On a Pulsating Cylindrical Vortex

This text presents an English translation of the significant paper [5] on vortex dynamics published by outstanding Russian scientist S.A. Chaplygin (1869-1942), which seem to have escaped the attention of later investigators in this field. Chaplygin's solution includes that of an elliptical patch of uniform vorticity in an exterior field of pure shear. Although it was published more than a century ago, in our opinion it is still interesting and valuable.