Distribution of Frequency of the Barometric Height, 493 



neous or not, at one, two, three, or more other stations, are considered. 

 It is indicated that with a proper arrangement of times and dis- 

 tribution of stations it must be possible to make the probable devia- 

 tion zero or nearly zero, and hence to predict with very great 

 accuracy the height at one station from a knowledge of heights 

 at other selected stations. The suggestion is made that this prin- 

 ciple might very possibly be applied to closely predict future baro- 

 metric heights at a given station from antedated observations at 

 other selected stations. 



Various theorems are deduced from the general principles of 

 correlation : thus, it is shown that — 



(a) There is a balance height for every pair of stations, such that 

 when the barometer stands above this height at one station it will 

 usually stand below it at the other, and vice versa,. 



(I) That for a very considerable number of triplets of stations 

 which are positively correlated together, so that a high barometer 

 at one means usually a high barometer at a second, it can still be 

 predicted that if the barometer be steady at one, a rise or fall at 

 the second denotes a fall or rise respectively at the third member of 

 the triplet. 



These principles are illustrated from actual observations at stations 

 in the British Isles. The memoir concludes with an appendix, giving 

 an account of a frequency-recording barometer devised by Mr. Gr. U. 

 Yule. 



The writers hope that their paper may draw attention to the 

 importance of rendering the large amount of barometric observa- 

 tions now made, available for the easy calculation of the variation 

 and correlation coefficients. They consider that if a chain of stations 

 round a large continental area could have their correlation for a 

 series of intervals of time worked out, much might be done in the 

 way of very close prediction of barometric changes. 



The authors have heartily to thank Mr. R. H. Scott, F.R.S., for 

 assistance in a variety of ways. 



