OF FREQUENCY OF THE BAROMETRIC HEIGHT AT DIVERS STATIONS. 467 
at different intervals of time. Nor should it be forgotten that theoretically we have 
much power of varving the magnitude of our correlation coefficients. They decrease 
from about 1 at the distance zero to zero as the distance increases. We have thus a 
zone round every station of zero-correlated stations ; beyond this it is highly probable 
that the correlation becomes negative as we reach places which have cyclones corre¬ 
sponding to anticyclones at the given station. This zone is of course not reached 
in such a small area as the British Isles, Passing through an area of negative 
correlation, we should in all probability ultimately reach an extended area of zero 
correlation. In the next place the time interval is under our control, and the 
coefficient of correlation can be reduced by increasing this. Lastly, it varies also, 
although probably to a much less extent, by varying the direction in which the 
distance between two stations is taken. We can imagine no more useful piece of 
work than the determination of the correlation for a period of 10 or 20 years of a 
series of stat’ons taken so far as possible round, say, a parallel of latitude. We 
believe that lurure oi barometric prediction, i.e., the accurate foretelling of the 
arrival of depressions, &c., lies in an extended knowledge of the correlation between 
a system of barometric stations widely diffused over the surface of the earth; special 
attention being paid to the changes of the correlation with intervals of time. 
The object of the present writers has not been to make an elaborate investigation 
of the numerical values of barometric variation or correlation, but rather to indicate 
to those more directly occuj^ied with meteorological investigations how the mathe¬ 
matical theory of statistics may be applied to barometry with novel and, they believe, 
valuable results. 
Appendix. 
On a Frequency-registering Barometer by G. U. Yule. 
In all ordinary forms of registering barometer the resulting diagram shows the 
height of the barometer at each instant of time. To construct a frequency curve 
from such a diagram, the heights must be read off for all the times desired, corrected 
if necessary, grouped, and replotted in the manner described in the preceding paper. 
This procedure is somewhat tedious, and it may be obviated by so constructing the 
barometer that it shall give the frequency record automatically. 
/XTj 
A 1 + — !_) 5- 
fJlc} 
- + + 
witli a probable deviation 0'6745 
\4 
V( 
1 
np“ 
, , .. N / . Hence we should have absolute prediction 
Y 1 4- (n — 1) rj 
/ __ \ i 
if p = (1 + — 1 r) j . Similar propositions follow for partial correlation and for I'ise corresponding 
to fall. It seems doubtful, however, whether such a system of correlation could possibly be arranged 
for more than four stations. 
3 o 2 
