212 
PROCEEDINGS OF SOCIETIES. 
decrease in a fixed ratio the number of molecules acting from each ele¬ 
ment of volume of the segment. The same reasoning applies to the action 
from the second side of the plane on any other molecule on the first side 
which is sufficiently close; and as the number of molecules thus acted 
on will also increase directly as the density, and as the interpolated mo¬ 
lecules will, from hypothesis (5), be acted on to the same amount, and 
in the same direction, as the original molecules between which they lie, 
it follows that the pressure per square inch within the medium will vary 
as the square of the density * 
IY°. This pressure will of course be transmitted to the walls of the 
containing vessel, so that it becomes necessary to consider the conditions 
which must hold at the boundary of the medium. For this purpose 
three cases must be distinguished. The first arises along the surface of 
contact of two media, which obey, in the forces which they exert on one 
another, conditions consistent with our hypotheses. In this case, if 
the density of either medium vary after a state of equilibrium has been 
established, that of the other must vary in like proportion, otherwise 
the medium of increased density will force back the other. Again, if 
the range or law of the mutual molecular action of the two media differ 
from what hold with respect to the action of the molecules of either 
medium among themselves, it is evident that the d ensity of this medium 
cannot be uniform, but must be different from its average value in the 
vicinity of the other medium. This alteration in the density of the su¬ 
perficial stratum will react on the stratum behind, and so on, producing 
a strained condition of the density throughout the medium, | which 
would even in some cases go the length of occasioning the precipitation 
of that medium upon the surface of the other. Another case, which is 
quite distinct, will arise when the medium is confined by a containing 
vessel, the walls of which are both rigid and immovable, but which acts 
on the medium within, not merely from its superficial layer of molecules, 
but from all those lying within a certain distance of the surface in such 
a way that no one molecule of the containing vessel contributes more 
than an infinitesimal part to the effect on a molecule of the medium. ITp 
to a certain density and pressure the medium will be contained by such 
a vessel; but as soon as the density is made to exceed this limit, the 
medium will begin freely to permeate the vessel, and escape. The re¬ 
marks made with reference to the last case apply equally to the present 
one, so long as the medium continues of sufficiently low density to be re¬ 
strained. The third case of limiting conditions arises where the medium 
is kept in by the wall of a containing vessel which it can neither press 
* In the particular hypothesis of modified action introduced by Professor Jellett there 
will be another term containing the fourth power of the density. 
t Somewhat like the strains which are found to exist in substances which need careful 
annealing. Thus, it is well known that if a chip be broken from a sharply defining 
object-speculum or lens of a telescope, the strains which held the fragment in its place 
being annihilated, the distribution of the density and strains throughout the whole of the 
rest of the mass are so altered that the accuracy of the defining power is lost. 
