Chase. ] 306 (Jan. 18, 
In the Saturnian system there is a slight uncertainty in the satellite ele- 
ments, except in the case of Titan, whose orbit was well determined by 
Bessel. It will be seen that Titan’s great mass introduces a secondary 
harmony. The following harmonic denominators are based upon relative 
mean distances which would represent the orbital times, as furnished by 
Professor Hall : 
Satellites. Times. Denominators, Theoretical. 
Japetus, 79.38292d 1.000 1.000 
Hyperion, 21.8113 2,402 22001 == Msg 
Titan, 15.9454 2.914 2.920 1+0 
Rhea, 4.5175 6.756 6.760 1+ 3d 
Dione, 2.7369 9.436 9.384 14+ 64 
Tethys, 1.8878 12.087 12 = One: 
Enceladus, 1.3702 14.966 14.974 14104 
Mimas. 9425 19.206 19.166 1+ 1384 
Semi-diameter, 64.359 64.360 1+ 33d 
It is well to notice that } (1.920) is very nearly the square of a@ (1.397). 
In the column of times, Japetus, divided by Titan, is nearly 5 ; Hyperion, 
by Rhea, 5; Dione, by Enceladus, 2; Tethys, by Mimas, 2; Titan, by 
Rhea, $; Rhea, by Dione, 3 ; Hyperion, by Titan, +; Hyperion, by Dione, 
8; Hyperion, by Mimas, 4°; Titan, by Mimas, 17. 
The satellite system of Jupiter, our Sun’s ‘‘companion star,’’ exhibits 
harmonies of distance, time and mass. The mean distance of the outer 
satellite, Callisto, is 3° semi-diameters of its primary (26.9984). Using this 
as a common numerator, we find that the other satellites are phyllotacti- 
cally, as well as harmonically, arranged : 
Satellites. Distances. Denominators. Theoretical. 
Callisto, 26.9984 1.000 
Ganymede, 15.3502 1.759 ioe 
Europa, 9.6235 2.807 2.769 8 a. 
To, 6.0485 4.464 4.500 13. a. 
Semi-diameter, 1.0000 26.998 26.998 78 a. 
The harmonies of time and mass are as follows : 
Satellites. Limes. Theoretical. Mass. Theoretical. 
Callisto, 16.6894 16.684 — 28 ¢ 4266 4408 = 4 m. 
Ganymede, 7.155 7.150 12 ¢ 8850 8806 1m 
Europa, 3.051 3.575 6 ¢ 2324 2202 im. 
To, 1.769 1.788 3 ¢ 1733 1761 im. 
The interesting and valuable communications of Professor Alexander, to 
the last semi-annual meeting of the National Academy, exhibit various har- 
monies in the several satellite systems, some of which are closer than my 
own, others are the same, and others are not so close. He recognizes the 
important influences of linear centres (3), centres of linear oscillation (3, 4), 
n 
centres of atmospheric dissociation (7), mean or extreme apsidal 
distances, mean eccentricities, and a resisting medium, to all of which I 
