_Every writer must seek his own Flowery Kingdom in imagination's wide demesne, and if that search can begin and end on Earth his problem has been greatly simplified. In post-war Japan Walt Sheldon has found not only serenity, but complete freedom to write undisturbed about the things he treasures most. A one-time Air Force officer, he has turned to fantasy in his lighter moments, to bring us such brightly sparkling little gems as this. _

 houlihan's equation

 _by ... Walt Sheldon_

 The tiny spaceship had been built for a journey to a star. But its small, mischievous pilots had a rendezvous with destiny--on Earth. 

I must admit that at first I wasn't sure I was hearing those noises. Itwas in a park near the nuclear propulsion center--a cool, green spot, with the leaves all telling each other to hush, be quiet, and the softbreeze stirring them up again. I had known precisely such a secludedlittle green sanctuary just over the hill from Mr. Riordan's farm when Iwas a boy. 

Now it was a place I came to when I had a problem to thrash out. Thatmorning I had been trying to work out an equation to give thecoefficient of discharge for the matter in combustion. You may call itgas, if you wish, for we treated it like gas at the center forconvenience--as it came from the rocket tubes in our engine. 

Without this coefficient to give us control, we would have lacked aworkable equation when we set about putting the first moon rocket aroundthose extraordinary engines of ours, which were still in the undevelopedblueprint stage. 

I see I shall have to explain this, although I had hoped to get rightalong with my story. When you start from scratch, matter dischargedfrom any orifice has a velocity directly proportional to the square rootof the pressure-head driving it. But when you actually put thingstogether, contractions or expansions in the gas, surface roughness andother factors make the velocity a bit smaller. 

At the terrible discharge speed of nuclear explosion--which is what thedrive amounts to despite the fact that it is simply water in whichnuclear salts have been previously dissolved--this small factor makesquite a difference. I had to figure everything into it--diameter of thenozzle, sharpness of the edge, the velocity of approach to the point ofdischarge, atomic weight and structure-- Oh, there is so much of thisthat if you're not a nuclear engineer yourself it's certain to wearyyou. 

Perhaps you had better take my word for it that without thisequation--correctly stated, mind you--mankind would be well advised notto make a first trip to the moon. And all this talk of coefficients andequations sits strangely, you might say, upon the tongue of a man namedKevin Francis Houlihan. But I am, after all, a scientist. If I had notbeen a specialist in my field I would hardly have found myself engagedin vital research at the center. 

Anyway, I heard these little noises in the park. They sounded like smallworking sounds, blending in eerily mysterious fashion with a chorus ofsmall voices. I thought at first it might be children at play, but thenat the time I was a bit absent-minded. I tiptoed to the edge of thetrees, not wanting to deprive any small scalawags of their pleasure, andpeered out between the branches. And what do you suppose I saw? Notchildren, but a group of little people, hard at work. 

There was a leader, an older one with a crank face. He was beating theair with his arms and piping: "Over here, now! All right, bring thoseelectrical connections over here--and see you're not slow as treacleabout it!"

There were perhaps fifty of the little people. I was more than startledby it, too. I had not seen little people in--oh, close to thirty years. I had seen them first as a boy of eight, and then, very briefly again, on my tenth birthday. And I had become convinced they could _never_ beseen here in America. I had never seen them so busy, either. They werebuilding something in the middle of the glade. It was long and shiny andupright and a little over five feet in height. 

"Come along now, people!" said this crotchety one, looking straight atme. "Stop starin' and get to work! You'll not be needin' to mind thatman standin' there! You know he can't see nor hear us!"

Oh, it was good to hear the rich old tongue again. I smiled, and theforeman of the leprechauns--if that's what he was--saw me smile andbecame stiff and alert for a moment, as though suspecting that perhapsI actually could see him. Then he shrugged and turned away, clearlydeeming such a thing impossible. 

I said, "Just a minute, friend, and I'll beg your pardon. It so happensI _can_ see you. "

He whirled to face me again, staring open-mouthed. Then he said, "What?What's that, now?"

"I can see you, " I said. 

"Ohhh!" he said and put his palms to his cheekbones. "Saints be with us!He's a believer! Run everybody--run for your lives!"

And they all began running, in as many directions as there were littlesouls. They began to scurry behind the trees and bushes, and a slopingembankment nearby. 

"No, wait!" I said. "Don't go away! I'll not be hurting you!"

They continued to scurry. 

