Spiral orbits and the law of recession

Abstract

From certain considerations of isotropy, one of us has obtained, in a paper communicated elsewhere for publication, the line-element where μ=log(A+Bt½t²) and ν=2logr, A and B being arbitrary constants of integration. If A=B=0, the geodesies give a straight line motion according to the law where c=-2 or ±2. The two-dimensional motion is given by so that which gives an equiangular spiral. If the spiral structure of the nebulæ is due to particles describing equiangular spirals as given by (4), and if the law of recession of the nebulæ themselves is of the form (2), then the line-element (1) seems to be of great interest in the relativistic theory of world-structure.