## Chapter 18THE EQUATIONS OF POTENTIAL, WAVES, AND HEAT CONDUCTION

Divide et impera.

LOUIS XI.

### 18·01.

The gravitational potential in free space satisfies Laplace’s equation

The same equation is satisfied in free space by the electric and magnetic potentials if the field is steady, and by the velocity potential in incompressible fluid. In a uniform compressible fluid the velocity potential satisfies

where *c* is the velocity of sound, provided that the velocities are small. For elastic waves in a uniform solid the same equation is satisfied by the ...