| ( | 45π | ) | 1⁄5 | ( | v | ) | 2⁄5 | r, |
| 256 | V |
where r is the radius of either, and V the velocity of longitudinal waves in a thin bar of the material. The duration of the impact is approximately
| (2.9432) ( | 2025π² | ) | 1⁄5 | r | . |
| 512 | v1/5V4/5 |
For two steel spheres of the size of the earth impinging with a velocity of 1 cm. per second the duration of the impact would be about twenty-seven hours. The fact that the duration of impact is, for moderate velocities, a considerable multiple of the time taken by a wave of compression to travel through either of two impinging bodies has been ascertained experimentally, and constitutes the reason for the adequacy of the statical theory here described.
75. Spheres and Cylinders.—Simple results can be found for spherical and cylindrical bodies strained by radial forces.
For a sphere of radius a, and of homogeneous isotropic material of density ρ, strained by the mutual gravitation of its parts, the stress at a distance r from the centre consists of
(1) uniform hydrostatic pressure of amount 1⁄10 gρa (3 − σ) / (1 − σ),
(2) radial tension of amount 1⁄10 gρ (r²/a) (3 − σ) / (1 − σ),
(3) uniform tension at right angles to the radius vector of amount
1⁄10 gρ (r²/a) (1 + 3σ) / (1 − σ),