The Head of Experiment House, whose name is unknown, was a woman who believed that boys and girls should be allowed to do what they like. As a result, she gave her students very little supervision and a large amount of unregulated free time. This policy resulted in very little classroom learning, and a large amount of bullying, mostly by ten or fifteen of the oldest children whom everyone called The Gang.
She was the Head of Experiment House from an unknown date (probably as early as at least 1939) until 1942.
In addition to her lack of emphasis on classroom learning and supervision, the Head saw no moral problem with bullying. She did not expel or punish bullies, but called them "interesting psychological cases", and talked to them for hours. The bullies who knew the right sort of things to say to the Head became her favorite students as a result of these conversations, and nothing was done about their behavior.
The events of 1942
Two weeks into a thirteen-week school term during 1942, Jill Pole and Eustace Scrubb were called into Narnia by Aslan to rescue Prince Rilian. The Head was never aware of their disappearance, because travelers from Earth to Narnia always return at the same moment they left. (For more information about the differences between Earth Time and Narnian Time, see here.)
When the two returned, they were wearing bright clothes that had been given to them by the Giants of Harfang. They were accompanied by Aslan, although those at Experiment House saw only his back, and Caspian X. Aslan broke down the school wall with his roar, allowing Caspian and Eustace to run through and use the flats of their swords to attack and scare the male bullies, while Jill used a riding crop on the girls.
All this commotion caused the Head to have hysterics and call the police with stories of escaped circus animals and armed convicts. But before they arrived, Caspian and Aslan had gone back into Narnia, the wall was made whole at Aslan's word, and Jill and Eustace (whom the Head had failed to recognize) changed clothes, so that when the police did come, they found no disaster, except for the Head behaving like a lunatic. This caused an inquiry into the whole administration of Experiment House, in which about ten students were expelled.
- From the way that Lewis wrote the above quote, it seems he was deliberately playing a dirty joke on Parliament, obviously voicing his disdain of it.