1877.] 



the Rainfall with the Sun-spot Period. 



251 



In the above calculation the first year of the cycle of eleven is 1813, so 

 that the average period of maximum sun-spots will be about the third or 

 fourth year of the cycle, and the period of minimum will be about the 

 tenth or eleventh of the cycle. This Table certainly seems to indicate a 

 period of maximum between the third and the seventh years, and of 

 minimum between the eighth and the second years. 



But to estimate the true weight of these results we must look a little 

 deeper. Now the only signification of the arithmetical mean of a series 

 of observed quantities is that it is a quantity above and below which there 

 is an equal amount of deviation in the aggregate of individual observations. 

 Further, conformity to a law of any sort in a series of observations in 

 relation to quantity is obviously to be tested by the extent of deviation of 

 the observed quantities from the results that such law requires. Conse- 

 quently, in the present case, the question whether or not the mean values 

 shown in Table I. can be accepted as showing a definite law of variation 

 from year to year in the cycle must be determined by examining the differ- 

 ences between those means and the individual observations on which they 

 are based. 



Treating the observations in this manner, the following results are 

 obtained : — 



Table II. 



Number of 



Years of cycle. 



cycie. 





1st. 



2nd. 



3rd. 



4th. 



5th. 



6th. 



7th. 



8th. 



9th. 



10th. 



11th. 





h. 



in. 

 - 4-0 



in. 

 -13-8 



in. 

 - 2-3 



in. 



- 9-8 



in. 

 + 13-2 



in. 

 +21-9 



in. 

 -16-6 



in. 

 +24-9 



in. 



+io-i 



in. 

 + 10-4 



in. 

 - 8-4 



is! . 



2. 



-154 



+ 6-8 



+ 2-4 



+37-5 



-12-5 



-174 



-20-5 



- 0-8 



-18-6 



-12-1 



4- 4-0 





3. 



- 7-6 



+30-7 



- 4-5 

 +31-8 



- 9-0 



- 3-5 



+ 14 



-li-i 



+ 2-7 

 -13-5 



+ 4-3 

 + 10-0 



+ 5-4 

 + 19-8 



- 8-6 



- 9-3 



+13-3 

 + 6-2 



4-16-2 

 -16-9 



4- 3-0 

 4-12-0 



1 s a | 



5. 



+ 3-8 



- 0-7 



- 3-2 



-23-3 



-13-4 



-16-1 



+ 1-7 



+ 2-1 



+ 4-6 



4- 2-2 



-10-6 



p 



,6. 



- 7-7 



-16-9 



+ 15-8 



+ 5-4 



+23-3 



- 2-5 



4-10-0 



- 8-0 



-15-5 







Mean differ- ~\ 

























ence, irre- I 

 spective of j 

 sign J 



11-5 



12-9 



6-0 



14-8 



13-1 



12-0 



12-3 



9-0 



11-4 



11-6 



7-6 



Mean of mean differences 11 -2 inches. 



Thus it appears that the mean difference of the individual observations 

 from the calculated means shown in the last line of Table I. differs but 

 little from the mean difference of the individual observations from the 

 arithmetical mean of the whole series. In other words, the supposed law 

 of variation obtained from the means of the six 11-year cycles hardly 



