224 DB. CHARLES DAVISON ON THE [May 1 904, 



through places in which the percentage of observers who heard the 

 sound is the same. If, from any cause, such as the superposition 

 of sound-waves from two foci, the amplitude of the vibrations be 

 locally increased without a corresponding increase in their period, 

 the percentage of audibility will rise, and there will be an expansion 

 outwards of the isacoustic lines in the neighbourhood of the region 

 in question. 



In the Derby earthquake, the smallness of the sound-area and 

 the scarcity of observations from places near its boundary, render 

 impossible the construction of a complete series of isacoustic lines. 

 On the map of the earthquake (PI. XIX), only two such curves 

 (indicated by dotted lines) are shown, namely, those corresponding 

 to percentages of 95 and 90. In order to draw them, the whole 

 disturbed area was divided into squares by north-to-south and east- 

 to-west lines 10 miles apart ; the percentage of observers within 

 each square who heard the sound was supposed to correspond to the 

 centre of the square, and the curves were then drawn through points 

 dividing the lines that join adjacent centres in the proper ratios. The 

 meaning of the curve marked 95, then, is that, if with any point on 

 it as a centre, a small circle be described, 95 per cent, of all the 

 observers within the included district heard the earthquake-sound. 



The inner line (that marked 95) is 33 miles in length and 1G 

 miles in greatest width, and the outer line (marked 90) 49 miles in 

 length and 19 miles in width. The greatest of these dimensions 

 being not more than five times a side of one of the squares, it 

 follows that details in the form of the curves are smoothed away by 

 the process of construction, and that the only important feature 

 that possesses a physical meaning is the general trend of the 

 curves in the direction of the rectilinear band within which the 

 single shock was observed. At places inside this band, the vibra- 

 tions from the two foci coalesced ; and so the earthquake-sound was 

 reinforced, and was consequently heard by a greater proportion of 

 observers. Thus, the evidence of the sound-phenomena supports the 

 conclusion to which we were led by the nature of the shock, namely, 

 that the earthquake was caused by simultaneous fault-slips within 

 two detached foci. 1 



Excluding a few records from very distant places, the sound was 

 observed within the area bounded by the outer dotted line in PI. XIX 

 — an area 101 miles long in the direction of the major axis of the 

 isoseismals, 98 miles wide, and containing about 7800 square miles, 

 or nearly two-thirds of the whole disturbed area. The exceptional 

 records come from Ashton-in-Eibble, Lytham, and Southport in 

 Lancashire, and from Aysgarth and Settle in Yorkshire. 



"Within the isoseismal 7, no fewer than 97 per cent, of the 



1 The insensible distortion of the isoseismal lines and the marked expansion 

 of the isacoustic lines in the direction of the rectilinear band, is due to the 

 brevity of the two principal vibrations of the shock and the long duration of the 

 two parts of the sound. Within the rectilinear band, there must have been a 

 still narrower band within which the two principal vibrations absolutely 

 coalesced ; but the area of the latter band Mas so small that the observations 

 from places within it seem to be entirely wanting. 



