1878. | 305 | Chase. 
tances of Uranus and Jupiter ; the ‘‘Extreme secondary radius ’’ is Uranus’s 
aphelion radius, or the semi-diameter of the ring of secondary condensa- 
tion ; the ‘‘ Nebular radius”’ not only represents the theoretical incipience 
of Mars’s nebular condensation, but it also corresponds, almost precisely, 
with the sum of the secular perihelia of Jupiter (4.886) and Saturn (8.784), 
in units of Earth’s semi-major-axis—the secular perihelion being the time 
of greatest orbital v7s viva; ‘‘ Moon’s major-axis’’ is also Earth’s ‘‘ Nebular 
radius ;’? the ‘‘ Terrestrial acceleration ’’ represents the theoretical in 
crease in the angular velocity of Earth’s rotation, since its rupture from 
the central nucleus, or the ratio of its day to its year ; ‘‘Jupiter’s semi-major- 
axis’’ is measured in units of Sun’s mean perihelion distance from the 
centre of gravity of Sun and Jupiter. 
The sum of the infinite series, to and including 3—®%, is 2, which repre- 
sents the ratio of o/s viva between undulatory velocity and the velocity of 
the particles of a medium constituted according to the Kinetic theory.* 
Alexander has shown the importance of that ratio in planeto-taxis,+ and I 
have shown that it represents ‘‘ centres of explosive oscillation,’’ or the 
centre of secondary oscillation between the primary centre of oscillation 
and the centre of gravity, in a homogeneous line of particles (3 — 2 of t 
= 3). Adding the next term of the series, we get 3, which represents the 
centre of linear oscillation. Neptune’s major-axis (60.06) is, within + of 
1 per cent., (8 — 3° + 3? — 3! = 60) times Earth’s mean radius vector. 
These harmonies embrace orbital radii of the largest five planets of the 
solar system, of the inner planets, and of the asteroidal belt, together with 
nebular-, satellite-, and planetary-radii, for the outer and the middle planets 
in the theoretically primitive central belt, or the belt of greatest condensa- 
tion. Can any interpretation be rightly put upon such a chain of har- 
monies, which does not recognize the fundamental laws of harmonic oscil- 
lation and harmonic design ? 
Neither of Mars’s moons is of sufficient magnitude to cause any great per- 
turbations. To this fact, perhaps, as much as to the proximity of the den- 
sity-centre, we may attribute the regularity of the Mavortian system. In 
the solar system, as we have seen, t the preponderating mass of Jupiter sets 
up a new order of differences in the harmonic denominators ; and we may 
find probable indications of similar influence in some of the satellite 
systems, and in the elementary spectra. 
In the satellite system of Uranus, if we take the semi-major-axis of the 
outer satellite as the common numerator (22.75), we find the following 
harmony : - 
Satellites. Distances. Denominators. Theoretical. 
Oberon, 22.75 1.006 1.000 
Titania, 17.01 1.337 1.348 =1+2a 
Umbriel, 10.37 2.194 2.199 =1+ 7a 
Ariel, 7.44 3.058 3.055 =1-+ 124 
Semi-diameter, 1.00 22.750 22.750 ==1 + 1274 
* Maxwell and Preston, Phil, Mag., June, 1877. 
+Smithsonian Contributions, 280. ® 
t Ante, xii, 4U3sqq. ; xiii, 237-9; ete. 
PROC. AMER. PHILOS. soc. xvir. 101. 2L. PRINTED MARCH 27, 1878. 