I knew what it was they feared. "I don't intend catching one of you!" Isaid. "Come back, you daft little creatures!"

But the glade was silent, and they had all disappeared. They thought Iwanted their crock of gold, of course. I'd be entitled to it if I couldcatch one and keep him. Or so the legends affirmed, though I've wonderedoften about the truth of them. But I was after no gold. I only wanted tohear the music of an Irish tongue. I was lonely here in America, even ifI had latched on to a fine job of work for almost shamefully generouspay. You see, in a place as full of science as the nuclear propulsioncenter there is not much time for the old things. I very much wanted totalk to the little people. 

I walked over to the center of the glade where the curious shiny objectwas standing. It was as smooth as glass and shaped like a huge cigar. There were a pair of triangular fins down at the bottom, and stubbywings amidships. Of course it was a spaceship, or a miniature replica ofone. I looked at it more closely. Everything seemed almost miraculouslycomplete and workable. 

I shook my head in wonder, then stepped back from the spaceship andlooked about the glade. I knew they were all hiding nearby, watching meapprehensively. I lifted my head to them. 

"Listen to me now, little people!" I called out. "My name's Houlihan ofthe Roscommon Houlihans. I am descended from King Niall himself--or soat least my father used to say! Come on out now, and pass the time o'day!"

Then I waited, but they didn't answer. The little people always had beenshy. Yet without reaching a decision in so many words I knew suddenlythat I _had_ to talk to them. I'd come to the glen to work out a knottyproblem, and I was up against a blank wall. Simply because I was solonely that my mind had become clogged. 

I knew that if I could just once hear the old tongue again, and talkabout the old things, I might be able to think the problem through to asatisfactory conclusion. 

So I stepped back to the tiny spaceship, and this time I struck it aresounding blow with my fist. "Hear me now, little people! If you don'tshow yourselves and come out and talk to me, I'll wreck this spaceshipfrom stem to stern!"

 * * * * *

I heard only the leaves rustling softly. 

"Do you understand? I'll give you until I count three to make anappearance! One!"

The glade remained deathly silent. 

"Two!"

I thought I heard a stirring somewhere, as if a small, brittle twig hadsnapped in the underbrush. 

"_Three!_"

And with that the little people suddenly appeared. 

The leader--he seemed more wizened and bent than before--approached meslowly and warily as I stood there. The others all followed at a safedistance. I smiled to reassure them and then waved my arm in a friendlygesture of greeting. 

"Good morning, " I said. 

"Good morning, " the foreman said with some caution. "My name is Keech. "

"And mine's Houlihan, as I've told you. Are you convinced now that Ihave no intention of doing you any injury?"

"Mr. Houlihan, " said Keech, drawing a kind of peppered dignity up abouthimself, "in such matters I am never fully convinced. After living formany centuries I am all too acutely aware of the perversity of humannature. "

"Yes, " I said. "Well, as you will quickly see, all I want to do istalk. " I nodded as I spoke, and sat down cross-legged upon the grass. 

"Any Irishman wants to talk, Mr. Houlihan. "

"And often that's _all_ he wants, " I said. "Sit down with me now, andstop staring as if I were a snake returned to the Island. "

He shook his head and remained standing. "Have your say, Mr. Houlihan. And afterward we'll appreciate it if you'll go away and leave us to ourwork. "

"Well, now, your work, " I said, and glanced at the spaceship. "That'sexactly what's got me curious. "

The others had edged in a bit now and were standing in a circle, intently staring at me. I took out my pipe. "Why, " I asked, "would agroup of little people be building a spaceship here in America--out inthis lonely place?"

Keech stared back without much expression, and said, "I've beenwondering how you guessed it was a spaceship. I was surprised enoughwhen you told me you could see us but not overwhelmingly so. I've runinto believers before who could see the little people. It happens everyso often, though not as frequently as it did a century ago. But knowinga spaceship at first glance! Well, I must confess that _does_ astonishme. "

"And why wouldn't I know a spaceship when I see one?" I said. "It justso happens I'm a doctor of science. "

"A doctor of science, now, " said Keech. 

"Invited by the American government to work on the first moon rockethere at the nuclear propulsion center. Since it's no secret I can adviseyou of it. "

"A scientist, is it, " said Keech. "Well, now, that's very interesting. "

"I'll make no apologies for it, " I said. 

