1904.] Time Factor on Correlation between Barometric Heights. 407 



4. It therefore appears that the maximum correlation between 

 Halifax and Wilmington in the summer occurs when the barometer at 

 Halifax is read about 16 hours later than that at Wilmington, and that 

 the corresponding interval for the winter is about 23 hours. The 

 intervals for St. Helena and Cape Town are about 11 hours and 

 24 hours respectively. Some caution may be necessary in accepting 

 the values obtained for the summer intervals, since it is possible that 

 the diurnal variation may affect the correlation; this point could only 

 be settled by means of observations taken at other hours of the day. 

 This effect of the diurnal variation, if it really exists, may conceivably 

 account for some part of the difference between the intervals obtained 

 for the summer months of the two decades for the American stations. 

 Nevertheless, it seems reasonable to conclude that, in order to predict 

 the barometric height at Halifax at 9 A.M., it is desirable to use the 

 reading taken at Wilmington at 10 A.M. on the previous morning in 

 the winter, while in the summer the Wilmington reading should be 

 taken at about 5 P.M. 



Diagram I (next page) shows the interpolation curves used. 



5. The physical interpretation of these intervals for which the 

 correlation is a maximum, is not obvious to me, although it may 

 possibly be so to practical meteorologists. Of course, the intervals, 

 11 to 24 hours, are too short to be looked upon as corresponding 

 to the transfer of an actual disturbance between the stations. Even if 

 this were not the case, they could not give the average intervals 

 between the arrival of the same isobar at the two places considered, 

 since none of the pressures correlated may be alike. I should be glad 

 to see the point adequately treated by one with practical meteoro- 

 logical experience, and will merely remark here that the correlation 

 depends not upon equality of pressure, but upon proportionality 

 of deviations from the local means. A full explanation must also 

 account for the fact that the winter and summer relations differ in a 

 very marked way. 



6. Another point which seemed to deserve investigation was the 

 correlation between the daily rise or fall of the barometer at Halifax 

 and Wilmington. This investigation would have involved considerable 

 labour if it had been necessary to proceed by the direct method of 

 preparing tables of the daily rise or fall, and then calculating the 

 correlations from them. The work has been considerably lessened by 

 the use of the following method, which is due to Professor Pearson. 



Let a?i be the reading on one day and x- 2 that on the following day at 

 the first station, x{ and x% the corresponding readings at the second 

 station after any interval. Let mi, w 2 , m/, m% be the means, 

 <TI> <?* o"i' 5 0*2' the standard deviations, r i2 the correlation of xi and ajg, 

 that of xi and z 2 ' 5 ^2/, that of Xi and o^, and so on, and^ that of 

 - xz) and (xi - xi). The mean values of (xi - x- 2 ) and (x l - x 2 ') will 



VOL. LXXIV. 2 H 



