110 THE UNIVERSITY SCIENCE BULLETIN. 



cycles in the eastern third of the United States. The second 

 table shows the same for each of seventeen consecutive cycles 

 of a large western group. These tables are peculiarly well 

 adapted for application of Professor Marvin's Periodocrite. 



In table 1 of this paper I have formed the means of the first 

 n cycles for each column of the Eastern group table described 

 above, allowing n to assume each integral value from one to 

 twenty-four. These means are the tabular values printed 

 under each phase number. From these I have computed x and 

 y, beginning with n = S. In table 2 I have done the same 

 thing for the Western group. 



The last columns show the ratios y/x. Each of these thirty- 

 five ratios is greater than one, the mean for the first table be- 

 ing about 1.4 and for the second about 1.2. 



In plate VII I have shown these results graphically, and for 

 purposes of comparison have copied the curves representing 

 the annual cycles of Washington, D. C, and of Boston from 

 ' the figure given by Professor Marvin in his paper. 



The following has no connection with the application I have 

 just made of the periodocrite to rainfall, but I believe that a 

 slight modification of its graphical representation, not in any 

 way changing its principle nor the method of analysis, will 

 make it even more useful to discriminate between accidental 

 and real periodicities of small amplitude. 



When X is plotted as the abscissae corresponding to suc- 



cessive va]ues of n become very closely crowded together, so much 

 so that in the case ot of 24 cycles the last half of them are rep- 

 resented by a very short portion of the curve, one easily over- 

 looked in comparison with the much longer part representing the 

 first half of the data. For a larger number of cycles the case be- 

 comes even worse.' Yet these are the cycles in which accidental 

 errors have been damped, to a large extent, and in which any 

 true periodicity of small amplitude will show itself most clearly. 



Furthermore -^ has become small, if the amplitude of a real 



periodicity is small, and the distance that is plotted above the 

 line of perfect fortuity seems to the eye to be negligible, despite 

 the fact that y/x, the real criterion, may rapidly be increasing 

 to a large value. 



