( 558 ) 
constants in the formulae, so that no average values higher than those 
of the second order need to be calculated and, as the phenomenon 
presents an annual and a semi-annual variation, it is reasonable to 
expect that this number will be sufficient to arrive at a suitable 
expression for the law of distribution. 
Then, in the first place, the frequency-formula known as Type III 
of Prof. Pkarson’s formulae finds an application. 
As the quantities under consideration are rainy hours, with the 
exclusion of hours in which no rain has fallen, the funetion must 
vanish for «=O if we take the duration zero for origin of coordinates, 
then for increasing values of v the function will rapidly rise to a 
maximum-value and decrease in a continuous way without any 
definite limit. 
In this case Pearson’s Type III assumes the form: 
wiee pp Oe hs i eS EN 
If we put 
mt =z 
the expression for the mean of the n‘' order becomes: 
0 
U 
n= | er? eet de 
{in AT { d 
0 
and 
KE 
Mo met! met 
0 
adi AP(pr1 
| ep de = Eden | 
from which we find for the determination of the two constants m 
and p the expressions: 
M= en a al +. 3 en 
a Hy, u, 
A being defined so that the area of the curve becomes equal to unity, 
this quantity must not be regarded as a characteristic of the curve. 
Applying these formulae to the frequencies of Table I, we find 
the values given in Table III. ‘ 
In computing the means it is to be noted that the duration of a 
shower of say 3 hours is not to be regarded as a duration between 
2.5 and 3.5 hours, but as a mean duration of 2.5 hours, because 
any duration beyond 3 hours would transfer the quantity into the 
4 hours group. Further it must be noted that for February and 
March the excessive durations of 100 and more hours have been 
excluded from the calculation. 
