516 



REPORT — 1902. 



the time of minimum X = 0-01, and n is equal to 2,000,000, showing the large 

 number of events required to prove an effect v^hich is small. If the effect is 5 per 

 cent, the number of events required to establish it is 80,000. 



To further illustrate these results, I take, as a second example, a suggested con- 

 nection between the occurrence of thunderstorms and the relative position of sun 

 and moon. Among the various statistical investigations which have been made on 

 this point, that of Mr. McDowall lends itself most easily to treatment by the theory 

 of probability. One hundred and eighty-two thunderstorms observed at Greenwich 

 during a period of fourteen years have been plotted by Mr. McDowall as distri- 

 buted through the different phases of the moon, and seem to show a striking 

 connection. I liave calculated the principal Fourier coefficient from the data 

 supplied, and find that it indicates a lunar periodicity giving for the ratio of the 

 number of thunderstorms near new moon to that near full moon the fraction 8-17 

 to 4-83. 



This apparently indicates a very strong effect, but the inequality is only twice 

 as great as that which we should expect if thunderstorms were distributed at random 

 over the month, and the probability of a true connection is only about twenty to 

 one. No decisive conclusions can be founded on this, the number of thunderstorms 

 taken into account being far too small. We might dismiss as equally inconclusive 

 most of the other researches published on the subject were it not for a remarkable 

 agreement among them, that a larger number of storms occur near new moon than 

 near full moon. 



I have put together in the following table the results of all investigations that 

 are known to me. Following the example of Koeppen, I have placed in parallel 

 columns the number of thunderstorms which have occurred during the fortnight, 

 including new moon, and the first quarter and the fortnight, including the other 

 two phases. 



It will be seen that out of fourteen comparisons thirteen show higher numbers 

 in the first column, there being also, except in two cases, a general agreement on 

 the magnitude of the effect. Two of the stations given in the table, Gottingen and 

 Gotha, are perhaps geographically too near together to be treated as independent 

 stations, and we may therefore say that there are thirteen cases of agreement, 

 against which there is only one published investigation (Schiaparelli) in which the 

 maximum eflect is near full moon. 



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