88 REPORTS ON THE STATE OF SCIENCE. — 1919. 



20 days. We must apparently recognise two distinct periodicities 

 connected in some way with our earth, and our attention is naturally 

 directed to possibilities of interference. 



Now 21 X 1-23698 years = 25-97658 years. 

 22 X 1-18333 years = 26-03333 years. 



So that the two periodicities interfere in approximately 26 years. 

 But the differences from 26 years are by no means negligible. If we 

 adopted exactly 26/21 years for the former we should be returning 

 to the period of 104/7 months tentatively deduced from the Catalogue 

 of Destructive Earthquakes and shown by the Chinese Earthquakes 

 to be in error by about one month in 78 years. The length of the 

 Chinese series warrants our retaining 5 significant figures. 



The astronomical determination, though deduced from observations 

 of a much higher order O'f accuracy, depends on a much shorter series, 

 and the number of significant figures is fewer. Dyson contents 

 himself with 3, and if we vary his last figure by a few units we get : — - 



22 X 7-08/6 = 22 X 1-18000 = 25-9600 



22 X 7-09/6 = 22 X 1-18167 = 25-9967 



22 X 7-10/6 = 22 X 1-18333 = 26-0333 



22 X 7-11/6 = 22 X 1-18500 = 26-0700 



In the first case interference with the earthquake period would 

 take place in rather less than 26 years, in the other cases in rather 

 m.ore. To put the point in another way, let us calculate the period 

 of the earth's axis which would interfere with that deduced from 

 earthquakes (supposed accurate) in various assigned times, say 25 years, 

 26, years, and 27 years. 



It will be seen that if this period of interference could in any way 

 be independently identified we might deduce a close value for the period 

 of the earth's axis. 



Now, although this actual period has not as yet presented itself in 

 other connections, its multiples, and perhaps its submultiples, have 

 8o presented themselves several times over. 



Thus we have: — 



3 X 26 years = 78 years 

 6 X 26 years =156 years 

 9 X 26 years = 234 years 



The last may possibly be the 240-year period already mentioned 

 as conspicuous in the Chinese earthquakes {Mon. Not. Ixxix., p. 531) in 

 the Nile floods, and possibly in the motion of the moon. A period 

 of 156 years approximately was found by Mr. A. E. Douglass in the 

 growth of trees (Bull. Amer. Geog. Soc. xlvi., pp. 321-335, 1914), 

 and is illustrated by a striking diagram in Professor D'Arcy Thompson's 



