Without loss of generality let us assume that the observer is moving at a speed with velocity v along the positive x-axis. As seen by the observer, the body is moving along the negative x-axis with a speed v. Let be its density be
.Consider an infinitesimally small cuboidal piece of the body of dimensions dx, dy and dz. The mass dm of this infinitesimally small piece is given by,
As seen by the observer, the mass of the inifinitesimally small cuboid would be
Further, also as seen by the observer, the cuboid would appear to have shrunk along the x dimension to
.Let the density of body as seen by the moving observer be
then we have,
