Previous attempts to find empirical linear relationships between the magnitude, M, of an earthquake and the logarithm of one or more of the source parameters (length L, width W, displacement D) are reviewed. The fault parameters associated with a set of 27 earthquakes with strike-slip movement in the magnitude range 3.4 to 8.3 are used to test these empirical relationships. It is found that there is no linear relationship between M and log L or log W that is valid over the whole magnitude range. However, a rather good linear relationship is found between M and log D. Using all of the present data, this relationship is
If only large magnitude events are used, this becomes
Some improvement in determinations of the displacement D for low magnitude events is necessary in order to distinguish between these two formulas. It is surmised that the second may be closer to the truth. The consequences of such a relationship are discussed.