70 REPORTS ON TflE STATE OF SCIENCE. 



the statement made nine years ago, so far as it relates to megaseisms, 

 requires modification. In many instances it appeared that as a given 

 world-shaking earthquake travelled away from its origin, there had 

 been an increase in its duration. The matter seems to be of sufficient 

 interest to demand close examination. This was undertaken by Mr. H. C. 

 O'Neill, and the results at which he arrived are as follows : — 



' The difficulty in attacking this problem plainly emerged when a num- 

 ber of earthquakes had been plotted on squared paper, with distance and 

 duration as ordinates and absciss* respectively. It is known that 

 earthquake motion starts from (what may be regarded as) a point, and 

 that it communicates its motion to distant parts of the earth's surface. 

 At times the intensity of the shock is not sufficient to send waves as far 

 as the antipodes of the centrum. "We have therefore a point whence the 

 motion starts and a point beyond which it is not recorded ; and as the latter 

 has zero duration, it seems probable that the former has the maximum dura- 

 tion, and that the durations grow less as they approach the zero position. 

 It was with the object of testing this inference that the investigation was 

 commenced. The " Katalog der im Jahre 1904 Registrierten Seismischen 

 Storungen," published by the Central Bureau of the International Seis- 

 mological Association, offered the material ready made. Twenty-six 

 earthquakes were taken from Liste A, giving 991 observations in all. 

 Several of these were plotted on squared paper, but the curves were too 

 irregular to yield any satisfactory conclusion, and an attempt to delete 

 the most irregular observations offered too much opening to unconscious 

 selection. Professor Pearson's method ' for deriving correlation between 

 two variables was therefore selected in order to avoid this. But it was 

 necessary to secure a large number of comparable observations. Taking 

 the mean of all the observed durations for a given earthquake, it is clear 

 that the durations of different earthquakes are not comparable as they 

 stand. The means for several earthquakes (in minutes) were 108'7, 

 94-13, 56-66, 52-42, 86-96, 67-6-2, 29-11, 49-62, 93-0, 199-2 ; and these 

 show with sufficient clearness the point suggested. Some method was 

 therefore required to obtain figures that should be more or less indepen- 

 dent of any given earthquake. The readiest and simplest method that 

 seemed to achieve this (suggested by Professor Pearson) is as follows : 

 if X be the duration of a given earthquake at a given distance d, and if 

 X be the mean of all the observed durations for the same earthquake, 

 then the new duration character X at the given distance d is given by 



ac — X X , 



Since —1 is common to all, it may be neglected for calculating the corre- 

 lation when X for distance c? = -. The 991 observations treated by this 



method were then arranged for correlation, when the result was "06, with 

 the probable error ± -02. This means that if 1 represents perfect corre- 

 lation and complete absence of it, then -06 represents the degree of 

 correlation between distance and duration. And the result is to be 

 interpreted as showing that the correlation is very small, but may be 

 just significant, as it is three times the probable error ; or, that the^ 



' A good account of this method and the nature of problems it is designed to 

 treat is to be found in Frequency Curves and Correlation, by W. Palin Elderton. 



