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finally the effective volume becomes infinitesimal. Or, mathematically, the then range of cogitation, integrated between the limits of plus and minus infinity, approaches zero as a limit. . ."
    "Huh? What are you talking about?" the Lensman demanded.
    "Poor mathematics, perhaps, but sound psychology," Lacy grinned. "It got your undivided attention, didn't it? That was what I was after. In plain English, if you keep on thinking around in circles you'll soon be biting yourself in the small of the back. Come on, you and I are going places."
    "Where?"
    "To the Grand Ball in honor of the Grand Fleet, my boy— old Doctor Lacy prescribes it for you as a complete and radical change of atmosphere. Let's go!"
    The city's largest ball-room was a blaze of light and color. A thousand polychromatic lamps flooded their radiance downward through draped bunting upon an even more colorful throng. Two thousand items of feminine loveliness were there, in raiment whose fabrics were the boasts of hundreds of planets, whose hues and shades put the spectrum itself to shame. There were over two thousand men, clad in plain or beribboned or bemedaled full civilian dress, or in the variously panoplied dress uniforms of the many Services.
    "You're dancing with Miss Forrester first, Kinnison," the surgeon introduced them informally, and the Lensman found himself gliding away with a stunning blonde, ravishingly and revealingly dressed in a dazzlingly blue wisp of Manarkan glamorette—fashion's dernier ori.
    To the uninformed, Kinnison's garb of plain gray leather might have seemed incongruous indeed in that brilliantly and fastidiously dressed assemblage. But to those people, as to us of today, the drab, starkly utilitarian uniform of the Unattached Lensman transcended far any other, however resplendent, worn by man: and literally hundreds of eyes followed the strikingly handsome couple as they slid rhythmically out upon the polished floor. But a measure of the tall beauty's customary poise had deserted her. She was slimly taut in the circle of me Lensman's arm, her eyes were downcast, and suddenly she missed a step.
    " 'Scuse me for stepping on your feet," he apologized. "A fellow gets out of practice, flitting around in a speedster so much."
    "Thanks for taking the blame, but it's my fault entirely— I know it as well as you do,"
    she replied, flushing uncomfortably. "I do know how to dance, too, but . . . well, you're a Gray Lensman, you know."
    "Huh?" he ejaculated, in honest surprise, and she looked up at him for the first time.
    "What has that fact got to do with the price of Venerian orchids in Chicago—or with my clumsy walking all over your slippers?"
    "Everything in the world," she assured him. Nevertheless, her stiff young body relaxed and she fell into the graceful, accurate dancing which she really knew so well how to do. "You see, I don't suppose that any of us has ever seen a Gray Lensman before, except in pictures, and actually to be dancing with one is . . . well, it's really a kind of shock. I have to get used to it gradually. Why, I don't even know how to talk to you! One couldn't possibly call you plain Mister, as one would any ord . . ."
    "It'll be QX if you just call me 'say'," he informed her. "Maybe you'd rather not dance with a dub? What say we go get us a sandwich and a bottle of fayalin or something?"
    "No—never!" she exclaimed. "I didn't mean it that way at all. I'm going to have this full dance with you, and enjoy every second of it And later I'm going to pack this dance card—which I hope you will sign for me—away in lavender, so it will go down in history that in my youth I really did dance with Gray Lensman Kinnison. Perhaps I've recovered enough now to talk and dance at the same time. Do you mind if I ask you some silly questions about space?"
    "Go ahead. They won't be silly, if I'm any judge. Elementary, perhaps, but not silly."
    "I hope so, but I think you're being charitable again. Like most of the girls here, I