Page:Proceedings of the Royal Society of London Vol 69.djvu/445

Rh The rate of degradation of the transverse waves, i.e., the dissipation resulting from the angular redistribution of the energy or viscosity is

5-603 x 10- = /,,

or such as would require 56,000,000 years to reduce the total energy in the wave in the ratio 1/V 2, or to one-eighth, thus accounting, by mechanical considerations, for the blackness of the sky on a clear dark- night, while the degradation of the normal wave, i.e., the dissipation resulting from the linear redistribution of energy is such that the jnitial energy would be reduced to one-eighth in the 3'923 x 10~"th part of a second, or before it had traversed 2200 metres ; and thus would account, by mechanical considerations, for the absence of any physical evidence of normal waves, except such evidence as might be obtained within some thousand metres of the origin of the waves, as in the case of Rontgen rays.

2. In spaces in which there are local unequal inequalities in the medium about local centres owing to the absence or presence of a number of grains in deficiency or excess of the number necessary to render the piling normal, such local inequalities arc permanent, and are attended with inward or outward strains, as the case may be, extending indefinitely throughout the medium, causing dilatation equal every- where to the strains, but of opposite sign, i.e., dilatation equal to the volume of the grains, the presence or absence of which causes the inequality.

When the arrangement of the grains about the centres is that of a nucleus of grains in normal piling, on which the grains in the strained normal piling rest, the nucleus in normal piling cannot gear with the grains outside in strained normal piling ; so that there is a singular surface of misfit between the nucleus and the grains in strained normal piling. Such singular surfaces are surfaces of weakness, and may be surfaces of freedom, or surfaces of limited stability with the neigh- bouring grains.

These singular surfaces, when their limited stability is overcome, are free to maintain their motion through the medium, by a process of propagation in any direction, the number of grains entering the surface on the one side being exactly the same as the number leaving on the other side, so that when the inequalities are the result of the absence of grains, they correspond to the molecules of matter.

If the singular surface of a negative inequality is propagating through a medium which is at rest, the grains forming the nucleus will have no motion, whatever may be the motion of the singular surface. But the strained normal piling which surrounds the singular surface and moves by propagation with the singular surface, being of less density than the mean density of the medium, represents a displacement of the negative mass of the inequality, ?>., of the grains absent,