E 
72a 
2 al coe 
G. Hinrichs on Planetology. 135 
Now, by 8 ian a of the particles, the nebula is 
continually dense, or r is continually decreasing j 
hence, by ‘8, the iokstaied force of any particle in the nebula 
continually inereasing. 
But the force of gravity at the surface is likewise constantly 
nresing for we may without materially erring conceive the 
ss below the particle to remain constant, but then gravity is 
tateiecly as the neg = the radius, or rapidly increasing with 
the progress of condensa 
But these two forces ae ne the figure of the Nebula. However 
irregular the figure may be at first, we see that the moulding 
orces, by constantly i pS keer! will at length shape the nebula 
accordingly. From Plateau’s Experiments (see above, § 6, re- 
sult 1, 2) we know this bane to he a flat ellipsoid. Laplace? 
has demonstrated that but one she oblate ellipsoid of revolution 
will be produced by these forces, 7. 
224 m (x? + 92) = (9) 
‘the plane a, y, cointiding with the ee ‘gibic being the 
equator, z the axis of rotation = 2a, and 
ee ‘a Lt ee 
= ve 4=1t76, sind=e (10) 
‘ seal ay eccentricity of the meridian; hence the equatorial 
semi-a 
Ot N Iie ee (UD 
Assuming, for a moment, the nebula to be homogeneous, we 
can determine the eccentricity by the density 6, and the angular 
velocity » (i.e. by (6) proportional to the square root be 
cen oe force g at a unit of distance). Laplace found, if the 
f the whole nebula be M, and its moment of inertia E, 
B= ppxdas(1ia)fg= Vl aM; . (12) 
M=4¢20a S+¥) = 429 sas ; . (18) 
q = dof rs oto Sir eee 4 ee 
are (tg = 4) = yemeeenet, ji . (18) 
Which last equation he shows to have but one single positive real 
Toot, so that a # e has bas ar value, if g, the centrifugal force, 
and % the den are giv 
Bat the atte i is serainly not constant throughout the whole 
* Mécanique Céleste, Liv. iii, chap. III, § 21. 
