Abstract :
The first circle diagrams of the character herein described were published almost simultaneously by Thielemans in Europe and Evans and Sels in this country. The diagram of Evans and Sels is not nearly as complete as Thieleman´s, but is more easily constructed because of the mathematical methods employed to determine the circle centers and radii. The present paper is an elaboration of the work done by these two investigators. It coordinates the graphical and mathematical methods of construction and extends their application. The principal contributions of this article ore incorporated in Tables I and II and in the paragraphs concerning geometrical checks that may be applied to the circle diagram. Tables I and II include formulas for determining the coefficients of a large number of circular loci which have not been heretofore constructed by mathematical methods. Other formulas given in Tables I and II are to be found elsewhere, buit generally in a somewhat more complicated, although equivalent, form. The graphical checks that result from the geometrical properties of the circle diagram, as first investigated by Thielemans, have not heretofore been applied to diagrams derived by mathematical computations. By establishing the identity of the Thielemans and Evans and Sels diagrams, it has been possible to utilize the numerous geometrical properties of the diagram that Thielemans has worked out, as well as to make use of other graphical properties.
