She progressed in Greek, although she was somewhat muddled about the accents, being differently informed by Jenny and Sandy who took turns to impart to her their weekly intake of the language. But she was determined to enter and share the new life of her special girls, and what she did not regard as humane of their new concerns, or what was not within the scope of her influence, she scorned.

She said: “It is witty to say that a straight line is the shortest distance between two points, or that a circle is a plane figure bounded by one line, every point of which is equidistant from a fixed centre. It is plain witty. Everyone knows what a straight line and a circle are.”

When, after the examinations at the end of the first term, she looked at the papers they had been set, she read some of the more vulnerable of the questions aloud with the greatest contempt: “A window cleaner carries a uniform 60-lb. ladder 15 ft. long, at one end of which a bucket of water weighing 40 lb. is hung. At what point must he support the ladder to carry it horizontally? Where is the c.g. of his load?” Miss Brodie looked at the paper, after reading out this question as if to indicate that she could not believe her eyes. Many a time she gave the girls to understand that the solution to such problems would be quite useless to Sybil Thorndike, Anna Pavlova and the late Helen of Troy.

But the Brodie set were on the whole still dazzled by their new subjects. It was never the same in later years when the languages of physics and chemistry, algebra and geometry had lost their elemental strangeness and formed each an individual department of life with its own accustomed boredom, and become hard work. Even Monica Douglas, who later developed such a good brain for mathematics, was plainly never so thrilled with herself as when she first subtracted x from y and the result from a; she never afterwards looked so happy.