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 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. december 1885.

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.