Helmholtz and most, if not all, subsequent writers on vortex motions have, except in obtaining the fundamental equations, confined themselves to fluid of invariable density.

In the following paper are considered some simple systems of vortices in a compressible fluid. To show that such systems are of considerable importance it is sufficient to refer to the phenomena of cyclonic storms. It may be as well, however, to state that though the vortices are here treated as compressible, the circumstances are still so different from those found in nature that the results obtained could bear only a general resemblance at most to the phenomena of storms.