Sept. 26, 1878] 



NATURE 



565 



Table 111.— Rainfall 0/ Madras {Maximum Years in Sixth 

 Line), 



The " mean cycle " in the above table has been formed (in 

 the way already mentioned) with the view of reducing the 

 effects of what are called "accidental" irregularities in the rain- 

 fall, and its mean value is 48*5 inches, while the mean of the 

 thirteen "means " is 47*3 inches. Now it will be observed 

 that, as was the case when only the years 1813 to 1867 were 

 taken (Nature, vol. xvii. p. 449), there is apparently a double 

 oscillation of the Madras rainfall during the sun-spot cycle. It 

 will be seen also — and it is important to bear this point in mind — 

 that the mean rainfall of the seven maximum years not only does 

 not exceed, but barely reaches, the mean for the whole cycle. 

 There are apparently two maxima and two minima, and one of 

 the minima seems to occur very soon after the sun-spot maxi- 

 mum. In fact, there was a great deficiency of rainfall at 

 Madras in the maximum year i860, and in the years 1830, 1861, 

 and 1869, immediately following or preceding a maximum year, 

 but whether there were famines in one or more of these years, I 

 do not know. (The years of minimum sun-spots are marked 

 with an asterisk.) 



Coming now to the second half of the method, so far as 

 Madras is concerned, we get the following results : — 



Table IV. 



-Rainfall of Madras {Minimum Years in Eighth 

 Line), 



The above table shows that the minimum rainfall, both for 

 the "means" and the "mean cycle," coincides with the mini- 

 mum of sun-spots (see Table II.), and that, upon the whole, 

 the spots and the rain decrease and increase together. But as 

 the maximum years (with an asterisk) are not all in the same 

 line, nor the minimum years in Table III., all in the same line, 

 it is necessary to confine our attention to the results for about 

 two years on either side of the epochal years in Tables III. and 

 IV., and in doing so we find evidence of a double oscillation. 



To ascertain whether there is some probability of such an 

 oscillation in the rainfall of Madras, we must have recourse to 

 the more efficient method of the harmonic analysis. I have not 

 had leisure to do so in this particiilar case, but Mr. J. Allan 



Broun (Nature, vol. xvi. p. 334), in a thorough examination 

 of the rainfalls of Madras and Trevandrum for the years 1838- 

 76, gives for the mean oscillations of the Madras rainfall dm-ing 

 that period the following equation, where y is the mean yearly 

 rainfall in inches : — 



y - 5-4 sin (fl + 50°) -f 4-6 sin (26 -}- 552°) ; 



and he remarks that these angles give the epochs of minimum 

 rainfall both in the years of minimum and of maximum sun- 

 spots, and that the single oscillation (of about five years) has 

 held good in seven successive periods. Now this is nearly M'hat 

 we should expect from Tables III. and IV. 



Leaving the Madras rainfall for the present, let us come to 

 that of Edinburgh for the years 1824 to 1872. The following 

 table gives a comparison of the Edinburgh rainfall with the 

 sun-spots from 1824 to 1867 : — 



Table V. — Rainfall of Edinburgh {Maximum Years in Sixth 

 Line). 



An inspection of the above table will show that there is a 

 remarkable coincidence between the rainfall and sun-spot varia- 

 tions — much more remarkable than at Madras. The years of 

 maximum and minimum rainfall and sun-spot for the mean 

 cycles coincide, and, on the whole, there is a regular gradation 

 from minimum to maximum and from maximxmi to the next 

 minimum. 



The next table (the second half of the process for Edinburgh) 

 gives almost equally remarkable results. 



Table VI. — Rainfall of Edinburgh {Minimum Years in Eighth 

 Line), 



We find from the preceding table that the year of minimum 

 rainfall was, on an average, the year immediately before the 

 year of minimum sun-spot, and that the year of maximum sun- 

 spot coincided with the year of maximum rainfall. Another 

 coincidence is that the ratio of the rainfall to the sun-spots in 

 the eleventh year of the "mean cycle " is nearly the same as 

 the corresponding ratio in the first year of the cycle. Whether 

 these relations are constant is another question ; in a case of 

 » Interpolated. 



