242 ON THE PERIODICITY OF THE AURORA BOREALIS. 



The constants A and B are computed by the method of least squares and found to be 

 50.31 and 3.73. This formula gives results which exhibit a rough agreement with tin- 

 relative number of solar spots observed between the years 1836 and 1839, but tin- 

 discrepancies between the conclusions of theory and observation, which are great in- 

 deed for the whole interval between 1850 and 1858, are enormous in the years 1834 

 and 1835. The period of Jupiter, which is 11.86 years, enters largely into the calcu- 

 lated disturbance, but this alone fails to explain satisfactorily the periodicity of the 

 solar spots, the duration of which is 11.11 years. It is intimated by Wolf that the 

 tropical revolution of Jupiter may possibly match the period of the solar spots ex- 

 actly, since the great oblateness of that planet must produce a large amount of 

 precession in the equinoxes. But he decides that the observations of the sun's spots 

 are better satisfied by his period of 11.11 years than they can be by Jupiter's period 

 of 11.86 years, orLamont's period of 1043 years; the first period being nearly the 

 mean of the two other periods. 1 



The term in the formula which comes next in importance to that of Jupiter is one 

 depending on the mass and distance of Venus from the sun. The period of this term 

 is 7.65 months; and it causes, as Wolf supposes, the subordinate swell in the annual 

 curve of solar spot frequency, the period of which is about .637 of a year. If the 

 solar spots are in any way associated with the aurora, this almost semi-annual period 

 may correspond to that portion of the second terms, in the formulas given on page 211 

 of this memoir, which cannot be explained by differences in the duration of daylight. 



De la Rue - has endeavored to obtain evidence of planetary influence on the be- 

 havior of the solar spots by measuring their area under different exposures. He finds 

 changes depending on the variable configuration of the heavens, Jupiter exercising a 

 great though not a predominating influence. The period of about twenty months 

 which he deduces from the observations, points to Venus as the most influential 

 planet, this period being not unlike the time of the synodical revolution of this 

 planet. 



The possible dependence of the spot-periods on the united influence of all the 

 planets has been discussed by Schmidt 3 with this result, — that the periods of max- 

 ima concur with the times when the centre of gravity of the solar system is in the 

 surface of the sun, and the periods of minima with the times when the centre of 



1 Vierteljahrsschrift der Naturforsch. Gesellsch. in Zurich, II. 353, IV. 73 and X. 161. 



2 Researches in Solar Physics, Second Series, p. 42, 3. 



3 Resultate aus eilf jahrrigen Beobacht. neber Sternschnuppen. 



