OF FREQUENCY OP THE BAROMETRIC HEIOHT AT DIVERS STATIONS. 455 
Now the distribution of frequency at each station being skew, the correlation 
surfaces as based upon these tables will also be skew, and the curves giving the 
mean height at one station for a given height at the other are no longer straight 
lines. We do not pro|)Ose on the present occasion to discuss at length the properties 
of this type of skev.^ correlation, but to refer the reader to a paper by Mr. -G. U. 
Yule, published in the ‘Roy. Soc. Proceedings,’ vol. 60, pp. 477 et seq., 1897. In 
that paper it is shown that the coefficient of regression is still significant in the case 
of skew correlation, it gives the slope of the line of closest fit to the curve of regres¬ 
sion, or the locus of the mean heights of one station for successive heights at the 
other. Since the locus is net very far removed from a straight line in any of the 
cases dealt with, it follows that the line of closest fit will very approximately 
represent it. Calculating the coefficients of correlation and the regressions for the 
three pairs of stations by the usual formulae (see “ Mathematical Contributions to the 
Theory of Evolution, III.,” ‘Phil. Trans.,’ A, vol. 189, pp. 265-6, 275-7), we have 
the following results ;— 
Table XI.—Barometric Correlation. 
Pairs of stations. 
Coefficient of Cor¬ 
relation. 
Coefficient of Re¬ 
gression. 
Probable deviation 
of array. 
Babbacombe . . . 
Cburcbstoke . 
j 0-9824 1 
. 
0-8901 
1-0818 
- 
obtOl 
0-0441 
Southampton . 
Laudale .... 
1 0-7572 1 
0-6260 
0-9159 
0-1449 
0-1752 
Hillington 
Cburcbstoke . . . 
1 0-9576 1 
0-9267 
0-9895 
1 
0-0663 
0-0685 
The application of this table to predict the height of the barometer at one station 
from a knowledge of the contemporaneous height at a second will be clear to 
readers familiar with the mathematical theory of correlation. For example, if the 
height of the barometer at Babbacombe be .x” above the mean Babbacombe height, 
then the height to be predicted at Churchstoke is 1*0818 x" above the Churchstoke 
mean, with a probable error of 0"‘0441. We may give a numerical illustration. The 
barometer at Churchstoke stands at 30”*0176 ; what are its probable heights at 
Babbacombe and Hillington ? 
The mean height at Churchstoke = 29”-9545 (see Table IV.) ; hence the observed 
height at Churchstoke is 0”‘0631 above the mean. The most probable heights at Bab¬ 
bacombe and Hillington will accordingly be 0*8901 X 0”’063l and 0*9267 X 0 *0631, 
or 0”'0562 and 0''''0585 above the respective means of those places. Extracting these 
means from Table IV., we find: 30''*0349 and 30”*0014 for the probable heights 
