  We show that the image by the Lorentz transformation of a spherical
(circular) light wave, emitted by a moving source, is not a spherical
(circular) light wave but an ellipsoidal (elliptical) light wave. Poincare's
ellipsoid (ellipse) is the direct geometrical representation of Poincare's
relativity of simultaneity. Einstein's spheres (circles) are the direct
geometrical representation of Einstein's convention of synchronisation.
Poincare adopts another convention for the definition of space-time units
involving that the Lorentz transformation of an unit of length is directly
proportional to Lorentz transformation of an unit of time. Poincare's
relativistic kinematics predicts both a dilation of time and an expansion of
space as well.
