Produced by Chris Curnow, Carla Foust, Lindy Walsh and the Online Distributed Proofreading Team at https://www.pgdp.net. Music transcribed by Linda Cantoni. Transcriber's note Minor punctuation errors have been changed without notice. Printer errors have been changed and are listed at the end. All other inconsistencies are as in the original. In this version the square root symbol is indicated by [** sqrt], the superscript by ^, and the therefore symbol by [** therefore]. A TANGLED TALE [Decoration] [Illustration: "AT A PACE OF SIX MILES IN THE HOUR." _Frontispiece._] A TANGLED TALE BY LEWIS CARROLL _WITH SIX ILLUSTRATIONS_ BY ARTHUR B. FROST Hoc meum tale quale est accipe. _SECOND THOUSAND._ London MACMILLAN AND CO. 1885 [_All Rights Reserved_] RICHARD CLAY & SONS, BREAD STREET HILL, LONDON, E.C. _And Bungay, Suffolk_. To My Pupil. Beloved pupil! Tamed by thee, Addish-, Subtrac-, Multiplica-tion, Division, Fractions, Rule of Three, Attest thy deft manipulation! Then onward! Let the voice of Fame From Age to Age repeat thy story, Till thou hast won thyself a name Exceeding even Euclid's glory! PREFACE. This Tale originally appeared as a serial in _The Monthly Packet_, beginning in April, 1880. The writer's intention was to embody in each Knot (like the medicine so dexterously, but ineffectually, concealed in the jam of our early childhood) one or more mathematical questions--in Arithmetic, Algebra, or Geometry, as the case might be--for the amusement, and possible edification, of the fair readers of that Magazine. L. C. _October, 1885._ CONTENTS. KNOT PAGE I. EXCELSIOR 1 II. ELIGIBLE APARTMENTS 4 III. MAD MATHESIS 13 IV. THE DEAD RECKONING 19 V. OUGHTS AND CROSSES 27 VI. HER RADIANCY 34 VII. PETTY CASH 43 VIII. DE OMNIBUS REBUS 52 IX. A SERPENT WITH CORNERS 58 X. CHELSEA BUNS 66 ANSWERS TO KNOT I. 77 " " II. 84 " " III. 90 " " IV. 96 " " V. 102 " " VI. 106 " " VII. 112 " " VIII. 132 " " IX. 135 " " X. 142 A TANGLED TALE. KNOT I. EXCELSIOR. "Goblin, lead them up and down."