324 A STUDY OF CORKELATIONS AMONG TERRESTRIAL TEMPERATURES. 



Now let US treat the mean departure t in the same way. We put e, the mean of the 

 purely accidental jjart of r. Then in each time-term, 



T = T„ + e 



Squaring and summing the r values of t we have 



For the same reason as in the individual deviations we have 



Probable Ser^ = 



and thus the equation becomes 



Probable e^ = - 

 11 



2.T- = S.vH 



J J ^ n 



Eliminating e^ between this equation and (8) we find by using (4) 



.Kn-l)S.V=»^2/-S/ = A (9) 



The second member of this equation is computed by summing the squares of all 

 the t's, which are r in number, and also the squares of all the nr individual depart- 

 ures. Having thus found r values of A, the sum of which we shall call A simply, the 

 probable mean world-deviation t^ is given by tlie equations 



A 



Probable mean r^ = — -^ HO) 



° nr{n — 1) ^ ' 



When several periods, for which the number of regions was unequal, are to be 

 combined, the final equation for t,," should be put into the form 



Sr«(« - i)v = 2;a 



This value of v will be subject to a probable error arising from the probable 

 accumulation of accidental deviations in the sum of all the quantities which form it. 

 Our conclusions as to its value must depend upon how far its actual value exceeds 

 this probable accidental deviation. If within the limits of probable deviation, we 

 must consider that the evidence is against its having any determinable value. The 

 probabiUty of its having a real value increases with its magnitude as compared with 

 the probability of the accidental value. 



It may happen that SA comes out negative. This would signify that, instead of 



