422 



ANNALS NEW YORK ACADEMY OF SCIENCES 



The ten other series of observations were each tabulated and investigated 

 for periodicity in the same manner. It does not seem necessary, however, 

 to give the individual residuals and products in detail. But the following 

 table gives the footing for each column of products in the different series, 

 and shows the date of beginning and the number of seven-day periods in 

 each. 



Table XV. 



Sums 



+ 4.3281 +0.0700 —0.0718 

 + 0.0162 —0.0166 



+ 0.2958 +0.2949 —0.4491 

 + 0.0683 +0.0681 —0.1038 



The series of x's are again distinctly periodic, and indicate a tendency 

 towards a twentj'-eight-day period. This tendency is not only shown by 

 the final series of x's, but it is also shoAvn by nearly every one of the indi- 

 vidual sets of footings as given in the above table. In six cases the increase 

 is marked in the ao a/th column; in two cases, in the a^ ag'd column; and in 

 one case, in the ao aj'th column. Two series only show no tendency towards 

 periodicity, and of these one is a short series of six weeks only, beginning 

 March 7, 1892, The other series, vrhich shows no periodicity, is the rela- 

 tively long one beginning Jan. 23, 1899, and extending over nine weeks. 

 On the whole, however, the tendency towards a recurrence at the end of 

 approximately twenty-eight days is quite marked. 



Continuing the products for the two long series up to ao ag, we have for 

 the series of products: 



* Broken series. 



