92 Prof. Challis on a Theory of Molecular Forces. 
force varies very rapidly with the distance. We have now to con- 
sider how this repulsion is controlled by attraction. 
2. Conceive the atoms contained in a spherical surface of 
radius R to be centres of undulations propagated from them 
equally in all directions, and take any point at a distance D from 
the centre of the sphere, such that the straight lines drawn to it 
from the atoms are quam proxime parallel. Then . being a very 
small but fixed ratio, let the number of atoms included within 
the spherical surface of radius R be avery large given number N. 
It is conceivable that this number may be so large that the 
resultant consecutive values of the condensation at the given 
distance D, which must be as often plus as minus, may be ex- 
pressed by one or more circular functions, in which the values 
of X are very much larger than those for the component undula- 
tions. In fact, as the components may be supposed to have 
values. of X very nearly consecutive, there will be epochs of 
coincidence, or greatest proximity, of their maximum condensa- 
tions, and equidistant epochs of coincidence, or greatest proximity, 
of their maximum rarefactions. The fixed number N is deter- 
mined by the condition, that the resultant of the different series 
of waves of the first order propagated from the individual atoms, 
becomes at the distance D a series of waves of another order, 
analytically expressible like the first by periodic functions. As 
the waves of the second order cannot, any more than those of 
the first, be regarded as due to a specific disturbance, but as re- 
sulting from the mutual action of the parts of the fluid, both 
ought, according to the hydrodynamical principles which I 
have adopted, to be equally expressed by periodic circular func- 
tions. 
The effect above described is analogous to what takes place at 
the surface of water disturbed within a limited space, it being 
observable that, whatever be the mode of disturbance, at a short 
distance from it are formed and propagated concentric rings 
of alternate depression and elevation, which to all appearance 
have continuous boundaries, and are probably the resultant of 
subordinate series of waves, which have their origins at innume- 
rable points at the place of disturbance. 
3. For the sake of distinction, the portion of any given sub- 
stance which consists of the fixed number of atoms N, will be 
called a molecule, whether the space containing them be cubical 
or spherical. If the molecule be of the form of a cube, the 
quantity represented by R must be understood to be the 
radius of the sphere which has the same solid content as the 
cube. First, let the substance be in the state of aggregation 
of a solid. Then, the mean interval between the atoms being 
