¢ 
Chase. } 302 (Jan. 18, 
Kirchhoft’s (Table [X) differ by less than a unit. The groups may be con- 
nected by the equations, 2l1a=0,;10b=9c;6b=—74d. 
The foregoing investigations were undertaken in consequence of a sug- 
gestion by Professor Henry Draper, that I should test my theory of har- 
monic undulatory influence by an examination of spectral lines. Professor 
Asaph Hall led me to the discovery of further corroborative tests, by the 
query, ‘‘ Will the inner moon of Mars fall into harmony, or will it make a 
discord ?’’ * 
If we start from a point near the theoretical beginning of nebular con- 
densation for the outer satellite,+ and take 2 x 3 — 1 harmonic divisors, of 
the form div.n +1—3 div.n — div.1 =div.n + 32—1, we find the follow- 
ing accordances : 
Numerator. Divisors. Quotients. Observed, 
13.7 Cia 13.700 13.692 = Nebular radius. 
d, = 3d,—d;= 2 6.850 6.846 = Deimus. t 
d, = 3d,—d,= 5 2.740 2.730 = Phobus.t 
d, = 3d,—d,=14 979 1.000 = ¢ semi-diam. 
d, = 3da,—d,= 41 884 .d33 = GC. of rad. ose. 
In a letter to the editors of the American Journal of Science and Arts 
(Oct., 1877, p. 327), Professor Kirkwood calls attention to the rapid motion 
of the inner satellite, and asks: ‘‘ How is this remarkable fact to be recon- 
ciled with the cosmogony of Laplace?’’ He suggests a partial explanation, 
based upon the motions of Saturn’s ring, and concludes with the remark : 
“Unless some such explanation as this can be given, the short period of the 
inner satellite will doubtless be regarded as a conclusive argument against 
the nebular hypothesis.’’ 
This is undoubtedly true, if we accept the nebular hypothesis in the form 
in which it is popularly taught, and in which Laplace is commonly sup- 
posed to have held it. But there are probably very few among the students 
who have given the subject much careful attention, who have supposed 
that all the planet-building has taken place at the ‘‘ limit of possible atmos- 
phere,’’ or the point of equal centripetal and centrifugal force. It may 
well be doubted whether the illustrious French Astromomer ever held such 
an opinion, and it is certain that Sir William Herschel never did, for he 
speculated on the ‘‘gradual subsidence and condensation’’ of nebulous 
matter ‘‘by the effect of its own gravity, into more or less regular spherical 
or spheroidal forms, denser (as they must in that case be) towards the 
centre.’’ § 
As necessary consequences of such subsidence, there would be an accelera- 
tion of velocity in all the nebular particles, the acceleration being more 
rapid in the nucleus, than near the outer surface of the nebula. Many in- 
*See Journal of the Franklin Institute, Noy., 1877. 
+ Phil. Mag. Oct., 1877, p. 292. 
{These are the names proposed for the satellites by their discoverer, Prof. 
Asaph Hall. 
? Herschel’s “Outlines of Astronomy,” 2 871. 
