86 



On some recent Researches in Solar Physics. [Dec. .21, 



We, on the other hand, have, by an inspection of our curves (vide Phil. 

 Trans. 1870, p. 393), been induced to make the following remark on the 

 same question : — 



" We see that the second curve, which was 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 other two curves, and the same takes place for the 

 second or descending branch. On the other hand, the maximum of this 

 curve is not so high as that of either of the other two ; in fact the curve 

 has the appearance 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 conclusion, 

 viz. that ascent and descent are connected by a law, still they differ essen- 

 tially in this respect, that if A, B, C represent the three following consecu- 

 tive events, descent, ascent, descent, Professor Wolf's law refers to the 

 connexion between A and B, while our remark refers to B and C. We 

 consider two successive minima as the beginning and end of a single period, 

 while M. Wolf, at least in this particular research, places the minimum 

 within the period, and compares the descent from the preceding maximum 

 with the ascent to the next one. 



9. We have considered the connexion thus indicated of sufficient im- 

 portance to apply to it the following test. If, using the previous notation, 

 a definite relation exists between A and B, the ratio of the times which 

 the events occupy in every epoch ought to be approximately constant ; 

 similarly with respect to B and C ; and this ratio should not be influenced 

 by the absolute duration of the two successive events. It is clear that the 

 greater uniformity of these ratios will be a test for their interdependence. 

 The following is the result of the comparison : — 



a. Professor Wolf's law : comparison of A and B. 



Duration of Duration of 



Periods. descent (A). Periods. ascent (B). 



I. 1829-5 to 1833-8 4-3 years 1833 8 to 1837'2 3*4 years. 



II. 1837*2 to 1844-0 6*8 „ 1844-0 to 1846 6 2-6 „ 



III. 1846-6 to 1856-2 9 6 „ 1856 2 to 1860 2 4-0 „ 



A 



Ratl0 J}* Difference from mean. 



1 1-265] -0-728. 



II 2-615 \ Mean 2*093 +0*522. 



Ill 2-400 J +0 307. 



These differences from the mean are so considerable, that in the present 

 state of the inquiry a connexion between any descent and the immediately 

 succeeding ascent appears highly improbable. A very new and apparently 

 important relation seems, however, to result from a similar comparison of 

 any ascent and the immediately succeeding descent, or between B and C. 



