188 Prof. Challis on the Hydrodynamical Theory 



centre of the group large compared with its radius, to be & very 



nearly, fi being a certain constant. In case the pressure act 

 repulsively, the quantity in brackets will be positive ; and 

 it may readily be shown that the repulsion is a maximum 



if irknh 2 be equal to -%, which is equal to 2 nearly, the 



numerical value of k being, according to theory, P2106 

 (' Principles,' p. 224). Hence that maximum repulsion is 



^J %, or ^(0-1828 ^nearly. 



It will thus be seen that on account of the exceedingly minute 

 value of b the radius of an atom, this repulsion is of insensible 

 magnitude at very small distances from the centre of the 

 group. If we now suppose the atoms of the group to con- 

 stitute a molecule, the numerical quantity kn would be very 



much larger, and the factor 1 -~ — might become a large 



negative quantity. Yet, as the expression, for the attractive 



? 2 



action thus indicated would still contain the factor r— ~. an d it 



is known that the diameter of a molecule must be a very 

 small quantity, the attraction would become insensible at very 

 minute distances from the centre of the molecule, although 

 the sphere of sensible activity would be very much larger 

 than in the preceding case of maximum repulsion. Accord- 

 ingly in all cases repulsion is controlled by attraction (with 

 the exception, under certain conditions, of the atomic repul- 

 sion of gases) ; and the theory thus accounts for an excess of 

 attraction above repulsion at the boundaries of bodies, such 

 as that to which the phenomena of capillary attraction have 

 been attributed. 



23. On proceeding to the consideration of spherical atomic 

 groups of larger magnitude than those the attractive action 

 of which suffices to make a molecule self-contained, special 

 hydrodynamical circumstances have to be taken into account, 

 the discussion of which is necessary as a preliminary to the 

 hydrodynamical theory of the attraction of g?>avity. It has 

 been shown (art. 19) that the intensities of the composite 

 waves originating in two spherical atomic groups are to each 

 other, at distances nR, nR f from their centres which are 

 large multiples of their radii R and R/, in the proportion of 

 R 2 to R /2 . Hence it follows that the intensity might be in- 

 definitely increased by increasing the magnitude of the atomic 