"Oh, there's no need for apology, " said Keech. "Though in truth weprefer poets to scientists. But it has just now crossed my mind, Mr. Houlihan that you, being a scientist, might be of help to us. "

"How?" I asked. 

"Well, I might try starting at the beginning, " he replied. 

"You might, " I said. "A man usually does. "

Keech took out his own pipe--a clay dudeen--and looked hopeful. I gavehim a pinch of tobacco from my pouch. "Well, now, " he said, "first ofall you're no doubt surprised to find us here in America. "

"I am surprised from time to time to find myself here, " I said. "Butcontinue. "

"We had to come here, " said Keech, "to learn how to make a spaceship. "

"A spaceship, now, " I said, unconsciously adopting some of the oldmanner. 

"Leprechauns are not really mechanically inclined, " said Keech. "Theirmajor passions are music and laughter and mischief, as anyone knows. "

"Myself included, " I agreed. "Then why do you need a spaceship?"

"Well, if I may use an old expression, we've had a feelin' lately thatwe're not long for this world. Or let me put it this way. We feel theworld isn't long for itself. "

I scratched my cheek. "How would a man unravel a statement such asthat?"

"It's very simple. With all the super weapons you mortals havedeveloped, there's the distinct possibility you might be blowin' us allup in the process of destroying yourselves. "

"There _is_ that possibility, " I said. 

"Well, then, as I say, " said Keech, "the little people have decided toleave the planet in a spaceship. Which we're buildin' here and now. We've spied upon you and learned how to do it. Well--almost how to doit. We haven't learned yet how to control the power--"

"Hold on, now, " I said. "Leaving the planet, you say. And where wouldyou be going?"

"There's another committee working on that. 'Tis not our concern. I wasinclined to suggest the constellation Orion, which sounds as though ithas a good Irish name, but I was hooted down. Be that as it may, my ownjob was to go into your nuclear center, learn how to make the ship, andproceed with its construction. Naturally, we didn't understand all ofyour high-flyin' science, but some of our people are pretty clever atgettin' up replicas of things. "

"You mean you've been spying on us at the center all this time? Do youknow, we often had the feeling we were being watched, but we thought itwas by the Russians. There's one thing which puzzles me, though. Ifyou've been constantly around us--and I'm still able to see the littlepeople--why did I never see you before?"

"It may be we never crossed your path. It may be you can only see uswhen you're thinkin' of us, and of course truly believin' in us. I don'tknow--'tis a thing of the mind, and not important at the moment. What'simportant is for us to get our first ship to workin' properly and thenwe'll be on our way. "

"You're determined to go. "

"Truly we are, Mr. Houlihan. Now--to business. Just during these lastfew minutes a certain matter has crossed my mind. That's why I'm wastin'all this time with you, sir. You say you are a scientist. "

"A nuclear engineer. "

"Well, then, it may be that you can help us--now that you know we'rehere. "

"Help you?"

"The power control, Mr. Houlihan. As I understand it, 'tis necessary toknow at any instant exactly how much thrust is bein' delivered throughthe little holes in back. And on paper it looks simple enough--thesquare of somethin' or other. I've got the figures jotted in a book whenI need 'em. But when you get to doin' it it doesn't come out exactly asit does on paper. "

"You're referring to the necessity for a coefficient of discharge. "

"Whatever it might be named, " said Keech, shrugging. "'Tis the one thingwe lack. I suppose eventually you people will be gettin' around to it. But meanwhile we need it right now, if we're to make our ship move. "

"And you want me to help you with this?"

"That is exactly what crossed my mind. "

I nodded and looked grave and kneaded my chin for a moment softly. "Well, now, Keech, " I said finally, "why should I help you?"

"Ha!" said Keech, grinning, but not with humor, "the avarice of humans!I knew it! Well, Mr. Houlihan, I'll give you reason enough. The pot o'gold, Mr. Houlihan!"

"The one at the end of the rainbow?"

"It's not at the end of the rainbow. That's a grandmother's tale. Nor isit actually in an earthen crock. But there's gold, all right, enough tomake you rich for the rest of your life. And I'll make you aproposition. "

"Go ahead. "

"We'll not be needin' gold where we're goin'. It's yours if you show ushow to make our ship work. "

"Well, now, that's quite an offer, " I said. Keech had the goodness tobe quiet while I sat and thought for a while. My pipe had gone out and Ilit it again. I finally said, "Let's have a look at your ship's driveand see what we can see. "

"You accept the proposition then?"

"Let's have a look, " I said, and that was all. 

