1871.] 



on some recent Researches in Solar Physics. 



85 



visible hemisphere, while the conclusions of M. Wolf are founded on cer- 

 tain ** relative numbers," which give the amount of observed spots on an 

 arbitrary scale, chiefly designed to make observations made at different 

 times and by various observers comparable with each other. This will 

 obviously, in addition to the sources of error to which our own method is 

 liable, introduce an amount of uncertainty arising from errors of estima- 

 tion and the possibility of using for a whole series an erroneous factor of 

 reduction. Nevertheless we shall find a very close agreement in various 

 important results ; and this seems a sufficient proof of the great value and 

 reliability of M. Wolfs " relative numbers," especially for times previous 

 to the commencement of regular sun observations. 



6. The following is a comparison of the data of periodic epochs, as fixed 

 by ourselves and M. Wolf : — 



i. n. in. iv. 



Minima f De La Rae, Stewart, 1 g fi g fi . 3 im . l2 



epocns. [ RudolfWolf _ m 1833 . 8 1844 . 1856 . 2 i 8 67-2 



i. n. m. 



Maxima f De La Rue, Stewart, and Loewy 1836*98 1847*87 1859*69 

 epochs. \ Rudolf Wolf . 1837'2 1846*6 1860*2 



It will be seen from this comparison that only one appreciable difference 

 occurs, viz. in the maximum of 1847, which M. Wolf fixes nearly one and 

 a quarter years before our date. 



The mean length of a period is found by us to be 11*07 years, which 

 agrees very well with M. Wolf's value, viz. 11-1 years. 



7. We found the following times for the duration of increase of spots 

 during the three periods, and for the corresponding decrease, or for ascent 

 and descent of the graphic curve, beginning with the minimum of 1833 : — 



Time of ascent. Time of descent. 



T 3*06 years. 6*77 years. 



II 412 „ 8*44 „ 



III 3*37 „ 7*43 „ 



Mean.... 3*52 „ 7*55 „ 



Professor Wolf gives 3*7 years and 7*4 years for the ascent and descent 

 respectively ; and considering that he derived these numbers only from 

 an investigation of a portion of each period, the agreement is indeed sur- 

 prising, and would by itself suggest that the times of ascent and descent 

 are connected by a definite law. 



8. M. Wolf has expressed in general terms the following law with refer- 

 ence to this relation of increase and decrease of spots : — 



" The character of a single period may essentially differ from the mean 



behaviour ; but on the whole it appears that a { ret * rded 1 descent cor- 



1 accelerated J 



responds to a { retarded 1 ascent." 

 I accelerated J 



