458 
PBOFESSOR K. PEARSON" AND MTSS A. LEE ON THE DISTRIBUTION 
suggests—we wish especially to note that it does not prove—that correlation differs 
in its variation with the distance according as the two stations have their distance 
practically along or orthogonal to the generalised isobars. Unfortunately, without 
crossing the Irish Channel, it was impossible to find two stations along a generalised 
isobar so far apart as Southampton and Laudale. There can be little doubt, we 
think, that such stations would, however, give a sensibly less correlation than the 
north and south stations. Although the diagram (owing to the very considerable 
labour of calculating the correlation for a pair of stations even for eiffht 3 ^ears) is 
based upon a very inadequate number of measurements, yet we should expect, with 
continuity in the correlation coefficient, which can hardly fail to be the case, that it 
would give fairly approximate values. For example, we should anticipate that the 
correlation between Southampton and Stonyhurst would be about 0'94 to 0*95. Since 
Stonyhur,st is, roughly, about equally distant from Southampton and Laudffie, the 
correlation between Stonyhur.st and Laudale may with somewhat smaller probability 
be also put at 0’94 to 0‘95. Clearly the general relationship between correlation, 
di.stance, and direction of distance will only be determined Avhen a very great number 
of pairs of stations have been worked out, and these stations ought to be distributed, 
not over a small area like the British Isles, but over a large continental area. 
12, Case (ii .).—Prediction from two Correlated Stations. 
Here ; 
13 
With a probable deviation 
’A 
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' 1.3 
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3 ^ 'h 
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4' 27’2;yy,?Y: 
Hence it we wish to predict the height of the barometer as closeU as possible at 
one station from either an earlier or contemporary observation of the heights at two 
other stations, we ought to choose out intervals of time and the distribution of the 
three stations, so that may lie as small as possible. It would thus seem, 
considering the great variety of times and places available, within our power 
to predict almost exactly the height at any selected station from a knowledge of the 
heights at two other selected stations at selected intervals of time. The importance 
of testing this principle seems to us very great; it might lead to quite novel methods 
of predicting barometric change. Unfortunately the needful knowledge of the 
correlation coefficients of widely separated pairs of stations for divers intervals of 
observation is still wholly wanting. The following example is merelv illustrative. 
Suppose the second and third stations, so selected that they have equal correlation 
~ U 2 ~ '^’]3 with the first, and a correlation p — r^^ with each other. Then pj 
Avould be alisolutelj^ zero if 
