My heart gave a sudden leap; I had to swallow before I could choke, "Tie us--What do you mean, Hank? We _are_ tied--and to something far above our heads. We can't even reach the bar we're chained to--" "We don't have to, Jim. They give us a loophole almost within reach. You notice that there skylight chain is a right thin one. I can't get these rope loops off'n my wrists but I think I c'n squeeze the skylight chain through a loop." He straightened his legs, and I realized suddenly he had purposely kept them _slightly_ bent at the knees during the time our enemies had been in the room. Now his toes gave him a reasonable foothold on the floor. Using this, he leaped up and gripped the steel chain _above_ his ropes ... drew himself up hand-over-hand until he was swinging comfortably in the loop. What he did then was weird and inexplicable to me--until, of course, a long time afterward. He pushed the steel chain through one of the rope loops about his wrist, pulled a wide, metal bight through this opening, stepped into the loop--and dropped lightly to the floor, _free_! The only encumbrance on him was a length of hemp between his arms. Now that he was at liberty to approach us it was a matter of minutes for him to unloose our bonds and have us untie his! * * * * * Grimper's jaw had dropped to his bottom vest button. Slow comprehension dawned on his features. He gasped, "A--a problem in applied topography![2] Astounding! I can hardly believe my eyes--but it's completely logical. Mr. Cleaver--I owe you an apology. Please allow me to--" [Footnote 2: Hank's problem here was similar to those interesting ones presented by Messrs. Krasna and Newman in their fascinating volume, _Mathematics and the Imagination_: The captives were not truly bound so long as freedom of leg movement permitted them to convert their bonds into a simply-connected manifold. [Illustration] By way of illustration (and for your own amusement) tie a 36" piece of string to each of your wrists. Tie a second piece of string to each of the wrists of a friend in such a fashion that the second piece loops the first. By experiment, you will discover it is quite possible to disengage yourself from your companion without breaking or cutting the string. Another interesting example of topological freedom is that achieved in removing the vest without first removing the coat. Try it. The coat may be unbuttoned, but your arms must not slip out of the coat sleeves.--Ed.] "Topogra-which?" asked Hank interestedly. "I didn't know it had no name, Mr. Grimper. Just 'peared to me like as if a circle's got an inside an' an outside, an' we was in the inside, so we wasn't tied up at all, rightly speakin'. Well, let's git out o' here!"