344 A STUDY OF COKRELATroNS AMONG TERRKSTRIAL TKM 1>EKATURKS. 



The weight assigned to each station and region being taken as constant we have 



l.jc' = >\W + 'V'V + • • • + '•„"'„- 



r being, in each case, the number of years through which the observations extend. 

 To find the mean cosmical fluctuation indicated we have, for use in (17) 



2 W'- - T-w^ = 20766 



A 

 Mean t/ = ^ ^p _ ^^^ =-012 



.-.mean t^ = ± 0°.ll C. 



This is the mean general fluctuation of temperature of the earth from year to year 

 which is indicated by the data of observation. 



But, before we accept this as really cosmical, we must find whether it aflfects all 

 the stations, or whether the correlation exists only between stations so situated that 

 they may be subject to like departures of temperature through tlie great movements 

 of the air from one region to another. 



The four Indian stations are especially in close proximity ; we shall therefore 

 discuss their departure by themselves, to decide whether they show any well-marked 

 correlation. In doing this it will be unnecessary to make any distinction of weights.' 

 We shall therefore put w = 1 in each case, which will make W identical with the 

 number of stations. Of course we must then use for t the unweighted means, which 

 are slightly different from those of Table V. Starting with 1871, we find these to be 

 T = + 0°.29, + 0°.06, + 0°.02, etc., instead of + 0°.31, 0°.00, - 0°.04, etc. For use 

 in the equation (9) the values of m- are .252, .01 1 , .001 , etc. These we sum by periods 

 during which the number of stations remains unchanged. Then we sum the individual 

 departures in the same way, and divide each annual sum by ii. We have for 1871, 

 tv'' = .42^ + .32- + .12- = 0.293. This gives, for 187 1 , 2;-^ ^n= .098, in using which 

 two decimals are amjjly sufficient. Carrying through this computation for each year 

 and summing by jjeriods, we find the following results : 



