yufy26,iS77'] NATURE 



extensive application in physical research, but also, and 

 more immediately that the conclusion arrived at seriously 

 affects the great modern problem of Indian administration, 

 viz., the food-supply of the people. The conclusion is that 

 in the case of the rainfall observations of Madras, which 

 have been discussed by Dr. Hunter, the Director-General 

 of Statistics to the Government of India, the evidence is 

 not sufficient to establish either any periodicity or a 

 correspondence such as Dr. Hunter points out. The 

 correctness or incorrectness of Gen. Strachey's views will, 

 it is evident, materially influence the line of action taken 

 by the Government in dealing with the disastrous famines 

 consequent on the recurring droughts of Southern India. 



The criterion of periodicity brought fonvard by Gen. 

 Strachcy will appear from what follows. The mean 

 rainfall at Madras for the sixty-four years is 48-5 1 inches ; 

 if we take the difference between this mean and the rain- 

 fall of each individual year, and average the results, we 

 obtain 12-40 inches as the arithmetical mean of the sixty- 

 four differences. If we now partition the sixty- four years' 

 rainfall into six sun-spot cycles of eleven years each, and 

 take the difference between each individual year's rainfall 

 and the mean of that term of the sun-spot cycle in which 

 that year's rainfall stands, and then average these sixty- 

 four new differences, we obtain 11-20 inches as the 

 arithmetical mean. Since 12-40 inches, the mean differ- 

 ence of the individual observations from the mean of the 

 whole series, is, by the latter process, only reduced to 

 11-20 inches, or about 10 per cent., Gen. Strachey 

 concludes that the supposed law of variation obtained 

 from the means of the six eleven-year cycles hardly gives 

 a closer approximation to the actual observations than is 

 got by taking the simple arithmetical mean as the most 

 probable value for any year ; and that the evidence, there- 

 fore, is not sufficient to establish any periodicity in the 

 rainfall of Madras, or any correspondence between it and 

 sun-spots. 



In illustration of his meaning Gen. Strachey applies 

 his criterion of periodicity to the diurnal barometric 

 oscillations at Madras, in which a well-ascertained period- 

 icity exists. The result of the calculation is that the 

 mean difference of all the individual observations from 

 the mean of the whole series is 30, whereas the mean 

 of the differences between the two-hourly individual 

 observations and the averages of the same hours is 

 reduced to 7, thus indicating, it is added, the distinct 

 presence of a periodicity. 



In concluding against the presence of any periodicity 

 in the rainfall of Madras, Gen. Strachey makes these two 

 assumptions:— (i) If there be a periodicity in the rain- 

 fall of this part of India, it would be made apparent by 

 applying his criterion of periodicity to the observations ; 

 and (2) the difference between the two arithmetical means 

 calculated as above must exceed at least 10 per cent. 



The diurnal barometric oscillation at Madras is so 

 regular a phenomenon that it was scarcely worth while 

 to make the calculations, since one could have made a 

 close approximation to the averages 30 and 7 by a simple 

 inspection of the figures. Further, this periodicity which 

 has been selected is altogether inappropriate to the sub- 

 ject in hand, as no one could possibly imagine for a 

 moment that any periodicity which might characterise 

 the rainfall of Madias would exhibit an approach to such 

 regularity of occurrence as characterises the curve of the 

 diurnal oscillation of the barometer at that place. The 

 periodicities which suit the subject before us are such as 

 are presented by the curves of the diurnal barometric 

 oscillation in the British Islands. 



Let us then apply Gen. Strachey's true criterion of 

 periodicity in the examination of such a curve, taking for 

 our ex imple the barometric observations at Valencia for 

 the month of December, 1876, as published in the Hourly 

 Kcaditii^s at their seven observatories, by the Meteoro- 

 logical Committee for that month. The examination will 



253 



at the same time test the value of this new criterion as an 

 implement of scientific research. 



The mean of the whole 744 observations is 29-256 inches. 

 The differences of the individual 744 observations from 

 29-256 inches give an arithmetical mean difference of 0-3372 

 inch : and the differences between each of the individual 744 

 observations and the means of their respective hours give 

 an arithmetical mean difference of 0-3369 inch. Looking at 

 the individual hours the largest differences are o 3434 inch 

 and 03413 inch at 10 p.m., and 0-3444 inch and 0-3459 inch 

 at 6 A.M. Thus the difference of these two arithmetic 

 means is only 00003 inch, and the largest difference for 

 any hour amounts only to 0-002 1 inch. 



Now Gen. Strachey concluded against the presence of 

 a periodicity in the rainfall of Madras on the ground that 

 the two arithmetical means differed only 10 per cent, from 

 each other. It follows A. fortiori^ if this new criterion is 

 of any value, that the presence of a periodicity in the 

 diurnalbarometric oscillation at Valencia during December 

 last be concluded against, inasmuch as the difference 

 between the two arithmetical means is only J^ per cent., 

 and not rising quite to I per cent, for any of the 

 twenty-four hours. 



The averages for the month, however, show in an 

 unmistakable manner the presence of such a periodicity. 

 The mean pressure there fell to 29-245 inches the morning 

 minimum at 7 a.m., rose to 29-263 inches the morning 

 maximum at 1 1 a.m., fell to 29-238 inches the afternoon 

 minimum at 3 P.M., and rose to 29-273 inches the after- 

 noon maximum at 10 p.m., the time of occurrence of these 

 phases of the curve differing no more than an hour from 

 the mean periods for Valencia at this season of the year. 

 The periodicity is, as stated, a well-marked one, the 

 sum of the diurnal oscillations amounting to o-io6 inch, 

 being three-fifths of the sum of these oscillations for 

 Madras which average for December 0-174 inch. We 

 do not require to remind our readers that the phenomena 

 of the diurnal oscillations of the barometer take their 

 place among the most uni-/ersally accepted and best 

 established periodicities of science. 



In the concluding paragraph of his paper Gen. Strachey 

 apparently applies another criterion to the Madras rain- 

 fall, which consists in the comparison of the successive 

 combination of the observations, beginning with one 

 eleven-year cycle, and then combining two cycles, and so 

 on, till the whole six cycles were united. The result 

 arrived at by this treatment of the figures, is that the suc- 

 cessive means of the differences between the mean rainfall 

 for the combined cycles and the mean for the several 

 years of the cycle when combined, show no appreciable 

 periodicity. 



With reference to this mode of testing the question, it 

 may be enough to say that even were the result of such 

 an examination as adverse as possible, it could not be 

 used as a conclusive argument against the existence of 

 periodicity, for the very plain reason that we are investigat- 

 ing a periodicity for which only six terms or separate cycles 

 are available, and in these cycles the non-periodical 

 elements bulk largely. But the following table, referring 

 to the portion of the diurnal barometric curve between the 

 morning and evening minima at Valencia for December 

 last will illustrate the point : — 



