Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/160

 two constants, k and n, appear instead of one. The reason for this is that a body constituted from point-centres of force in Navier's fashion has its moduli of rigidity and compression connected by the relation

Actual bodies do not necessarily obey this condition; e.g. for india-rubber, k is much larger than $$\frac{5}{3}n$$; and there seems to be no reason why we should impose it on the aether.

In the same year Poisson succeeded in solving the differential equation which had thus been shown to determine the wave-motions possible in an elastic solid. The solution, which is both simple and elegant, may be derived as follows:—Let the displacement vector e be resolved into two components, of which one c is circuital, or satisfies the condition

while the other b is irrotational, or satisfies the condition

The equation takes the form