Byerly has shown that when stations are plotted in extended position the initial motion will be compressional in two lunes of the earth and rarefactional in two others, the direction of displacement being opposite in alternate segments. These lunes are formed by the intersection of the earth's surface with the fault plane and with a plane through the epicentre perpendicular to the motion direction. Certain geometrical consequences of the orthogonality of this second plane and the motion direction are here deduced. The extended theory is applied to four earthquakes, one in the Aleutians, one in central Alaska, one in the Queen Charlotte Islands, and one in Vancouver Island, the strike and dip of the fault and the direction of slipping being determined in each case. The seismic results are discussed in the light of other information available.