432 
PROFESSOR K. PEARSOR AND MISS A. LEE ON THE DISTRIBUTION 
would mark a frequency distribution corresponding to a curve like (v.), but for 
practical statistical purposes a curve like (ii.), which fits closely when the criterion is 
even as large as 0-38421 (see Plate 10, fig. 6 , of ‘ Phil. Trans.’ memoir cited above), 
will suffice to describe the distribution of barometric frequency. The standard devia¬ 
tions of IB. 2 , and 6 + 3^] — 2/5^ are 0'03673, 0’12022, and 0-2068 ; these give for 
the probable errors of the means of the same three quantities (duly weighted), 0-00568, 
0-01860, and 0-03200 respectively. Thus the probable errors are about 3-9, 0-5, and 
71 per cent, of the observed means. Thus, while it is exceedingly improbable that the 
mean values of and differ much from their observed values, it is very possible 
that the true mean value of the criterion is zero and not — 0-04495.* The compara¬ 
tively large and opposite values of the criterion at Markree Castle and Stonyhurst 
must, of course, be duly regarded, and a longer series of observations at these two 
stations may some day serve to indicate how far their barometric conditions are 
peculiar to local conditions of climate or of observation. 
As a matter of fact, the curves corresponding to equations (iv.) or (v.) above were 
oi’iginally calculated for all the stations, and drawn upon the diagrams as well as those 
corresponding to (ii.), but the mean percentage error in frequency, when tested by a 
planimeter, showed no very sensible improvement. An examination of Plates 9-17, 
giving the graphical representation t of the observed frequency by the theoretical 
distribution (the negative direction of x being towards high barometer) 
2/ = Z/o (1 -P 
amply demonstrates that tliis limit to the skew binomial suffices to satisfactorily 
describe barometric frequency. The closeness of the approximation is one rarely met 
witli in the usual representation of variation by the normal curve of errors. 
To illustrate how closely curve (ii.) corresponds to curve (v.), even with a value 
(— -28970) of the criterion relatively large compared with the majority of those with 
which we are dealing, we give in the following table the frequencies annum for 
Babbacombe as observed, and as calculated from (ii.) and (v.) respectively :_+ 
* The probable error of the criterion for skew variation will be discussed, in a forthcomiuo' memoir 
by one of the present authors, and it will there be seen that this pi’obable error is frequently large. 
t We have to thank Mr. C. Jakeman, Demonstrator in University College, for much aid in the 
preparation of our diagrams. 
X Another instance of the same closeness is exhibited in the ‘ Phil. Trans.’ memoir above cited for a 
curve like (iv.) with (ii.). Cf. Curves I. and II. of fig. 6, Plate 10. The criterion is here still larger, 
e.g., ,38-421. 
