Summary --Equations for the motions in a galaxy which is controlled by gravitational forces and inertial effects are formulated. It is found that for the motions relative to the rotating system formulae analogous, and of similar form, to the geostrophie wind equations may be written. From these formulae and from the distribution of the relative gravitational potential in the disc of the galaxy, it is found that a spiral tendency in the mass distribution carries the implication of an inward flux of angular momentum by advective processes. This is to be compared with an outward flux through gravitational torques obtained in previous studies in which the writer participated.
1. Introduction --A large tract of Newtonian theory can be more compactly and conveniently discussed in terms of the gravitational potential % a concept introduced subsequent to the time of Newton. The fundamental equation relating ~ to the spacial distribution of mass is the familiar equation of Poisson, namely, (1) V2~ = 4rsGp
where G is the universal constant of gravitation and p is the density of mass in space.
It is well known that certain philosophical difficulties arise in an attempt to apply (1) to the entire universe as was pointed out notably by EINSTEIN (1917), and modern cosmological theory may be said to have had its beginning in this source. If the mass density ~ is taken over some finite region of space, one property- of equation (1) is that it alone does not possess the competence to specify the motion of a given interior mass point. The solution of (1), speaking mathematically, consists of two parts, namely, a complimentary function which is not uniquely fixed by the interior mass, and a particular integral which is so determined.
For the specification of the complimentary function one must apply as a boundary condition added information, let us say, concerning the value of the potential at an infinite distance from the given mass distribution if it is one that is isolated in space, as we shall for our present purpose now assume. Under these conditions the subject takes on a simple form owing to the fact that the complimentary function, since it is a solution of (]) with the right hand member zero (i.e., of Laplace's.
by VICTOn P. STARR(*)
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