It has apparently been taken for granted by some astronomers
^{(2)}
that from observations on the internal rotations good values for the
masses *M*_{N} of nebulae could be derived. Values of the
order of *M*_{N} = 10^{9}
*M*_{} up to
*M*_{N} = 4 × 10^{10}
*M*_{} were
obtained in this way, ^{(2)}
where *M*_{} =
2 × 10^{33} gr is the mass of the sun. A closer
scrutiny of the behavior of suitably chosen mechanical models of
stellar systems, unfortunately, soon reveals the fact that the masses
of such systems, for a given distribution of average angular velocities
throughout the system, are highly indeterminate, and vice versa.
This conclusion may, for instance, be derived from the consideration
of two limiting models of a nebula as a mechanical system.

**A. Model of a nebula whose "internal viscosity" is
negligible**

This model consists of a heavy and small nucleus of mass
*M*_{0}
around which a given number, *n*, of stars of average mass
*M*_{8} << *M*_{0}/*n* describe
planetary orbits. The mutual gravitational interactions
between these outlying stars are negligible, and the system
may therefore be said to have an internal "viscosity" equal to zero.
It is obvious that under these circumstances we may build up models
that satisfy almost any specifications in regard to total mass, total
luminosity, and internal distribution of luminosity as well as
distribution of the average angular velocities. We may, for instance,
distribute our *n* stars over the six-dimensional manifold of all
possible planetary orbits (including the epochs or phases) in such fashion
that the average angular velocity of the resulting system
*S*_{0} is zero
in every point. Since all these orbits are essentially non-interacting,
we may reverse the sense of rotation (direction of stellar motion)
in an arbitrary number of these orbits. In this way a system *S* of
specified distribution of average angular velocities may be constructed
whose remaining characteristics, such as the mass, the luminosity,
and the external shape, are identical with those of
*S*_{0}. Thus, the
observed angular velocities in themselves give no clue regarding the
mass of the system.

^{2} E. Hubble,
*The Realm of Nebulae* (New Haven: Yale University Press, 1936),
p. 179; also *Ap. J.*, **69**, 150, 1929.
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