Physical models of the paramagnetic relaxation process are briefly reviewed, and a description is given of the pulsed microwave method of investigation. This method has been applied to the study at low temperatures of zinc/nickel fluosilicate at various magnetic dilutions, and an additional relaxation process has been observed which is associated with the sharing of energy among the spins. The results depend only on the temperature and magnetic concentration, and are independent of all other experimental conditions provided that excessive power levels are avoided. The lack of size dependence indicates that the relaxation rate is not controlled by spatial diffusion of phonons. The temperature dependence which has been observed is too acute to fit the 1T law of the simple "direct process" model, and suggests that the relaxation rate is controlled either by phonon combination probabilities or by a Raman type of interaction between phonons and spins.