Kirkwood.] 1^^ [April 2, 



fact that all of those dates given in Art. (1), except perhaps the last, har- 

 monise with the value which we have adopted for Schwabe's period of 

 variation. Thus, 



From 331, A.D. to 1860, we have 139 periods of 11.072+years each. 



The variability of the period will be hereafter considered. 



(5.) Wolffs Cycle of 56-57 Years. — The synodic revolution of Mercury 

 is 115^^87748, and 



llS.d 87748 X 177 = 20510.'i 31396 = 56-y 15324 = T^ . . (7) 



In this period the line of conjunction of Mercury and the earth 

 advances 56.15334 revolutions. Now, 



? = 24.d 82628 = 24a 19^ 49™ 50^ . . . . (8) 



826.15324 ^ ^ 



This value of the sun's period of rotation differs from that in (6) by only 

 29 seconds. Adopting it, therefore, we find that Mercury and the earth 

 will be in conjunction on the same heliographic meridian at regularly 

 recurring epochs of 56 years and 56 days. 



(c.) The 2dS-Day Period. — The mean interval between the consecutive 

 conjunctions of Venus and Jupiter is 336"993. The close agreement of 

 these periods, leaves little room to doubt that the latter is the true period 

 of spot variation. 



((Z.) The 2'7-Day Period. — This is at once satisfactorily accounted for 

 on the hypothesis prepared in Art (11). 



(e.) The 584r~Pap Period. — The identity of this period with that of the 

 synodic revolution of Venus has ali'eady been indicated by De La Eue, 

 Stewart and Lcewy. 



(15.) It would be easy to point out theoretically other periods of varia- 

 tion, which an exact discussion of observations would probably confirm. 

 It will be obvious, however, that the actual phenomena must be ex- 

 ceedingly complicated. The great eccentricity of Mercury's orbit; the 

 ever-varying configurations of the disturbing planets ; the probably 

 unequal susceptibility of different parts of the sun's surface to their 

 influence ; combined, perhaps, with other causes, but imperfectly under- 

 stood, must render the complete discussion of the phenomena both 

 operose and difficult. The subject, in short, presents a new and interest- 

 ing department of the theory of perturbations. 



(16.) A careful inspection of tables I. and II. will indicate that 

 Schwabe's cycle is liable to considerable variation, both in duration and 

 intensity. The epochs of greatest disturbance were 1837 and 1848, when 

 the number of spots was about 50 per cent, greater than in 1828 and 1860. 



