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    _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. It
was 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 soft
breeze stirring them up again. I had known precisely such a secluded
little green sanctuary just over the hill from Mr. Riordan's farm when I
was a boy.

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

Without this coefficient to give us control, we would have lacked a
workable equation when we set about putting the first moon rocket around
those extraordinary engines of ours, which were still in the undeveloped
blueprint stage.

I see I shall have to explain this, although I had hoped to get right
along with my story. When you start from scratch, matter discharged
from any orifice has a velocity directly proportional to the square root
of the pressure-head driving it. But when you actually put things
together, contractions or expansions in the gas, surface roughness and
other factors make the velocity a bit smaller.

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

Perhaps you had better take my word for it that without this
equation--correctly stated, mind you--mankind would be well advised not
to make a first trip to the moon. And all this talk of coefficients and
equations sits strangely, you might say, upon the tongue of a man named
Kevin Francis Houlihan. But I am, after all, a scientist. If I had not
been a specialist in my field I would hardly have found myself engaged
in vital research at the center.

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

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

There were perhaps fifty of the little people. I was more than startled
by 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_ be
seen here in America. I had never seen them so busy, either. They were
building something in the middle of the glade. It was long and shiny and
upright and a little over five feet in height.

"Come along now, people!" said this crotchety one, looking straight at
me. "Stop starin' and get to work! You'll not be needin' to mind that
man 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 the
foreman of the leprechauns--if that's what he was--saw me smile and
became stiff and alert for a moment, as though suspecting that perhaps
I actually could see him. Then he shrugged and turned away, clearly
deeming such a thing impossible.

I said, "Just a minute, friend, and I'll beg your pardon. It so happens
I _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 little
souls. They began to scurry behind the trees and bushes, and a sloping
embankment 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!" I
said. "Come back, you daft little creatures!"

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

I walked over to the center of the glade where the curious shiny object
was 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 stubby
wings amidships. Of course it was a spaceship, or a miniature replica of
one. I looked at it more closely. Everything seemed almost miraculously
complete and workable.

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

"Listen to me now, little people!" I called out. "My name's Houlihan of
the Roscommon Houlihans. I am descended from King Niall himself--or so
at 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 been
shy. Yet without reaching a decision in so many words I knew suddenly
that I _had_ to talk to them. I'd come to the glen to work out a knotty
problem, and I was up against a blank wall. Simply because I was so
lonely that my mind had become clogged.

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

So I stepped back to the tiny spaceship, and this time I struck it a
resounding blow with my fist. "Hear me now, little people! If you don't
show yourselves and come out and talk to me, I'll wreck this spaceship
from stem to stern!"

       *       *       *       *       *

I heard only the leaves rustling softly.

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

The glade remained deathly silent.

"Two!"

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

"_Three!_"

And with that the little people suddenly appeared.

The leader--he seemed more wizened and bent than before--approached me
slowly and warily as I stood there. The others all followed at a safe
distance. I smiled to reassure them and then waved my arm in a friendly
gesture 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 I
have no intention of doing you any injury?"

"Mr. Houlihan," said Keech, drawing a kind of peppered dignity up about
himself, "in such matters I am never fully convinced. After living for
many centuries I am all too acutely aware of the perversity of human
nature."

"Yes," I said. "Well, as you will quickly see, all I want to do is
talk." 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, and
stop 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 our
work."

"Well, now, your work," I said, and glanced at the spaceship. "That's
exactly 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 a
group of little people be building a spaceship here in America--out in
this lonely place?"

Keech stared back without much expression, and said, "I've been
wondering how you guessed it was a spaceship. I was surprised enough
when you told me you could see us but not overwhelmingly so. I've run
into believers before who could see the little people. It happens every
so often, though not as frequently as it did a century ago. But knowing
a spaceship at first glance! Well, I must confess that _does_ astonish
me."

"And why wouldn't I know a spaceship when I see one?" I said. "It just
so 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 rocket
here at the nuclear propulsion center. Since it's no secret I can advise
you 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 we
prefer 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 gave
him a pinch of tobacco from my pouch. "Well, now," he said, "first of
all you're no doubt surprised to find us here in America."

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

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

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

"Leprechauns are not really mechanically inclined," said Keech. "Their
major 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 that
we're not long for this world. Or let me put it this way. We feel the
world isn't long for itself."

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

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

"There _is_ that possibility," I said.

"Well, then, as I say," said Keech, "the little people have decided to
leave 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 do
it. We haven't learned yet how to control the power--"

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

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

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

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

"You're determined to go."

"Truly we are, Mr. Houlihan. Now--to business. Just during these last
few 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're
here."

"Help you?"

"The power control, Mr. Houlihan. As I understand it, 'tis necessary to
know at any instant exactly how much thrust is bein' delivered through
the little holes in back. And on paper it looks simple enough--the
square of somethin' or other. I've got the figures jotted in a book when
I need 'em. But when you get to doin' it it doesn't come out exactly as
it 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 thing
we 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 is
it actually in an earthen crock. But there's gold, all right, enough to
make you rich for the rest of your life. And I'll make you a
proposition."

"Go ahead."

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

"Well, now, that's quite an offer," I said. Keech had the goodness to
be quiet while I sat and thought for a while. My pipe had gone out and I
lit it again. I finally said, "Let's have a look at your ship's drive
and 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 was
out we had half the spaceship apart, and were deep in argument about the
whole project.

It was a most fascinating session. I had often wished for a true working
model at the center, but no allowance had been inserted in the budget
for it. Keech brought me paper and pencil and I talked with the aid of
diagrams, as engineers are wont to do. Although the pencils were small
and I had to hold them between thumb and forefinger, as you would a
needle, I was able to make many sensible observations and even a few
innovations.

I came back again the next day--and every day for the following two
weeks. It rained several times, but Keech and his people made a canopy
of boughs and leaves and I was comfortable enough. Every once in a while
someone from the town or the center itself would pass by, and stop to
watch me. But of course they wouldn't see the leprechauns or anything
the 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 by
and grinned all the while.

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

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

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

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

"Thank you," I said.

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

"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 to
take it for a service of this sort."

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

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

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

       *       *       *       *       *

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

And I lit my pipe and smoked it slowly and chuckled to myself at how I
had gotten the best of the little people. Surely it was not every mortal
who could accomplish that. I had given them the wrong equation, of
course. They would never get their spaceship to work now, and later, if
they tried to spy out the right information I would take special
measures to prevent it, for I had the advantage of being able to see
them.

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 of
discharge, which I never could have done so quickly without those
sessions in the glade with Keech and his working model.

It would go down in scientific literature now, I suppose, as Houlihan's
Equation, and that was honor and glory enough for me. I could do without
Keech's pot of gold, though it would have been pleasant to be truly rich
for a change.

There was no sense in cheating him out of the gold to boot, for
leprechauns are most clever in matters of this sort and he would have
had 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 to
the advantage of humankind, and when a man can do the first and include
the 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 would
have left our world. And this world, as long as it lasts--what would it
be in that event? I ask you now, wouldn't we be even _more_ likely to
blow ourselves to Kingdom Come without the little people here for us to
believe 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.