NOTE B. From the fundamental property of the Cissoid of Diocles we can obtain by inversion an interesting theorem concerning the parabola. In the figure of the Cissoid given in Salmon’s H. P. C. Art. 214, A M₁ = M R, whence A M₁ = A R - A M; or A R = A M + A M₁. Inverting from the cusp and representing the inverse points by the same letters, we have for the parabola 1 1 1 ——— = ——— + ————— . A R A M A M₁ This result is interpreted as follows:—draw the circle of curvature at the vertex of a parabola; this circle is tangent to the ordinate B D which is equal to the abscissa A D; draw a line through A cutting the circle in R, the ordinate B D in M, and the parabola in M₁; then 1 1 1 ——— = ——— + ————— . A R A M A M₁ Draw the circle with centre at D and radius A D; any chord of the parabola through the vertex is cut harmonically by the parabola, the circle, and the double ordinate through D. Footnotes: [1] See note A. [2] A few of the results of this section are due to the late Mr. H. B. Hall. [3] See note B. Foreign Settlements in Kansas. A CONTRIBUTION TO DIALECT STUDY IN THE STATE. Explanatory.—Some years ago when the subject of dialect study in Kansas, or rather of Kansas dialect, was mentioned, Mr. Noble Prentis, a gentleman who is warranted in speaking with authority on Kansas, was inclined to think that he settled the question in short order by declaring that there is no Kansas dialect. Probably the majority of intelligent citizens of the state would turn off the subject with the same reply. In the sense of a mode of speech common to the inhabitants of Kansas and peculiar to them, Mr. Prentis was indeed right. There is no vocabulary, at least no extensive vocabulary, by which the native of Kansas may be recognized in the American Babel. We have no distinctive pronunciation by which we may be known from the inhabitants of Nebraska or set apart from the citizens of Missouri. The verb fails to agree with its subject and the participle is deprived of its final ‘g’ with about equal frequency in Western Kansas and Eastern Colorado. But in the same sense it is true that there is no Kansas flora, no Kansas fauna; that is, there is no plant and there is no animal found quite generally in Kansas and found nowhere outside of Kansas. The remark that there is no such thing as a Kansas dialect rests upon a misapprehension of what is meant by the term. In just the same way that we speak of the flora and the fauna of Kansas we may speak of the dialect of Kansas. Yet to avoid popular misapprehension it may be better to speak of dialect in Kansas, rather than of Kansas dialect.