30 THE UNIVERSITY SCIENCE BULLETIN. 



States, instituted. The great shift in normal made it impossible to 

 compare the early and the later records. This investigation of 

 Australian rainfall ends, therefore, with 1907, although the later 

 results kindly sent by the meteorological director of the common- 

 wealth are published here for information: 



Group A. 



The Punjab, 

 Eastern India 



United States. Siberia. (smoothed). 



£ 2.7 2.4 3.6 



Range of curve from whole data 23 17 29 



Ratio 0.117 0.141 0.138 



Number phases on one side of normal.... 12 10 f*9 



The ratios in each of these cases are approximately one-eighth, 

 showing, as previously develope'd, a very small chance of such acci- 

 dental agreement. In the case of India the same e was derived from 

 the relationship of both the first and last of its three curves to the 

 middle one. Since the ratio given measures the possibility of chance 

 agreement of either of these curves with the middle one, the chance 

 that both agree in this manner by. accident is only the square of the 

 chance that one does. 



Group B. 



Pacific coast Northern 



(smoothed). Europe. Chile. 



c 3.8 2.5 3.9 



Range 43 22 25 



Ratio 0.088 0.114 0.156 



Number of phases on one side of normal. . [*11 12 10 



\ 12 



As would be expected from an examination of the curves, the 

 chance of mere accidental agreement between the two halves of the 

 Pacific coast and northern European curves is negligible. In the 

 case of Chile, just as one would judge from the appearance of the 

 curves, it is much larger than for the other two, but is still small. 



Group C. 



South Madagascar 



Australia. Jamaica. (smoothed). 



e 4.6 3.5 5.1 



Range 24 19 28 



Ratio 0.193 0.184 0.182 



Number of phases on one side of normal . . 8 10 8 



The results of group C, while favoring the true existence of the 

 periodicity to some extent, do not show the certainty of groups A 

 and B. This is to be expected in the case of Jamaica, which is a 



* Unsmoothed. 



