THE INTERNAL CONSTITUTION OF BODIES. 455 
43° Lee gapn-+ 2dp )Hasinodedg | 
+3 Ben KC oe rl ; ) Hnsinw dwde |. 
The double integral a fd is to be extended only to the points in 
respect to which the radius w from the surface of the molecule is Z 7, 
and the integral WY us iy is to be extended to the points in respect to 
i 
which «7 7. 
By means of a beautiful theorem which M. Poisson has demonstrated 
in the Memoir already quoted, and in the additions to the Connais- 
sance des Temps for the year 1831, the functions given by the integrals 
r u ut 
Ia 
J” gopr+2de S gapr+ 2dp, uf ere 
may be represented by series of integer and rational functions of the 
spherical co-ordinates. Let 2 An, = H'n, = H"n, be these series ; if 
the functions H'n, H'', shall be found, so that they may be discon- 
tinued, and such that they are reduced to zero, the first for all the 
values of « Zr, and the second for the values of w 2 7, we shall be able 
by means of the known theorems to reduce the expression for G to the 
form 
nD 
a8" EE (apiet a Pet"). 
9) 
Such are the expressions for F and G which should be introduced 
into the equation (III). We might directly employ those which give 
the values of G, because they are always determinable when the po- 
sition, figure, and density of the molecules are known; but the same 
thing cannot be done with the expression for #. This integral includes 
the quantity g, which is still unknown; and we should not be able to 
determine it by the condition that it would render the equation (III) 
identical without previously performing the integrations, an operation 
which would require the same function to be known. In order to 
avoid this difficulty, we are about to employ for the purpose of deter- 
mining g a differential equation corresponding with that marked (IIJ), 
but in which the density g is no longer included under the signs of 
integration. 
The sum of these equations (I)', when they are differentiated in re- 
ference to x, y, z, respectively, gives 
@? 
(VI.) b( Sh + Sh 4 aan. 
