On Lunar and Solar Periodicities of Earthquakes. 455 



General Conclusions. 



The final result of the discussion of the spectra of stars of the 

 £ Cephei class is to show that they must be placed on the ascending 

 arm of the temperature curve, at a stage higher than stars like 

 a Tauri, in which the mean temperature is not very different from 

 that of the sun. Stars of equal temperature on the descending side 

 of the curve, of which Castor may be taken as a type, show pre- 

 cisely the same lines, the enhanced and cool lines having the same 

 relative intensities, but with inverted intensities of the hydrogen and 

 metallic lines, and with somewhat less continuous absorption in the 

 ultra-violet. The difference between stars like 8 Cephei and those of 

 the sun is therefore partly due to a difference of temperature and 

 partly due to a difference of physical condition such as is demanded 

 by the meteoritic hypothesis. This result enables us to understand 

 why some members of the d Cephei class should show such a very 

 special kind of variability. 



a Cygni also finds a natural place on the ascending arm of the 

 temperature curve, at a stage higher than I Cephei, and all the diffi- 

 culties met with in attempting to classify it on Vogel's view of 

 decreasing temperature alone are removed. 



" On Lunar and Solar Periodicities of Earthquakes." By 

 Arthur Schuster, F.R.S. Received May 18, — Read 

 June 17, 1897. 



1. In a paper recently communicated to the Royal Society " On 

 Lunar Periodicity in Earthquake Frequency," Mr. C. G. Knott gave 

 some results, from which he argued that a real connexion between tidal 

 effects and earthquakes probably existed. These results are based on a 

 method which has frequently been employed. The records of earth- 

 quakes are grouped together and expressed by means of a Fourier 

 series, and conclusions are based on the greater or smaller values of 

 the coefficients of this series. In order to decide what value is to be 

 attached to such investigations, it seems necessary in the first instance 

 to discuss what would be the order of magnitude of the coefficients, 

 on the supposition that the events have happened perfectly at random 

 without any connecting law. It is the object of this paper to solve 

 this question, and to apply the solution to the periodicities which are 

 supposed to exist in the frequency of earthquakes. 



2. If it is required to investigate a possible period of p intervals of 

 time in a series of members, t u t 2 , U, &c, it is usual to arrange the 

 numbers according to the following scheme, where stands for t p + u 

 tj" for £ 2iM1 , &c. : — 



VOL. LXI. 2 K 



