EEACTION OF PLANETS UPON SUN PUISEUX. 



165 



months between the periods brings them from complete coincidence 

 to an absolute discordance. What now remains of our hoped-for 

 proof if the nearest approach of the planet must sometimes condition 

 an increase of spots, sometimes their disappearance ? 



We may suppose that Jupiter's action, though preponderant, is 

 modified by a somewhat slower disturbing force which increases the 

 interval between successive maxima. But the statistics of the num- 

 ber and extent of the spots, analyzed with the view of finding such 

 a force, assigns to it such a long period that we have no clue as to 

 its origin. A priori the most probable disturbing body would seem 

 to be Saturn. It must act in the same sense as Jupiter, although to 

 less extent. The spot maxima or minima should be particularly pro- 

 nounced when the two planets are in conj miction with the sun — that 

 is, every 20 years. Here again the evidence is negative. 



We get an even less favorable answer from the rest of the planets. 

 Either their, revolution periods are too short to render an account 

 of an 11-year fluctuation or their distances too great for their action 

 to be sensible compared with that of Jupiter. 



THE PLANETS AS A DISTURBING ELEMENT IN THE SOLAR CYCLE. 



No planet, then, or combination of planets seems to be the princi- 

 pal cause of the solar cycle. We may, however, suppose that this 

 or that planet may for a brief time trouble the cycle by rendering 

 the distribution of spots irregular in longitude. 



The sun rotates with reference to the fixed stars once in 25 days. 

 The planets rcA^olve about it in the same direction, but more slowly. 

 Therefore, to an observer on the sun, the successive passages of a 

 planet over his meridian occur in periods somewhat longer than 25 

 days, tending to approach this (sideral revolution) as the planet's 

 distance increases. This is called the synodical rotation. That cor- 

 responding to the transit of the earth is 27.35 days. 



Considering now the extreme mobility of the solar surface, we will 

 see whether each planet does not produce a tidal wave which passes 

 over the sun's surface with the corresponding sj^nodical rotation 

 period and capable of producing visible disturbances. 



According to the elemental^ law of Newton, the relative impor- 

 tance of the tidal waves for the various planets is given by what we 

 may call the deforming factor, the product of the mass by the inverse 

 cube of the distance. If we make the value of this factor unity for 

 the earth, the mean values for the planets are as follows: 



Mercui-y 1. 04 



Venus 2. 09 



Earth 1.00 



Mars . 03 



Jupiter 2. 20 



Saturn .106 



Uranus .019 



Neptune . 001 



