alter: investigation of rainfall. 103 



However, since the effect of changing this one date would 

 affect only the latter part of tables 1 and 2, and since they 

 were computed before the new estimate became available, I 

 have merely inspected them to see approximately what the 

 result of the shift in the latter cycles will be. The reader can 

 see by such an inspection that this will make the results 

 slightly more striking than they are at present. 



It is desirable to make some use of the rainfall data since 

 1913 if possible. Since it is impossible to use the period which 

 actually applies, it is only possible to use a constant periodicity 

 and thus get some approximation to the truth, although some 

 of the amplitude is certain to be damped. Every indication 

 from the sun spots and rainfall was that the period averaged 

 approximately fourteen months since the last sun-spot mini- 

 mum. I have, therefore, plotted all the data of these two sec- 

 tions on the basis of such a constant periodicity. The results 

 are given as table 3. These show once more the regularity 

 with which the phases hold for each cycle, although, since the 

 constant period is, of course, only an approximation to the true 

 variable one, the same accuracy cannot be expected as has 

 been found before. It should be noted that should the in- 

 vestigator be engaged in the entirely different problem of 

 hunting for a possible date of a future minimum instead of, as 

 in this paper, justifying the assumption of existence of the 

 period, he would no longer be bound by this constancy, but 

 could adjust the lengths as seemed best to fit the data in hand. 



The mathematical reason for the greater reliability of 

 minima in comparison with maxima is shown at once by table 

 10 of the first paper. The 15-month primary period has its 

 minimum at phase 13.4 and its maximum at 5.9 in the Eastern 

 group. The second harmonic has minima at 13.3 and at 5.8, 

 with maxima at 2.0 and 9.5. The third harmonic has minima 

 at 13.4, 8.4 and 3.4, with maxima at 10.9, 5.9 and 0.9. It is, 

 therefore, evident that amplitude variation between these 

 harmonics will have very little effect on the principal mini- 

 mum, but that changes in relative intensity will shift the 

 principal maximum from phase 6, its normal value, whenever 

 the second harmonic gains in relative strength sufficiently, to a 

 principal maximum between phases 1 and 2. 



