446 



NA TURE 



[March 8, 1900 



rises to a small maximum about 1873, and eventually 

 falls to a low minimum in 1888, from which it has since 

 been steadily proceeding to higher values, so that another 

 maximum may be expected in the near future. 



Now, to prove our assertion as to a connection be- 

 tween the periodic changes of solar activity and the 

 motion of our planet, we shall, in the first place, consider 

 the changes in the mean obliquity as observed at Green- 

 wich from Bradley's time up to 1896. If, besides the 

 gravitational effects produced by sun, moon and planets, 

 no other perturbing force were acting on the earth- 

 spheroid, the observed values of the mean obliquity 

 should be found to decrease uniformly with the time, 

 this " secular variation " being due to the perturbations 

 [produced by the planets. The measured arcs of the 



This method enables us to study the waves of long 

 period by themselves, independently of the shorter 

 cycle. 



Here, then, it will at once be seen that the observed 

 changes in the mean obliquity cannot be represented by 

 a linear function of the time, but that, besides the 

 secular term, they show three distinct relative maxima 

 and minima. Now the remarkable feature about these 

 turning points is that their positions agree almost 

 absolutely with those exhibited in the "great" sun-spot 

 period. The two high maxima about 1780 and 1840, as 

 well as the very low minimum in 181 5, nay even the less 

 pronounced oscillations indicated by the curve of solar 

 spots, are also most clearly recognisable in the curve-of 

 the obliquity represented in Fig. i. In view of so 



«x »» noo e IP IS 2* 30 36 12 u 5* eo 

 Fig. I. — Curve of obliquity. (From the Aslion. Nnchr. 3619.) 



7Jt »'> 90 SS 



obliquity would then 

 Leverrier's formula 



be very nearly represented by 



« = fia5o - o" -47594 (/ - 1850). 



Owing to the uncertainty of the values of the masses 

 adopted for some of the perturbing planets, the numerical 

 factor in this equation may have a somewhat different 



remarkable a coincidence, the observed changes in the 

 obliquity may be closely represented by the introduction 

 into Leverrier's formula of a term depending on the 

 great sun-spot period. If this term, after being evaluated 

 for all the epochs of observation, is subsequently sub- 

 tracted from the single values of 8e in Fig. i, the 

 followingf curve is obtained : 



Fig. 2. — Corrected curve of obliquity. (From the Astron. Kachr. 3619.) 



-value. But the differences between the observed arcs of 

 the obliquity and the values derived from Leverrier's 

 •equation ought in any case to be found to increase or 

 ■decrease uniformly with time. This, however, is far 

 from being the case, as may be readily seen from the 

 accompanying diagram, in which the abscissce are repre- 

 sented by the epochs of observation, and the ordinates 

 by the differences Observed Obliquity minus Leverrier. 

 The data from 1757 up to 18 12 are taken from Prof 

 Newcomb's treatise, "Elements of the Four Inner Planets, 

 &c., Washington, 1895." Since 1812 the data are de- 

 duced directly from the annual Greenwich observations. 

 In order to eliminate any possible influence of the 

 shorter sun-spot cycle, which shall be investigated 

 separately later on, these annual values are combined 

 into groups comprising twelve years of observation. 



NO. 1584. VOL. 61] 



Now, uniform increase or decrease with time implies 

 that the values of the obliquity should be grouped ap- 

 proximately along a straight line. While this was by no 

 means the case in Fig. i, it is perfectly true of Fig. 2 ; 

 and thus it is clear that, taking into account the additional 

 I perturbing force due to solar activity, the observed values 

 I of the mean obliquity are brought into entire agreement 

 with the deductions of planetary theory. 



The significance of the result just obtained is consider- 

 I ably enhanced by the remarkable fact that exactly the 

 ' same peculiarities appear in the variations of all the other 

 elements of our planet as in those of the obliquity. Not 

 one of the elements, as deduced from observation, can 

 be rigorously represented by a secular term alone ; they 

 all show in addition well-marked periodic fluctuations 

 I closely agreeing with those of the "great" spot period. 



