4(30 
PR04’I^3SS01i K. PEARSOX AND 3tlSS A. LEE OX THE DISTRIBUTION 
at and if we liad them and worked out the Whitby-Southampton and 
W]iitby-Lciuda.]e correlations, it is unlikely that they would both be exactly ecjual, 
anci ecjutd to 0 O-J/o. In fact the correlation for a number of Yorkshire stations, with 
both Laudale and Southampton, would have first to be worked out, and then the true 
station helving an exact causal relationship with Daudale and Southampton would 
require to be found by interpolation. 
Dut we should expect stations not so far removed from the rig’ht position to have 
theii barometric height given in terms of those of Laudale and Southampton by^’ an 
appioxiniately linear relation. Hence, to indicate to the reader that our conclusion 
namely, that a barometric correlation may pass into a causal relationship—is not 
so paiadoxical as may appear at first sight, we have endeavoured to test how far the 
Stonyhurst height is a linear function of the heights at Laudale and Southampton. 
In order to do this we have neither assumed nor ivorked out the Laudale-Stonyhurst 
and the Southampton-Stonynui'st correlations. The former was too risky,^ the 
latter loo laborious for the end to be desired. We have simply assumed a linear 
relr 
tionship between the heights at the three stations, i.e., 
Hgt — aiHgo + + z, 
where a; and y are numerical constants, and 5 : is a number of inches. To determine 
X, y, and 2 we chose twelve observations, taking the 15th day of each month for one 
year, and working by the method of least squares. Unfortunately the resulting 
equations for x, y, and 2 , throw back their determination on decimal fio-ures, which 
are the limit of what is usually tabulated in barometric observations. The resulting 
equations were 
SOT 59a; + S0-020_^ + 2 — SOT 30 = 0, 
SOTGla; 30-022y + 2 — 30T32 = 0, 
SOTOlsc-j- 30'024y T" 2 — 30T33 = 0. 
The solution of these equations is 
a; =0-50, y = (j-b0, 2=0-04'', 
eie the values of x and y are certainly not correct to the second place of decimals. 
wii 
The resulting formula gives 
H 
St 
0'5Hgo -j” 0"5 Hl “h 0'04 '. 
All attempt to approximate to the coehicients of correlation, gave the Southampton 
factor a somewhat higher value than the Laudale factor, and this is probably the 
case. But with the data available we shall hardly do better than the above formula. 
To test its degree of accuracy 50 values were taken out of the returns for Southampton, 
Laudale and Stonyhurst at fortnightly intervals, and the observed and calculated 
values at fetonyhurst are given in Table XII. The diflerences are distributed fairly 
evenly, positively and negatively, and their mean value is about 1/40". We consider 
^ W e luive already iiotetl that the Stunyluu'st data are not, in oiir opinion, very satisfactory : .see p. 14(3. 
