An equal meed of gratitude, though on other grounds, is due from me to the old mathematician, Henkel, who had been my father’s tutor in former days, and who now laboured hard, though with but poor results, to introduce the rudiments of his to me most dismal science into my very refractory brain! What endless trouble the dear old man took, and what inexhaustible patience he displayed in the attempt to initiate me into the mysteries of progressions and equations, or even the simple extraction of a square root! Under his kindly tuition I filled many note-books, covered whole pages with figures supposed to calculate the logarithm of a number, without even knowing what a logarithm was! Euclid I never understood at all; I can just remember that in every right-angled triangle the square on the hypothenuse is equal to the sum of the squares on the other two sides; but why? Ah! that is a very different matter! As for algebra, it was utterly incomprehensible to me, so I contented myself with learning a few of the formulæ by heart. Just as in a cousin of mine,--a man of great learning, considerable literary culture, and possessed of a fine taste in painting,--the musical sense is entirely wanting, so to me the properties pertaining to number and quality will forever remain a sealed book. To my French governesses I owe thanks for having so thoroughly grounded me in their language, that I could employ it for my literary work as well as my mother-tongue, one of my books being written originally in French. They too were my guides on my first incursions in the glorious domain of French literature, whose vast treasure-house I ransacked greedily, dwelling with special delight on the matchless beauty of the great prose-writers, my ear, accustomed to the more marked cadence of German verse, having always, I confess, been slightly deaf to the melody of the Alexandrine couplet. To the earlier poets of course this restriction does not apply, and Villon and Clément Marot became each in his own way dear to me, as were Ronsard and the other illustrious members of the Pléïade. Then came a moment, on which I can look back with a certain special satisfaction, during which I was left without either governess or preceptor of any sort to pursue my studies entirely on my own account, save for the advice given me for my reading by my parents. Those were the months which I devoured with avidity every book that came in my way--even history, I remember, and not only such works as Schiller’s “Thirty Years’ War” and “Revolt of the Netherlands,” rendered fascinating by their literary style, but, to please my mother, the drier pages of Becker’s great Universal History, in its fourteen volumes, were all waded through, rather more perfunctorily, I fear, than some of my lighter reading! Still, the hours spent thus were surely not altogether lost, and the habit of independent study, once acquired, never left me.