Transcriber’s Notes: Underscores “_” before and after a word or phrase indicate _italics_ in the original text. Equal signs “=” before and after a word or phrase indicate =bold= in the original text. Small capitals have been converted to SOLID capitals. Typographical errors have been silently corrected. Vol. I. OCTOBER, 1892 No. 2. THE KANSAS UNIVERSITY QUARTERLY CONTENTS UNICURSAL CURVES BY METHOD OF INVERSION, _H. B. Newson_ FOREIGN SETTLEMENTS IN KANSAS, _W. H. Carruth_ THE GREAT SPIRIT SPRING MOUND, _R. H. S. Bailey_ ON PASCAL’S LIMAÇON AND THE CARDIOID, _H. C. Riggs_ DIALECT WORD-LIST, _W. H. Carruth_ PUBLISHED BY THE UNIVERSITY LAWRENCE, KANSAS _Price of this number, 50 cents_ Entered at the Post-office in Lawrence as Second-class matter. COMMITTEE OF PUBLICATION E. H. S. BAILEY F. W. BLACKMAR W. H. CARRUTH C. G. DUNLAP E. MILLER S. W. WILLISTON V. L. KELLOGG, MANAGING EDITOR JOURNAL PUBLISHING HOUSE LAWRENCE, KANSAS 1892 KANSAS UNIVERSITY QUARTERLY. VOL. I. OCTOBER, 1892. NO. 2. Unicursal Curves by Method of Inversion. BY HENRY BYRON NEWSON. This paper contains a summary of the work done during the last school year by my class in Modern Geometry. Since many of the results were suggested or entirely wrought out by class-room discussion, it becomes practically impossible to assign to each member of the class his separate portion. Many of the results were contributed by Messrs. M. E. Rice, A. L. Candy, H. C. Riggs, and Miss Annie L. MacKinnon. The reader who is not familiar with the method of Geometric Inversion should read Townsend’s Modern Geometry, chapters IX and XXIV; or a recent monograph entitled, “Das Princep der Reziproken Radien,” by C. Wolff, of Erlangen. When a conic is inverted from a point on the curve, the inverse curve is a nodal, circular cubic. This is shown analytically as follows: let the equation of the conic be written ax² + 2hxy + by² + 2gx + 2fy = 0; which shows that the origin is a point on the curve. Substituting for x y x and y ————————— and ———————— , x² + y² (x² + y²) we have as the equation of the inverse curve ax² + 2hxy + by² + 2(gx + fy)(x² + y²) = 0.