84 Messrs. Warren De La Rue, Stewart, and Loewy [Dec. 21, 



and presuming that the behaviour is approximately the same throughout 

 the whole period of 11*1 years as during the five years investigated, we 

 have the proportion 



x : IM - 1 s 2, 

 whence x = 3*7, 



or the average duration of an ascent is 3*7 years, that of a descent 7*4 

 years. 



(3) The character of a single period may essentially differ from the 



mean : but on the whole it appears that a ' , \ descent cor- 



{ accelerated J 



responds to a \ ret ^ r( ^ e ^ \ ascent. Thus the minimum of 1844*0 be- 

 i accelerated J 



haved very normally, but that of 1856*2, and still more that of 1823*2, 

 shown in the above diagram, presents a retarded ascent and descent ; on 

 the other hand, in the minimum of 1833*8, and still more in that of 

 1867*2, also shown in the diagram, both ascent and descent are accelerated. 



4. Finally, Professor Wolf arranged in the manner shown in the follow- 

 ing Table the successive minima and maxima, in order to arrive at some 

 generalization which might enable him to foretell the general character and 

 length of a future period. Taking the absolute differences in time of every 

 two successive maxima, and the mean differences of every two alternating 

 minima, he shows that the greatest acceleration of both maximum and mi- 

 nimum happens together. This result strengthens our own conclusions, 

 to be immediately stated, by new evidence, as it is derived from observa- 

 tions antecedent to the time over which our researches extend. 





Differences of 







Differences 



Minima. 



alternating 

 Minima. 



Means. 



Maxima. 



of successive 

 Maxima. 



1810-5 







1816*8 





1823-2 



23-3 



11-65 



1829*5 



12-7 



1833-8 



20-8 



10-4 



1837*2 



7-7 



1844-0 



22*4 



11-2 



1846-6 



11-4 



1856-2 



23*2 



11*6 



1860-2 



11-6 



1867-2 











From this Professor Wolf predicts for the present period a very accele- 

 rated maximum — a prediction which seems likely to be fulfilled. 



5. Comparing, now, M. Wolf's results with our own, it must not be 

 overlooked, in judging of the agreement or discrepancy of these two inde- 

 pendently obtained sets, that our facts have been derived from the actual 

 measurement and subsequent calculation of the spotted area from day to 

 day since 1833 recorded by Schwabe, Carrington, and the Kew solar 

 photograms, which measurements are expressed as millionths of the sun's 



