1880.] Inquiry into the Periodicity of Rainfall. 71 



posing the series under consideration. Perhaps I shall make the opera- 

 tion clearer by explaining in detail the actual method of working finally 

 adopted. 



Taking the table of yearly totals, the dates were written down on 

 paper side by side, in horizontal rows, in red chromographic ink, and 

 then the corresponding rainfalls in blue. From this sheet a number 

 of impressions were worked off, each of which was cut into slips, 

 afterwards gummed together, so as to form a long strip, exhibiting in 

 a straight line the whole table of rainfall. 



The strips were next divided into short lengths corresponding to the 

 period to be investigated {e.g., for a five-year period, each piece con- 

 tained the values for five consecutive years), and then gummed on 

 a sheet of paper one beneath the other, so that eventually we had five 

 columns of figures, the means of which represented the average 

 rainfall for each of the years represented by 



(1 + 5)... 



...(1 + 2-5)... 



...(1 + 3-5)... 



...(l+»5) 



(2 + 5)... 



...(2 + 2-5)... 



...(2 + 3-5)... 



(2 + 72,5) 



(3 + 5)... 



...(3 + 2-5)... 



...(3 + 3-5)... 



(3 + w5) 



(4 + 5)... 



...(4 + 2-5)... 



...(4 + 3-5)... 



(4 + ?z.5) 



(5 + 5)... 



...(5 + 2-5)... 



...(5 + 3-5)... 



...(5 + »5) 



The mean of the whole series also being known, it became possible 

 to form a curve, showing the variation in the amount of rainfall upon 

 the assumption of a five-year period. 



By applying the same process to other copies, curves were finally 

 drawn for cycles extending respectively over six, seven, eight, nine, 

 ten, eleven, twelve, and thirteen years, and the points of maximum 

 and minimum noted for each curve. 



Tables I to IX, and figs. 1 and 2, exhibit the result of this process 

 as applied to the whole series of observations discussed, including the 

 Paris results. 



Next, the whole of the observations were plotted down, and a long 

 curve was drawn through them ; from this the maximum years of fall 

 were determined and noted. The dates of these maxima and minima 

 were then compared with the dates of corresponding maxima and 

 minima of a curve based upon the five-year cycle, as determined 

 above, and the number of coincidences and non-coincidences noted. 



The same operation was performed with each of the cycles, and 

 finally the ratio existing between the number of coincidences and non- 

 coincidences was calculated. The results are given in Table X. 



This table shows that in no one case is there any indication of a 

 period of any integral number of years from five to thirteen inclusive 

 running through them. 



Hence, whatever period of variation in rainfall there may be, coin- 

 cident with fluctuations in the spotted surface of the sun, either of ten, 



