Her curiously analytical mind is aptly illustrated by her novel method of measuring her lover's passion. He was in the habit of accompanying her home from the house of a friend. When he began to cross the square, instead of going round it, she concluded that his love had diminished in the exact proportion of two sides of a square to the diagonal. Promoted to the position of a companion, she devoted herself to the interests of her restless mistress, read to her, talked with her, wrote plays for her, and was the animating spirit of the famous Nuits Blanches. While the duchess was in exile she shared her disgrace, refused to betray her, and was sent to the Bastille for her loyalty. She resigned herself to her imprisonment with admirable philosophy, amused herself in the study of Latin, in watching the gambols of a cat and kitten, and in carrying on a safe and sentimental flirtation with the fascinating Duc de Richelieu, who occupied an adjoining cell and passed the hours in singing with her popular airs from Iphigenie. "Sentimental" is hardly a fitting word to apply to the coquetries of this remarkably clear and calculating young woman. She returned with her patroness to Sceaux, found many admirers, but married finally with an eye to her best worldly interests, and, it appears, in the main happily--at least, not unhappily. The shade of difference implies much. She had a keen, penetrating intellect which nothing escaped, and as it had the peculiar clearness in which people and events are reflected as in a mirror, her observations are of great value. "Aside from the prose of Voltaire, I know of none more agreeable than that of Mme. de Staal de Launay," said Grimm. Her portrait of her mistress serves to paint herself as well.
"Mme. la Duchesse du Maine, at the age of sixty years, has yet learned nothing from experience; she is a child of much talent; she has its defects and its charms. Curious and credulous, she wishes to be instructed in all the different branches of knowledge; but she is contented with their surface. The decisions of those who educated her have become for her principles and rules upon which her mind has never formed the least doubt; she submits once for all. Her provision for ideas is made; she rejects the best demonstrated truths and resists the best reasonings, if they are contrary to the first impressions she has received. All examination is impossible to her lightness, and doubt is a state which her weakness cannot support. Her catechism and the philosophy of Descartes are two systems which she understands equally well . . . . Her mirror cannot make her doubt the charms of her face; the testimony of her eyes is more questionable than the judgment of those who have decided that she is beautiful and well-formed. Her vanity is of a singular kind, but seems the less offensive because it is not reflective, though in reality it is the more ridiculous, Intercourse with her is a slavery; her tyranny is open; she does not deign to color it with the appearance of friendship. She says frankly that she has the misfortune of not being able to do without people for whom she does not care. She proves it effectually. One sees her learn with indifference the death of those who would call forth torrents of tears if they were a quarter of an hour too late for a card party or a promenade."
But this vain and self-willed woman read Virgil and Terence in the original, was devoted to Greek tragedies, dipped into philosophy, traversed the surface of many sciences, turned a madrigal with facility, and talked brilliantly. "The language is perfect only when you speak it or when one speaks of you," wrote Mme. de Lambert, in a tone of discreet flattery. "No one has ever spoken with more correctness, clearness, and rapidity, neither in a manner more noble or more natural," said Mlle. de Launay.