Jan. 4, 1872] 



NA rURE 



193 



the mean differences of every two alternating minima, he shows 

 that the greatest acceleration of both maximum and minimum 

 happens together. This result strengthens our own conclusions, 

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

 observations antecedent to the time over which our researches 

 extend. 



Differences of 



Uiffe 



of 



Ma 



1823-2 



i 

 1844-01 



1856-2 



U-6S 



i8i6-8 

 1829-5 

 18372 

 1S46-6' 

 1860-2 



12-7 



77 

 11-4 

 u-6 



From this Prof. Wolf predicts for the present period a very 

 accelerated maximum — a prediction which seems likely to be 

 fulfilled. 



Comparing now M. Wolfs results with our own, it must 

 not be overlooked, in judging of the agreement or discrepancy of 

 these two independently 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 visible 

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

 certain "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 estimation, and the possibility 

 of using for a whole series an erroneous factor of reduction. 

 Nevertheless we shall find a very close agreement in various im- 



portant results, and this seems a sufficient proof of the great \alue 

 and reliability of M. Wolf 's " relative numbers," especially for 

 times previous to the commencement of regular sun observations. 



The fullov/ing is a comparison of the data of periodic epochs, 

 as fixed by ourselves and M. Wolf : — 



Minima epoctis. I. H. HI- I'^'- 



De La Rue, Stewart, \ 5833-02 1843-75 1856-31 1867-12 



and Loewy ) 



Rudolf Wolf 18338 1844-0 1856-2 1867-2 



Maxima epochs. I. 11. lit. 



""'andL^o^ewy^''"."'' | '^36-98 1847-87 1859-69 

 Rudolf Wolf 1837-2 1846-6 i86o-2 



It will be seen from this comparison that only one appreciable 

 difference occurs, viz., in the maximum of 1S47, 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 1 1 07 years, 

 which agrees very well with M. Wolf's value, viz., ii-i years. 



We found the following times for the duration of increase of 

 spots during the three periwls, and for the corresponding decrease, 

 or for ascent and descent of the graphic curve, beginning with 

 the minimum of 1833 -, — 



Time of as-ent. Time of descent. 



I. 3-06 years. 677 years. 



II. 4-12 ,, 844 ,, 



III. 3-37 „ 7-43 .. 



Mean 3-52 



7-55 



Prof 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 surprising, and would by itself suggest 

 that the times of ascent and descent are connected by a definite 

 law. 



M. Wolf has expressed in general terms the following law 

 ■with reference 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 



\ retarded ) , . j » ( retarded ) . ,, 



i 1 . J J descent corresponds to a , , ,\ ascent. 



( accelerated \ ' ( accelerated ) 



We, on the other hand, have, by an inspection of our curves 

 {z'idc Phil. Trans. 1870, p. 393), been induced to make the fol- 

 lowing remark on the same question : — 



" We see that the second curve, which was no longer in period 

 as a whole than either of the other two, manifests this excess in 

 each of its branches, that is to say, its left or ascending branch is 

 larger as a whole than the same branch of the two other curves, 

 and the same takes place for the second or descending branch. 

 On the otlier hand, the maximum of this curve is not so high as 

 that of either of the other two — in fact, tlie curve has the appear- 

 ance as if it were pressed down from above and pressed out 

 laterally so as to lose in elevation what it gains in time." 



Although both statements appear to lead up to the same conclu- 

 sion — viz., that ascent and descent are connected by law— still 

 they differ essentially in this respect, that if A, B, C represent 

 the three following consecutive events, descent, ascent, descent, 



