326 A STUDY OF CORRELATrONS AMOXU TERRESTRIAL TEMPERATURES. 



be written in the form A = 0, where for anyone time-term 



A, = WV — {)'.\h\- + w/r/ + h whij') 



There being r time-terms in all, each will give a value of A; the sum of which we call 

 A simply. 

 Summing all r of these probable relations the criterion will become 



A = S.irV-SS,«',.V = (,- = ],2,...,r) (16) 



If the value of A comes out too large to be regarded as the accumulated effect of 

 chance deviations, we must, as before, find a mean deviation tq, common to all the 

 stations for each ~ separate term of observation, which will reduce the second member 

 to the value A. We do this by the same process as that when the weights are taken 

 as equal. We have, as before, the probable equations 



Substituting these values in (16) the terms in e^ all drop out by virtue of the relation 

 (15), and we have left the probable equation 



2.(Tr=-2,,r=)v = A (17) 



which determines a probable mean value of tq', and therefore of to on the same princi- 

 ples as when the weights are equal. 



§ 5. Comparison of Regions token Taken by Pairs. 



When only two regions are compared the process of § 3 may be simplified. Calling 

 r and v' the observed departures when only two regions are considered we shall have 



'2t = V -\- v' 



for each term of observation. Hence 



2t- - h{v- + r'-) = vv' 

 Summing for all r terms, as before 



Thus, putting ?i = 2 in (9) and (10) we find for each time-term the simple expres- 

 sion 



Mean t/ = —^ = Mean vv' (18) 



which is much .simpler in this case than the formula (10). 



