A method is suggested for determiing the velocity of ejection and the ages of the components of double radio sources. The derived variation of the radio luminosity with time suggests that nearly all extra-galactic radio sources, including the most compact quasi- stellar sources and the most extensive double radio galaxies, can be accounted for by a single model in which clouds of relativistic particles are ejected from the parent galaxy with an initial velocity close to C. This type of variation of radio luminosity with time may be derived independently from the luminosity distribution of radio galaxies. The cloud velocity and the radio luminosity both decrease to a small value after 3 X io6 years. The decrease of luminosity exhibits two main phases, and suggests that all classes of powerful source originate with the release of energetic particles having a total energy of io62 erg, in a galaxy containing a weak magnetic field ( I 0- gauss). The expansion from an extremely compact object exhibiting the effects of low-frequency selfabsorption, must be accompanied by amplification of the magnetic field at the expense of the particle energy, and equipartition may be attained after z X io5 years, when physical separation of the components is approximately equal to the diameter of the galaxy. The subsequent development, corresponding to the most extensive double sources, involves a rapid decrease of radio luminosity with age as the expansion proceeds without field amplification.