Nevertheless, whatever the distance may be, the sense of direction must be most perceptible in those houses whose principal walls are at right angles to the true direction of the earthquake-motion, and we should therefore expect to find the observations of direction most frequently made in such houses, or in others which approximate to this situation. Thus, the average of all the observations within a fairly small area should give a result not very far from the true direction of the shock; and, the smaller the area and the farther from the epicentre, the more reliable should be the result. Now, in Birmingham the mean direction of the shock is E. 39° N., which differs only by 2° from the line joining the city to the epicentre; in London it is E. 21° S., the difference being again 2°. In other cases, the observations from different counties are grouped together, and the mean direction is taken to correspond to the centre of the county. Yet, even then, there is often a close agreement between the mean direction of the shock and the direction of the county-centre from the epicentre; the difference being not more than two or three degrees in the counties of Buckingham, Devon, Stafford, Warwick, and York. In other cases, where the deviation exceeds this amount, either the number of observations is small or the county is near the epicentre and so subtends a large angle. Two results of some importance follow from this analysis: (1) that while, with a few isolated observations, the "method of directions" is almost sure to fail, with a large number of observations closely grouped, the position of the epicentre may be determined with a fair approach to accuracy; and (2) that, at any rate outside a radius of forty miles, the earth-waves travelled in approximately straight lines outwards from the epicentre. COSEISMAL LINES AND VELOCITY OF EARTH-WAVES. Coseismal lines were defined by Mallet as long ago as 1849, but, owing to the difficulty of ascertaining the correct time, they have so far been of little service in the investigation of earthquakes. In the case of the Hereford earthquake, the distances traversed by the earth-waves are small; but, on the other hand, the time-records are numerous and frequently trustworthy to the nearest minute. Rejecting all estimates earlier than 5.32 A.M., and later than 5.36, as well as a number at 5.35, there remain fairly good observations from 381 places, and exceptionally accurate ones from 33 places. The latter were obtained from signalmen and other careful observers who were in possession of Greenwich time, or who compared their watches shortly afterwards with well-regulated watches.