite to maintain the equilibrium 
the same fluid having a similar figure, and revolving with 
the same rotatory velocity about an axis similarly placed, 
will likewise be in equilibrio, supposing that its particles 
attract one another by the same law. 
Suppose that a homogeneous fluid body revolves about the 
axis AB, and is in equilibrio by the attraction of its particles 
and the centrifugal force ; and let another mass of the same 
fluid, similar in its figure to the first body, revolve, in the 
same time, about the axis ab, similarly situated to AB: this 
latter body will also be in equilibrio. 
Conceive that the body in equilibrio is divided into an in- 
definitely great number of thin level strata ; and let the 
other body be divided into the same number of strata by sur- 
faces, similar, and similarly situated to the level surfaces of 
the first body. Take any point H in a level surface of the 
body in equilibrio ; and in the corresponding surface of the 
other body, let the point h be similarly situated to H. Far- 
ther, suppose the two bodies are similarly divided into the 
same indefinitely great number of molecules, of which dm 
and dm' are any two situated alike, and therefore having 
their volumes and quantities of matter proportional to the 
volumes and quantities of matter of the two whole bodies : 
and let / and/' denote the respective distances of the points 
H and h from dm and dm' , and r and r' , their respective dis- 
tances from the axes A B and a b. 
The forces with which the molecules dm and dm' attract 
the points H and h (which must be considered as two equal 
particles of matter ) are proportional to ~ and ~ : and, in 
these fractions, the numerators being proportional to the 
