And such a lesson! No explaining,—some scolding, some shouting,—a good deal of cry and small wool. Then he came to me. ‘Can ye do proportion?’ ‘Yes (!) I want to do Algebra.’ ‘Ay,—but that’ll be Friday. But do ye know Fractions?’ I intimated an idea that I did. He didn’t seem at all to believe it,—‘did I understand them?’ I felt rather absurd and hypocritical, and again said I _did_ rather decidedly. However not a bit would he believe me,—gave me (as a severe test, I suppose) ¾ x ⅝ to do and explain. Well,—did it! ‘But why?’ I am sure I shall always hereafter have pity on unfortunate examinees pounced upon. The whole thing seemed so absurd,—I was so annoyed,—it seemed so silly standing up by that imp of a Sandy with a slate,—that I very nearly failed to give any rational explanation. However I did somewhat, and he had rather grudgingly to grant, ‘Ay, I see ye know it.’ Then, when I asked him about the Algebra, it seemed he had none but quite beginners (don’t I pity them?) and ‘it wasn’t his subject’! in fact, clearly enough he didn’t know as much as I did. Amazed at my astounding erudition, ‘Where had I learned?’ ‘Oh, in England.’ ‘Ay?’ (very surprised) ‘the English gairls generally come very bad at Arithmetic,—we’ve one just now doesn’t know her tables.’ I laughed out. ‘Well, you mustn’t take her for a specimen.’ He seemed to think that the national average! ‘Ay, but most we’ve had are very bad at it,’ very resolutely. He must be a good judge by the specimen I saw. Well, he kept hovering round me as a sort of strange animal, and told me how the girls changed every year, and how he went through from the First Rules to Decimals as the _ne plus ultra_.” Clearly there was nothing to be gained here, so next morning she “explained and apologised” to the Principal, and found him “very nice and pleasant.” Her first impulse was to go straight back to London (in fact arrangements were made for her to live with Miss Wodehouse and study at Bedford College) but in the end wiser counsels prevailed. That arithmetic class was not the high-water mark of Edinburgh achievement even as regarded the education of its women. S. J.-B. made the acquaintance of Miss Blyth, who introduced her to Mr. Begbie, Miss de Dreux and others, so she settled down to a varied course of work, living comfortably in lodgings with Alice to “do for her.” To Mr. Begbie she expresses her gratitude over and over again. “Mathematics not much with S. In answer to Miss de Dreux told the truth. They so nice sensible and honest,—teachers born, ‘without respect of persons’. Mr. Begbie glad to hear truth,—promises me a better far tomorrow. Mr. Weisse a good teacher,—right good. German less formidable than I expected.” One gathers from the letters that she made an extraordinarily vivid impression on her teachers: several of them refused to take fees, and Mr. Begbie persisted in his refusal.