Well, we had a look, and then several looks, and before the morning wasout we had half the spaceship apart, and were deep in argument about thewhole project. 

It was a most fascinating session. I had often wished for a true workingmodel at the center, but no allowance had been inserted in the budgetfor it. Keech brought me paper and pencil and I talked with the aid ofdiagrams, as engineers are wont to do. Although the pencils were smalland I had to hold them between thumb and forefinger, as you would aneedle, I was able to make many sensible observations and even a fewinnovations. 

I came back again the next day--and every day for the following twoweeks. It rained several times, but Keech and his people made a canopyof boughs and leaves and I was comfortable enough. Every once in a whilesomeone from the town or the center itself would pass by, and stop towatch me. But of course they wouldn't see the leprechauns or anythingthe leprechauns had made, not being believers. 

I would halt work, pass the time of day, and then, in subtle fashion, send the intruder on his way. Keech and the little people just stood byand grinned all the while. 

At the end of sixteen days I had the entire problem all but whipped. Itis not difficult to understand why. The working model and the fact thatthe small people with their quick eyes and clever fingers could spot allsorts of minute shortcomings was a great help. And I was hearing the oldtongue and talking of the old things every day, and truly that went farto take the clutter out of my mind. I was no longer so lonely that Icouldn't think properly. 

On the sixteenth day I covered a piece of paper with tiny mathematicalsymbols and handed it to Keech. "Here is your equation, " I said. "Itwill enable you to know your thrust at any given moment, under anycircumstances, in or out of gravity, and under all conditions offriction and combustion. "

"Thank you, Mr. Houlihan, " said Keech. All his people had gathered in aloose circle, as though attending a rite. They were all looking at mequietly. 

"Mr. Houlihan, " said Keech, "you will not be forgotten by theleprechauns. If we ever meet again, upon another world perchance, you'llfind our friendship always eager and ready. "

"Thank you, " I said. 

"And now, Mr. Houlihan, " said Keech, "I'll see that a quantity of goldis delivered to your rooms tonight, and so keep my part of thebargain. "

"I'll not be needing the gold, " I said. 

Keech's eyebrows popped upward. "What's this now?"

"I'll not be needing it, " I repeated. "I don't feel it would be right totake it for a service of this sort. "

"Well, " said Keech in surprise, and in some awe, too, "well, now, mushaLord help us! 'Tis the first time I ever heard such a speech from amortal. " He turned to his people. "We'll have three cheers now, do youhear, for Mr. Houlihan--friend of the little people as long as he shalllive!"

And they cheered. And little tears crept into the corners of some oftheir turned-up eyes. 

We shook hands, all of us, and I left. 

 * * * * *

I walked through the park, and back to the nuclear propulsion center. Itwas another cool, green morning with the leaves making only soft noisesas the breezes came along. It smelled exactly like a wood I had known inRoscommon. 

And I lit my pipe and smoked it slowly and chuckled to myself at how Ihad gotten the best of the little people. Surely it was not every mortalwho could accomplish that. I had given them the wrong equation, ofcourse. They would never get their spaceship to work now, and later, ifthey tried to spy out the right information I would take specialmeasures to prevent it, for I had the advantage of being able to seethem. 

As for our own rocket ship, it should be well on its way by next St. Patrick's Day. For I had indeed determined the true coefficient ofdischarge, which I never could have done so quickly without thosesessions in the glade with Keech and his working model. 

It would go down in scientific literature now, I suppose, as Houlihan'sEquation, and that was honor and glory enough for me. I could do withoutKeech's pot of gold, though it would have been pleasant to be truly richfor a change. 

There was no sense in cheating him out of the gold to boot, forleprechauns are most clever in matters of this sort and he would havehad it back soon enough--or else made it a burden in some way. 

Indeed, I had done a piece of work greatly to my advantage, and also tothe advantage of humankind, and when a man can do the first and includethe second as a fortunate byproduct it is a most happy accident. 

For if I had shown the little people how to make a spaceship they wouldhave left our world. And this world, as long as it lasts--what would itbe in that event? I ask you now, wouldn't we be even _more_ likely toblow ourselves to Kingdom Come without the little people here for us tobelieve in every now and then?

Transcriber's Note:

 This etext was produced from _Fantastic Universe_ September 1955. Extensive research did not uncover any evidence that the U. S. Copyright on this publication was renewed. Minor spelling and typographical errors have been corrected without note.