TEST OF THE NEBULAR HYPOTHESIS 63 
and other contingencies, it will be sufficiently accurate for the 
purposes of this discussion to assume that the planets were 
formed in the centers of their respective rings, and that the 
Space appropriate to each planet reached half way to the 
neighboring planets. 
The more important consideration, however, in determining 
the rotatory momentum of the ancestral nebula is the distribution 
of its internal density. Our method has been to compute this 
on the basis of the recognized laws, using in particular the 
formula of Lane, and to compare results with the previous deter- 
minations of mathematicians and physicists." 
The distribution of density in such a nebulous sphere has 
been the subject of investigation by Lane, Ritter, G. W. Hill, 
George Darwin, Lord Kelvin, and others.2, The results reached 
by all are in substantial agreement, though somewhat different 
analytical methods were followed. In obtaining the final numer- 
ical results used in this paper, the distribution of density found 
by Darwin was adopted. The method of computation is given 
in Dr. Moulton’s paper in the Astrophysical Journal. 
When the solar nebula extended to the orbit of Neptune and 
embraced the matter of the whole system and had a rotation 
*The laborious work of making the computation was undertaken by Mr. C. F. 
Tolman, Jr., under the direction of Dr. Moulton, and preliminary results were 
obtained by him, but before these had been sufficiently verified he was called to a 
position whose immediate requirements prevented the completion of the desired veri- 
fication. For this reason, and for the obvious advantage of resting the present argu- 
ment as far as possible on the computations of an acknowledged authority, results 
reached by Darwin, which are applicable to a gaseous or meteoroidal nebula in con- 
vective equilibrium, have been adopted. 
*LANE: On the Theoretical Temperature of the Sun under the Hypothesis of a 
Gaseous Mass Maintaining its Volume by its Internal Heat, and Depending on the 
Laws of Gases as Known to Terrestrial Experiments, Am. Jour. Sci., Vol. XLIX, pp. 
56-74, 1870. 
RITTER: Untersuchen iiber die Hohe der Atmosphare und die Constitution 
gasformiges Weltkoper, Wiedemann’s Annalen (New Series), Vol. XVI, 1882, p-. 166. 
G. W. HiLi: Annals of Mathematics, Vol. IV, 1888. 
DARWIN: On the Mechanical Condition of a Swarm of Meteorites, and on the 
Theories of Cosmogony, Trans. Phil. Soc., 1888. 
KELVIN: On the Origin and Total Amount of the Sun’s Heat, Popular Lectures 
and Addresses, 1891. Constitution of Matter, pp. 370-429. 
