214 TABLES AND RESULTS OF THE PRECIPITATION, 



Before making use of this table with a view of a study of the permanency in the 

 amount of the rain-fall during a long series of years, it will be desirable to inquire into 

 the degree of uncertainty, or the probable error, of the annual sums and the mean 

 amount there given. A cursory examination of the table reveals the fact of a limiting 

 variation in the annual amount at any place to the extent of nearly one-half and 

 of one and a half of the mean quantity, which itself, however, is subject to a con- 

 siderable uncertainty even when derived from a long series. Supposing the changes 

 in the yearly amounts to be due to accidental circumstances, and if subject to 

 periodic changes, that these be small and extend over a comparatively long time, 

 we may apply without sensible error the formulse 



e = 0.845 - ^^ and r ^- -^ 



yn^ — n v n 



where e the probable error of any annual amount and r that of the mean of the 

 whole series of n years ; 2 A equals the sum of the annual differences from the 

 mean irrespective of sign. 



Applying these formulBe to the Marietta, Ohio, results we find the probable error 

 of any observed annual amount = + 4.1 inches, of the mean amount from forty- 

 eight years of observation = + 0.59 inches, and it would take a hundred years of 

 record to reduce the probable error of the mean to 0.4 of an inch, as shown iu the 

 following table : — 



Probable Error in 



Mean Annual Amount of Main-fall, at Marietta, Ohio. 



Deduced from 



I year of observation . . . .+4.1 





5 years " . . . . 1.8 





10 " " .... 1.3 





20 " " .... 0.9 





30 " " .... 0.7 





40 " " .... 0.6 





50 " " .... 0.5 





100 " " .... 0.4 



Supposing these numbers to express the average variability in the rain-fall of a 

 country, the successive curves on a rain chart showing the annual distribution 

 should not be for a less difference than about three inches, even if we employ results 

 from stations occupied for at least five years, otherwise the graphical representation 

 becomes confused and expresses temporary instead of permanent features. In 

 accordance with the above principle, the proper selection of curves, as constructed 

 on each of the three accompanying rain-charts, was readily determined. 



The following table contains, for a number of selected stations in different parts 

 of the country and of long record, the probable error e of the amount of rain fallen 



in any one year, also the ratio of this quantity to the average yearly amount, or -- 



These fractions admit of comparison for different localities, and are an index of the 

 greater or less variability in the rain-fall from year to year. The last column gives 

 the probable error r, or the amount of uncertainty which attaches to the resulting 

 average rain-fall as made out from the present record. 



