164 PROF. B. STEWART ON THE LONG-PERIOD 



of the column representing observations at 2 p.m. would 

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

 other hand, in the 2 6 -hourly series^ provided it were suffi- 

 ciently extensive^ we should perceive no such differences. 

 Thus, in the 24-hourly series the differences of the means 

 of the various vertical columns from the mean of the 

 whole would be much greater than in the 26-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, therefore, applied to the subject in 

 hand, might be expected to reveal the presence or absence 

 of inequalities 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 occurs 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 con- 

 sequence 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 inequa- 

 lities 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. 



