1904.] Time Factor on Correlation between Barometric Heights. 409 



x^ -x 2 ' - ( mi ' - nfl] 

 ~ 



{( Xl - x 2 ) - (mi - m 2 ) 2 & {(xi - x 2 ) - (m{- m 2 ')} 



^ 2 + o- 2 2 - 



It may be noted that this formula would apply to any case in which 

 it was desired to correlate the difference of one pair of quantities with 

 the difference of another pair. If we were not dealing with the summer 

 ^nd winter months separately, we should have, with sufficient approxi- 

 mation, 



(7! = CT 2 , (Ti = 0- 2 ', r U , = r 22 , 



since the quantities included in the x\ and the x 2 groups would be the 

 same, with the exception of a single reading at each end of the period 

 -considered. The formula would then take the simple form 



E =- 

 " 



But in our case the x\ and x 2 groups differ by a reading at each 

 equinox of each year considered, and it was therefore decided to use 

 the accurate equation (i), although (ii) would have been sufficient 

 to give a good idea of the correlation. 



In order to use this formula, it was necessary to calculate the corre- 

 lations between the barometric heights on consecutive days at Halifax 

 .and at Wilmington. Table III gives these correlations, and Table IV 

 gives the correlations between the daily rise at the two stations for 

 various intervals. 



Table III. Correlation of Barometric Heights on Consecutive Days. 



The most noticeable fact which appears from these results is the 

 analogy between them and the space relations considered in the 

 previous note. In that case we found that with increasing distance 

 the correlation diminished to a negative minimum, and then began to 

 increase ; and the negative correlations obtained were of considerable 

 magnitude. This does not seem to occur for the time relations when 

 the actual readings are considered ; for, although the values given in 

 Tables I and II seem to indicate that a minimum has been reached, the 

 only negative correlations which have been found are so small as to be 



2 H 2 



