ON SUNSrOTS AND TEBRESTRIAL PHENOMENA. 457 



The numbers show that during the year of few sunspots the Larometer 

 stood higher with westerly than with easterly winds. The third row 

 gives the difference in the height of the barometer with north-westerly 

 as compared with south-westerly winds. The observations used were 

 those taken at the Radcliffe observatory. It would be interesting to see 

 how matters have been going on since 1868. 



General Remarks oh the Reduction of Observations. 



The task of proving a periodicity in meteorological phenomena coinci- 

 dent with that of the sunspots is by no means an easy one. For such 

 a periodicity, if it exists, is clearly mixed up with other and larger varia- 

 tions, which may hide the period in question. It becomes, then, necessary 

 to inquire what are the processes of reduction that are most suitable for 

 the purpose. In the first place, wherever it is necessary to hide short- 

 period inequalities, we may do so by taking means over suitable periods. 

 For instance, in investigating the effect of the sunspot period, it is quite 

 justifiable to take mean values of the quantities we are investigating 

 over three or five years. We shall thereby reduce the amplitude of the 

 longer inequalities, but they will be more clearly defined, as we have de- 

 stroyed completely all inequalities of less than three or five years. No 

 exception whatever can be taken to such a process as this ; and if the 

 curve thus smoothed down shows evidence of similarity to the sunspot 

 curve for a sufficiently long period of time, wc may take the connection to 

 be a real one. 



In some of the investigations, however, it seemed advisable to take a 

 slightly different plan. Thus, for instance, Professor Balfour Stewart, in 

 his consideration of temperature ranges, has compared certain daily values 

 with the average of the same values over twenty-four days. Now, in this 

 process the different periods are very unequally affected. Professor 

 Stokes * has given us the formula which enables us to see the way in 

 which such a reduction influences the amplitude of different periods. If 

 the amplitude cf the original period is taken as one, then the amplitude 

 of the reduced period is given by — 



n~ ■ mx 

 sin — sin 



N N 



. 7T . 7T 



n sin m sin - 



x M 



where n and m represent the periods over which the averages hare 

 been taken. 



Applying this formula to the case under consideration, I find that, 

 while a period of twenty-four days approximately would have its ampli- 

 tude reduced in the proportion of 1 to 096, a period of eighteen days 

 would be increased in the ratio of 1 to 1*13. For Dr. Stewart's purpose 

 it would have been better, therefore, to have taken his means over about 

 thirty days instead of twenty-four, as it was the inequalities of twenty- 

 four days that he was specially investigating, and wishing to increase 

 relatively. 



1 In a paper by J. H. Poynting, Proc. Stat. Soc, London, 188 1. 



