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The field is supposed to be independent of z but is periodic in x and y. m and n being integers, the field has neutral lines along the z axis for the coordinates: kx = (m + 1/2) pi and ly = (n + 1/2) pi , k and l being the wave numbers of the periodic structure. The force-free field considered here has been derived for further application to the theory of sunspots and solar flares. Consideration is given for the stability problem using a uniform gas in which the z free field is imbedded. The contribution to stability of an arbitrary perturbation in the neighborhood of the neutral lines is discussed. Compared to the case of cusped geometries, the fluid is not confined by the magnetic lines of force and, consequently, has no reason for being stabilized by the curvature of the lines of force. (B.O.G.)

One seeks the condition of spontaneous collapse of a layer of interstellar matter by the method of marginal stability. The radiation field is included in this treatment of the gas-dynamic properties of the interstellar material. The optical model used is that of Ambartsumian's, which neglects interlocking.

We examine here the problem of the gravitational instability of a medium in nonuniform rotation. We seek therefore to resolve a problem differing somewhat from that examined by Chandrasekhar and Fricke. We imagine a gaseous medium in rotation in a potential field, ɸ, and consider only the plane problem. In the unperturbed motion, the particles describe circular orbits in uniform motion. We examine the stability against perturbations.