Chase.] *• ^ [Oct. 3. 



series are in harmonic progression, and that the controlling influence of 

 Jupiter over the progression is strikingly marked. A closer examination 

 shows that the harmonic series which begins with Neptune's linear centre 

 of oscillation is interrupted by the great masses of Jupiter and Saturn, 

 and that the one which begins at Jupiter's mean perihelion is disturbed 

 by the masses of Earth and Venus. The value of v is very nearly an 

 arithmetical mean between Venus's mean distance and her mean peri- 

 helion distance. The radius of Jupiter's mean linear centre of oscilla- 

 tion (| of 5.2028 = 3.4685) is nearly equivalent to \ of Earth's mean 

 radius vector, or to a radius vector (3 513) at the extremity of which, if 

 the planetary masses were aggregated, the centre of gravity of the solar 

 system would be at the source of the Sun's radiant undulation. From 

 these three units we may derive the following harmonic series : 



Venus's mean perihelion = .698 

 Mercury's mean distance = .387 

 Radius of solar disturbance = .267 

 Vulcan ? = .209 



The value above given for Vulcan is the one which satisfies Kirkwood's 

 estimated period for that supposed planet. If the actual values of 

 Venus's mean perihelion and Mercury's mean distance be taken for two 

 of the harmonic terms, and Jupiter's mean distance for the fundamental 

 unit, we shall have the following harmonic series : 

 1 -s- 7.1343 = Venus's mean perihelion distance. 

 1 -f- 12.8604 = Mercury's " distance. ' 

 1 -v- 18.5865 = .2678 X Earth's mean distance. 

 1 -=- 24.3126 = .2048 X 



There is, therefore, an apparent break in the harmonic progression, at 

 a distance between .267 and .270 of the Earth's mean distance from the 

 Sun, and within those limits we may reasonably look for the source 

 of the peculiar sun-spot disturbances, which were pointed out by Messrs. 

 De La Rue, Stewart and Loewy, in the communication above referred to. 



The closeness of the approximations in my circular and harmonic 

 series is shown in the following table. I take as the basis of my calcu- 

 lations, Bessel's valuation of Jupiter's mass (1 ~ 1047. 87D), and Stock- 

 well's estimate of Jupiter's mean eccentricity (.0431601). Sun's radius 

 is taken as the unit. The error of the theoretical value is found by di- 

 viding the difference between the theoretical (T) and observed (O) values 

 by the observed value. 



Circular Centrifugal and Harmonic Centripetal Series. 



T. O. Error. 



a .680 .680 



[i 2,136 2.132 + .0020 



y 66.224 68.483 — .0330 



