542 



NATURE 



[Aprils, 1880 



It is even conceivable that some places might exhibit a 

 maximum when others showed a minimum, while others 

 again might exhibit a double instead of a single period. 



4. It appears to me that if we bear in mind these 

 considerations, it will not answer to add together the 

 rainfalls of a few selected stations as they stand, with the 

 view of determining by this means whether there be a 

 long-period inequality in the rainfall of the whole earth. 

 We are not yet in a position to reply experimentally to 

 this question. 



It does not, however, follow that nothing can be done. 

 Dr. Meldrum and others appear to have achieved good 

 preliminary work in the direction of indicating the ex- 

 istence of a rainfall inequality depending upon the state 

 of the sun. Dr. Meldrum began by pointing out that in 

 a good many places there is a greater rainfall during 

 years of maximum than during years of minimum sun- 

 spots, and that this phenomenon repeats itself from one 

 solar cycle to another. Again, Governor Rawson has 

 pointed out the existence of certain localities where the 

 rainfall inequality appears to be of a precisely opposite 

 character, while Dr. Hunter has shown the practical 

 importance of the investigation with reference to certain 

 tropical stations. The subject has likewise been discussed 

 by Piazzi Smyth, Stone, and others. 



5. The question has arisen whether it might be possible 

 to throw any light on this problem by the method of 

 deducing unknown inequalities proposed by Mr. Dodgson 

 and myself (see Proceedings of the Royal Society, May 29, 

 1879). The essence of this method consists in a way by 

 which we may numerically estimate the indications of an 

 equality. Let us suppose, for instance, that in ignorance 

 of the diurnal range of temperature we try to find whether 

 there be a temperature inequality of twenty-four hours, 

 or whether there be not rather one of twenty-six hours. 

 We should begin by taking a large number of hourly 

 readings of temperature, and we should group these into 

 two series, the one containing twenty-four numbers in 

 each horizontal row, and the other twenty-six. We should 

 thus have twenty-four vertical columns from the one 

 series and twenty-six from the other, and we should take 

 the mean of «a/-h vertical column of each series, as well 

 as the mean of the whole. Now it would speedily be 

 found that an inequality was indicated by the twenty-four 

 hourly series, and none by the twenty-six hourly series. 

 For in the first series the mean of that vertical column 

 representing observations at 5 a.m. would be greatly less 

 than the mean of the whole, while the mean of that 

 column representing observations at 2 p.m. would be 

 much higher than the mean of the whole. On the other 

 hand, in the twenty-six hourly series, provided it w r ere 

 sufficiently extended, we should perceive no such differ- 

 ences. Thus, in the twenty-four hourly series the differ- 

 ences of the means of the various vertical columns from 

 the mean of the whole would be much greater than in the 

 twenty-six hourly series, and the mean amount of these 

 differences might be taken to form a numerical criterion 

 of the presence or absence of an inequality. 



6. This method applied to the subject in hand might 

 be expected to reveal the presence or absence of inequali- 

 ties in rainfall, provided we have observations sufficient 

 for the purpose. It is clear that the successful application 

 of this method does not require a previous knowledge of 

 the exact form of the inequality. Whether a maximum 

 rainfall occur at epochs of maximum or at epochs of 

 minimum sun-spot frequency, whether there be only one 

 rainfall maximum corresponding to the solar period, or 

 two, or even three, is a matter of no consequence as far 

 as this method is concerned. All that is necessary is that 

 the rainfall should always be similarly affected by similar 

 states of the sun. 



Here, however, we must bear in mind that this method 

 of detecting inequalities by summing up and averaging 

 the departures from the mean caused by the inequality, 



likewise sums up and averages the accidental fluctuations. 

 Now these accidental fluctuations are particularly large 

 for rainfall, and it is therefore desirable to lessen their 

 disturbing effect as much as possible. This can only be 

 done by confining ourselves to long series of observations 

 in which the accidental fluctuations may be supposed to 

 counteract each other to a great extent, while the long 

 period fluctuations will remain behind. 



7. Through the kindness of Mr. Whipple, Director of 

 the Kew Observatory, I have received copies of those 

 catalogues of rainfall which he has himself made use of 

 in a paper which was recently communicated to the Royal 

 Society (January 8, 18S0). Of these Paris, Padua, 

 England, and Milan form the most extensive series, that 

 of Paris embracing 161 years, Padua, 154, England 

 (Symons's table), 140, Milan, 115. Mr. Whipple has 

 likewise furnished materials by which the labour of 

 applying the process in hand to these series will be greatly 

 abridged, and he has kindly allowed me to make use of 

 these. I will therefore apply the process to these four 

 stations. 



8. Let us begin by grouping the Paris Jyearly values 

 into series of 8. We thus obtain the following final 

 numbers (in centimetres) : — 



51-4, 47-5, 457, 487, 5i'i, 49'S, 46-S. 47'2, 

 the mean being 48'5. From this we obtain the following 

 series of differences : — 



+ 2 - 9 - vo - 2-8 + o'2 + 2 - 6 + 1 3 - To - 1*3. 

 In order to diminish the effect of accidental fluctua- 

 tions, let us equalise this series of differences by taking 

 the mean of each two. We thus obtain 



+ o-S+ vo - 1-9 - T3+ ''4 + i'9 ~ °'4 - '7- 

 If we now add these together, without respect of sign, 

 and divide by their number (8), we obtain 1*3 as the 

 mean departure from the mean of the whole, and bringing 

 this departure into a proportional shape by dividing it by 



the mean rainfall, we obtain —£- = 2'68 per cent. 

 4b'5 



9. These explanations will enable the reader at once to 

 perceive the principle of construction of the following 

 table : — 



Proportional rainfall inequality as exhibited by series of 



We ought to give the English, the Paris, and the Padua 

 observations a somewhat higher weight than those of 

 Milan, as the former embrace a longer period. This will 

 be done sufficiently well by giving the first three sets 

 weights of 3 each and the Milan set a weight of 2. If we 

 perform this operation, and then take the mean of these 

 stations, we obtain as under : — 



Proportional rainfall inequality J 

 8yrs. 9 yrs. 10 yrs. n yrs. 



exhibited by series of 



3 - oo 2'cg 1 "94 3^52 2 - Si 2-92 



Mean of 



the four 



stations 

 weighted 

 as above 



A maximum corresponding to nine years and a still 

 greater one corresponding to twelve years is thus exhi- 

 bited, each of these being recorded at three stations out 

 of four. 



The proportional numbers indicated are not large, but 

 it must be remembered that it is the mean difference for 

 all the years that is given, and that the maximum and 

 minimum rainfall will represent differences above and 



