(2) The acceleration of the element at the origin is - n 2 sin nt; so that the force which would have to be applied to the parts where the density is D' (instead of D), in order that the waves might pass on undisturbed, is, per unit of volume, (D' - D)n 2 sin nt.
Necessarily more complicated; but, on the supposition that the changes of rigidity (AN) and of density (AD) are relatively small, the results are fairly simple.
No form of the elastic solid theory is admissible except that in which the vibrations are supposed to be perpendicular to the plane of polarization, and the difference between one medium and another to be a difference of density only (Phil.
As Lord Kelvin has shown (Baltimore Lectures, p. 304, 1904) (16) may also be obtained by the consideration of the mean density of the altered medium.
If V be the potential, p the density of free electricity at a point in the atmosphere, at a distance r from the earth's centre, then assuming statical conditions and neglecting variation of V in horizontal directions, we have r2 (d/dr) (r 2 dV/dr) - - 4.rp = o.