22 THE UNIVERSITY SCIENCE BULLETIN. 



cycles. We will then use the month's data which we used for the 

 fourteenth phase of the seventh cycle again in the fifteenth phase. 

 Doing this, no month will fall more than a half phase from the 

 proper one as determined by the mean of all positions. If we assume 

 a period of 15^/i months we will merely skip one of the month's data, 

 or better still, average it with the next following one. In this man- 

 ner any period may be plotted with any number of phases desired, 

 and no month's data more than a half phase from its proper place. 



FIRST APPLICATION OF THIS METHOD TO RAINFALL. 



One-ninth of the mean sun-spot period is very nearly 14% months. 

 I tabulated all the rainfall data from Lawrence, Kan., beginning 

 with 1868, according to the method outlined above. The result 

 showed a variation of about 12 per cent each side of the normal. 

 Next I divided the data into halves and found the two to agree 

 fairly well. Following this I examined data from all of Kansas, 

 from Nebraska, New England and Ohio. The data from Ohio 

 checked fairly well; those from New England and Nebraska gave 

 results which were discordant with themselves. The variation of 

 the sun-spot period now came to mind. If there were any real 

 variations due to sun-spots or to a common cause they would cer- 

 tainly have to keep a constant relationship with the phases of the 

 sun-spot period. 



Table 1 shows the dates of maxima and minima of sun-spots as 

 determined by Wolf and Wolfer (7). It also shows the number of 

 years intervening between successive maxima or minima; in other 

 words, the actual sun-spot periods during those years. As a first 

 approximation to keeping the phases in step with the sun spots, I 

 plotted the rainfall between the dates of each pair of consecutive 

 minima on a period one-ninth that interval. Minima occurred in 

 1889, August, and in 1901, September. The interval is 145 months. 

 I therefore used a period of 161'4 months between those dates. The 

 next minimum occurred in 1913, May. This interval is 141 months, 

 and I used a period of 15% between these dates. When this was 

 done I secured very much better results than before, so much better 

 that I could not believe them due to accident. I obtained similar 

 curves for each state the whole length of the Atlantic and Gulf 

 coasts as far as Texas. When the data of New England and 

 Pennsylvania were divided in halves, curves of similar shape were 

 obtained for each, differing only in phase. This improvement over 

 the results from a constant period indicated that a more rigid 

 method of keeping constant relationship with the sun-spot phases 

 should be devised before definite conclusions were drawn. 



