Forrester mused over this for a time. He could not decide on other points which would be near enough to these to form an overlapping triangle. He tried several ideas without result. His own home was too far away. But how about other victims? Suddenly it came to him. The first and last victims, so far as he knew, were Prentice and Melville, and the homes of these were reasonably near. So Forrester placed a square for each of these men’s homes on his sketch. That still left a third point for his triangle. He finally decided to use the tree again for this point. The lines did not cross, at least in the way he imagined Humphrey had in mind, but they did serve to increase the size of his original triangle and bring it to a perfect form of the isosceles triangle. It was significant, moreover, that the line from Prentice, the _first_ victim, led directly through Lucy’s cottage to the tree, and he noted with a start that the line from the Melville home, where the girl had been deeply involved, led through Mary Sturtevant’s house. This is the rough sketch as Forrester completed it: The way to a solution unquestionably led through Lucy and Mary Sturtevant, if there were anything at all to Humphrey’s idea. Green pointed at the girl. Forrester’s inclinations led him to the negress, and the odd working out of the triangle theory seemed to confirm him in his impressions. Forrester decided to investigate Lucy at once. His reference to the police had amused instead of angered her. She had pithily expressed her disdain of them. Was it not possible that these feelings arose from a sense of victory? In searching her house, the police had failed to find something that she knew was there! Whatever it was, Forrester intended to locate it, and use his information for what it might be worth. Forrester took an electric pocket lamp from the top of his chiffonier, and a dark muffler from a drawer. These he placed in his pocket. Then he selected a cap of an unobtrusive shade and went down to the laundry. There he cut off a short length of clothesline, wound it around his body and buttoned up his coat. Unlocking the laundry door, which opened at the southern end of the house, Forrester looked carefully around. He could hear William whistling at his work in the garage, while above him his sister was playing the piano in the music room. No other sound reached him and no one was in sight. Forrester closed the laundry door softly and stole across the lawn to the road. CHAPTER XIX—FACE TO FACE