39 
TII°. Next let the medium be of uniform density within a closed 
space, and imagine any plane crossing this space; then the pressure per 
square inch of the part of the medium lying on one side of this plane 
against the part lying on the other side may be seen to be a function of 
the density as follows :—Let m be a molecule sufficiently near to the plane 
on one side to be within the range of molecular repulsion of particles 
lying at the other side, and describe round m a sphere including all the 
molecules which act on it. Part of this sphere will, therefore, lie beyond 
the plane, and from hypotheses (8), (4), and (5), we find that the action 
on m arising from that segment of the sphere will vary directly as the 
density; since to alter the density is the same thing as to increase or 
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.* 
Tv°. 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 density 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 
* In the particular hypothesis of modified action introduced by Professor Jellett there 
will be another term containing the fourth power of the density. 
+ 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 
#bject-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. 
