1. The following investigations deal with a Kármán street of vortices, or unsymmetrical double row, in a channel of finite width. A discussion on the symmetrical double row has also been incorporated. For the sake of convenience the work has been divided into two distinct parts—(1) Systems of Line Vortices in a Channel of Finite Breadth, and (II) The Kármán Drag Formula for a Channel of Finite Breadth. Part I has itself been divided into two sections headed Problem I and Problem II, and these sections deal with the stream lines and stability of the unsymmetrical and symmetrical double row respectively. Part II discusses Problem I from the point of view of hydrodynamics and contains a section dealing with the hydrodynamical significance of the stability investigations. Summaries of the investigations have been kept distinct and can be found in paragraphs (1.5) and (1.3) of Part I and Part II respectively.