“Saturday we will go over ourselves and see how little Peter is,” said Billie, as, pencil in hand, she prepared to wade into a geometry problem. “Listen, Laura,” she added, looking up at her friend hopefully, “if you will help me with this geometry I’ll coach you in history. Is it a go?” Laura declared it was a “go,” and so they settled down to work. But no amount of work could keep their thoughts from straying time and again to the Haddon family and the mystery of the stolen invention. As the girls who have read the former adventures of Billie Bradley already know, Billie and her chums had been admitted to the “Ghost Club,” a secret society to which only the most popular girls and those who stood highest in their studies were admitted. The membership had never exceeded fifteen, for the girls knew that to have too large a membership would only cheapen the club. Rose Belser was the president of it, and Connie Danvers and several other of the girls’ good friends were members. Caroline Brant had been asked to join long before, but had refused because she thought it would take too much time from her studies. Last year’s Commencement had taken two of the club’s members, so that now the girls were watching the freshmen for good material. They were very careful in choosing, however, for it was far easier to get members into the club than it was to get them out. The club was to have its first real meeting in two weeks, and it was at that meeting that the names of prospective members were to be tentatively submitted to the president. After that, a period of close watching, and then—the fun of initiations. But first came news that ran through the Hall like wildfire. Some of the boys from Boxton Military Academy were coming over to the big hill behind the Three Towers Hall for the first real sledding of the year, and they had invited as many of the girls as they knew—and their friends—to meet them there. Chet and Teddy and Ferd were coming over, of course, and as the day approached, anticipation grew accordingly until the girls could think and talk of nothing but the fun they were going to have. “I wonder if Teddy will bring Paul Martinson with him,” said Vi, after trying vainly for half an hour to fix her mind on an essay she must hand in the next morning. “He’s ever so much fun, don’t you think?” It was in Paul Martinson’s motor boat, which he had named the _Shelling_ in honor of Captain Shelling, who was master of the Military Academy, that the boys had visited the girls on Lighthouse Island the summer before. Paul Martinson was a splendid-looking, fine boy whom all the girls liked—Rose Belser, in particular—but who, himself, seemed to prefer Billie. Like Teddy, Paul thought that Billie was the “very best sport” he knew, and declared that “a fellow can have more fun with her any day than he can with another boy.”