24 THE UNIVERSITY SCIENCE BULLETIN. 



times. In the curve of the sun-spot values reproduced as Figure 1, 

 I have erased each part of the curve probably a hundred times. 

 Although very laborious, the process, with enough patience, yields 

 very good results. The accuracy of the period curve depends upon 

 the accuracy with which the epochs of maxima and minima are 

 obtained. A steep but narrow peak, such as that of 1861, may be 

 unreal for this reason. However, due to the short duration of such 

 a peak and the fact that it must almost immediately be counter- 

 balanced, there will usually be little effect in data extending over 

 a long range. 



In the preceding paragraph I have spoken of the sun-spot period 

 at any date as a varying quantity, not even approximately constant 

 through a single cycle. This may necessitate a definition of "period" 

 somewhat different from what is ordinarily understood. I there- 

 fore give the following definition, which will be adhered to whether 

 referring to sun spots or rainfall. 



The length of the period at any date is the reciprocal of the rate 

 of change of phase at that date and need not continue even approxi- 

 mately through a complete cycle. 



From this curve I have taken the mean value of the sun-spot 

 period for each year. These values are given as column 2 of table 2. 

 Column 3 gives the departures from 15 months of one-ninth these 

 values. Obviously, 15 months was chosen because it is the nearest 

 integral number of months to one-ninth of a period. If, for example, 

 the number given for any year in column 3 were + 9, it would mean 

 that during that year one-ninth of the sun-spot period was 16 

 months. If it were — 9 it would mean that the period was 14 

 months. In the first case it would be necessary, working on a 15- 

 phase basis, to skip a month every 16 months as long as that 

 length of period persisted; in the second case to repeat one every 

 14 months. We can thus construct a table of months to be re- 

 peated in the analysis of our rainfall data when the ninth of the 

 sun-spot period is less than 15 months, or to be skipped (or better 

 still, averaged with the next adjacent one) when the ninth is more 

 than 15, in order that Wolfer's sun-spot maxima may all fall in 

 one phase and his sun-spot minima in one. 



In this work I have in each case averaged the month to be skipped 

 with the next following one instead of actually skipping. Thus 

 three months' data give two phases, the result desired through skip- 

 ping, and all data are used. There is, however, such a slight gain in 

 accuracy that I scarcely believe it worth the slight extra work in- 

 volved. If this averaging and repeating is done correctly the epoch 



