1904.] Time Factor on Correlation between Barometric Heights. 411 



Table V gives the means, standard deviations, and regression 

 coefficients which were employed in the calculations. 



Table V. Barometric Constants for Halifax and Wilmington. 



The corresponding prediction equations are as follows, if H p denote 

 the probable height at Halifax corresponding to a height W observed at 

 Wilmington on the previous day. 



Summer 18791888 . 1L, = 11-527 + 0-6096W. 



Summer 18891898 H^ = 



Winter 18791888 H^, = 



Winter 18891898... R, = 



15-787 + 0-4681 W. 

 3-457 + 0-8764W. 

 6-713 + 0-7678W. 



These results bring out clearly the marked difference between 

 summer and winter, which has already been shown in the case of the 

 correlations. But in both cases there is also a difference between the 

 two decades reduced; this is partly due, no doubt, to the fact that 

 the Wilmington observations were taken at different hours in the two 

 decades, but this would not account for the whole difference, which 

 has been found also in dealing with other stations. It may be due 

 to variations corresponding to those of random sampling; or it may 

 indicate a gradual change, whether periodic or progressive, in the 

 physical constants involved; and this question can only be settled by 

 dealing with observations extending over a longer period. 



The results of the predictions are shown in Table VI. 



The theoretical mean error = 0'7979o- ^/l - r 2 



= 0-175 for summer and 0'239 for winter, 



taking the mean summer and mean winter values of o- and r for the 

 two decades. These theoretical errors are slightly larger than the 

 actual mean errors for the forty random dates here considered. We 

 should presumably improve the predictions by taking the interval for 

 which the correlation is a maximum ; but even without this improve- 

 ment the degree of accuracy attained, though not very great, might be 



