187'/.] 



the Rainfall with the Sun-spot Period. 



261 



The last cycle of tlie six is not complete, and the value of — is 



n 



therefore doubtful. As the observations only extend to six cycles, in 

 order to test the process I have continued the calculation to twelve, 

 eighteen, and twenty-four cycles, by combining with the real observations 

 the three series formed at hazard by a chance redistribution of the original 

 observations. This of course gives no support to any conclusions as to 

 the existence of periodicity in the case of Madras ; but it shows how, in 

 the absence of periodicity, the theory is completely verified. 



The Bombay, Calcutta, and Greenwich observations, similarly treated, 

 exhibit, similar results. 



In strong contradistinction to the above results are those that follow 

 on treating in a similar manner the barometric observations given in 

 Tables VIII. and IX. ; while these same observations, when their true 

 periodicity is destroyed, as in Tables X. and XI., show results quite 

 similar to those seen in Table XII. 



The following Table shows these results, both with the periodicity as 

 it really exists and after it has been destro}^ed : — 



Table XIII. 





Eeal periodicity. 



Periodicity destroyed. 



Number of 











cycles. 



From observation, 



Calculated, 



From observation,! 



Calculated, 



S 



E 



S 



E 





n 





n 



V m 





374 





29-4 













31-0 



252 



17-8 



262 



3 , 



294 



19 



14-7 



190 



4 „ 



29-5 



16-2 



10-7 



16-8 





29-5 



130 



5(5 



14-6 



6 „ 







1-9 



13-0 









The fact that the figures in the last column but one are so much less 



E 



than the calculated values of -7= evidently arises from the want of con- 



v m 



formity of the numerical values of the quantities which are found in 

 Table VIII. with, the assumed law of the probable numerical distribution 



E 



of errors on which the theoretical value -7= rests ; but the mutual de- 



V m 



struction of the non-periodical elements earlier than this theory would 

 have required does not affect the general reasoning. 



