ALTER: MARVIN'S PERIODOCRITE. Ill 



I would therefore suggest that the graphical representation 

 be changed to X ^ 7i and Y = ij x. If this be done Y will, in 

 general, decrease when X is small, even though there be a real 

 periodicity of small amplitude superimposed on observations 

 with large accidental errors; then, when n has become large 

 enough to damp out the major portion of these errors, increase 

 rapidly, no matter how small the real periodicity, to an infinite 

 limit. If, however, there are no real periodicity Y will ap- 

 proach one as a limit. Such cases as the annual cycle at Bos- 

 ton, where the amplitude is small but where 7i has become very 

 large, and which look doubtful as plotted by Professor Marvin, 

 despite our knowledge of their truth, will show clearly the 

 differences between themselves and accidental combinations. 

 In plate VIII I have replotted in this way the four curves of 

 plate VII. 



In conclusion, I wish to warn against a possible misunder- 

 standing on the part of the reader concerning Professor Mar- 

 vin's statement on page 118 of his article mentioned above, 

 that "other sequences 15 months, 16 months, one-ninth the 

 variable sun-spot period, like the circles, all fall in the class 

 of perfect fortuity." In a letter to me of later date he says: 

 "I would like to know what the testimony of the periodocrite 

 principle would be in reference to the alleged cycles you have 

 examined. I am sure it is easily possible for you to make the 

 application, as you have all the tabulations and data most 

 fully worked up, whereas for me to do the thing myself would 

 mean practically the entire duplication of the work you have 

 already done." It is evident from this statement that he 

 means to refer only to the five towns in Iowa and not, as some 

 might erroneously infer, to the great mass of data I have used. 



