etitteetencme 
ACTING INVERSELY AS THE SQUARE OF THE DISTANCE. 183 
dV\2 EN dy |, 
IG) +°4 apet= corn fee 
dV\? ne she dV dz 4 
S (a) +¥ g)at=—fve Fhe 
If we add these three gale together, and remember that 
in the space T 
Bev pe OV aN 
de® ' dp * ae 
ge) + ay) * Ge) =" 
dx dy hah}! in 2? 
and at the surface 
dV dx adVdy ,aV dz dv 
dx dp* dy dp dz dp dp’ 
=0 
we obtain f g?dT= — f vee ds, which is our theorem; and 
by combining the last proposition of the preceding article, we 
may express it still more generally thus: 
feat =fa- VW) 5p as, 
where A represents an arbitrary eit 
25. 
THEOREM.—If upon the same suppositions as in the pre- 
ceding article, the potential V have at all the points of the limit- 
ing surface of the space T the same value, this value will obtain 
also for all points of the space itself, and there is in the whole 
space a complete destruction of forces. 
Demonstration.—If in the more general theorem of the pre- 
ceding article, the constant limiting value of the potential be 
taken for A, it is evident that ifs q dT=0, so that necessarily 
dV dV 
q =O at every point of the space T, also ae 0, ra 
= Q, 
|a@V 
Je — % and consequently V is constant in the whole space T. 
26. 
THEOREM.—If the potential of masses which are distribu- 
ted entirely within the finite space T, or which are also distributed 
either continuously, wholly, or partially over its surface S, have 
