PRoblem

by Alan E. Nourse

The letter came down the slot too early that morning to be the regularmail run. Pete Greenwood eyed the New Philly photocancel with a dreadfulpremonition. The letter said:

 PETER: Can you come East chop-chop, urgent? Grdznth problem getting to be a PRoblem, need expert icebox salesman to get gators out of hair fast. Yes? Math boys hot on this, citizens not so hot. Please come. TOMMY

Pete tossed the letter down the gulper with a sigh. He had lost a bet tohimself because it had come three days later than he expected, but ithad come all the same, just as it always did when Tommy Heinz gothimself into a hole. 

Not that he didn't like Tommy. Tommy was a good PR-man, as PR-men go. Hejust didn't know his own depth. PRoblem in a beady Grdznth eye! WhatTommy needed right now was a Bazooka Battalion, not a PR-man. Petesettled back in the Eastbound Rocketjet with a sigh of resignation. 

He was just dozing off when the fat lady up the aisle let out a scream. A huge reptilian head had materialized out of nowhere and was hanging inair, peering about uncertainly. A scaly green body followed, four feetaway, complete with long razor talons, heavy hind legs, and a whiplashtail with a needle at the end. For a moment the creature floated upsidedown, legs thrashing. Then the head and body joined, executed ahorizontal pirouette, and settled gently to the floor like an eight-footcircus balloon. 

Two rows down a small boy let out a muffled howl and tried to buryhimself in his mother's coat collar. An indignant wail arose from thefat lady. Someone behind Pete groaned aloud and quickly retired behind anewspaper. 

The creature coughed apologetically. "Terribly sorry, " he said in acoarse rumble. "So difficult to control, you know. Terribly sorry. .. . "His voice trailed off as he lumbered down the aisle toward the emptyseat next to Pete. 

The fat lady gasped, and an angry murmur ran up and down the cabin. "Sitdown, " Pete said to the creature. "Relax. Cheerful reception these days, eh?"

"You don't mind?" said the creature. 

"Not at all. " Pete tossed his briefcase on the floor. At a distance thehuge beast had looked like a nightmare combination of large alligatorand small tyrannosaurus. Now, at close range Pete could see that the"scales" were actually tiny wrinkles of satiny green fur. He knew, ofcourse, that the Grdznth were mammals--"docile, peace-loving mammals, "Tommy's PR-blasts had declared emphatically--but with one of themsitting about a foot away Pete had to fight down a wave of horror andrevulsion. 

The creature was most incredibly ugly. Great yellow pouches hung downbelow flat reptilian eyes, and a double row of long curved teethglittered sharply. In spite of himself Pete gripped the seat as theGrdznth breathed at him wetly through damp nostrils. 

"Misgauged?" said Pete. 

The Grdznth nodded sadly. "It's horrible of me, but I just can't helpit. I _always_ misgauge. Last time it was the chancel of St. John'sCathedral. I nearly stampeded morning prayer--" He paused to catch hisbreath. "What an effort. The energy barrier, you know. Frightfully hardto make the jump. " He broke off sharply, staring out the window. "Dearme! Are we going _east_?"

"I'm afraid so, friend. "

"Oh, dear. I wanted _Florida_. "

"Well, you seem to have drifted through into the wrong airplane, " saidPete. "Why Florida?"

The Grdznth looked at him reproachfully. "The Wives, of course. Theclimate is so much better, and they mustn't be disturbed, you know. "

"Of course, " said Pete. "In their condition. I'd forgotten. "

"And I'm told that things have been somewhat unpleasant in the East justnow, " said the Grdznth. 

Pete thought of Tommy, red-faced and frantic, beating off hordes ofindignant citizens. "So I hear, " he said. "How many more of you arecoming through?"

"Oh, not many, not many at all. Only the Wives--half a million orso--and their spouses, of course. " The creature clicked his talonsnervously. "We haven't much more time, you know. Only a few more weeks, a few months at the most. If we couldn't have stopped over here, I justdon't know _what_ we'd have done. "

"Think nothing of it, " said Pete indulgently. "It's been great havingyou. "

The passengers within earshot stiffened, glaring at Pete. The fat ladywas whispering indignantly to her seat companion. Junior had halfemerged from his mother's collar; he was busy sticking out his tongue atthe Grdznth. 

The creature shifted uneasily. "Really, I think--perhaps Florida wouldbe better. "

"Going to try it again right now? Don't rush off, " said Pete. 

"Oh, I don't mean to rush. It's been lovely, but--" Already the Grdznthwas beginning to fade out. 

"Try four miles down and a thousand miles southeast, " said Pete. 

The creature gave him a toothy smile, nodded once, and grew moreindistinct. In another five seconds the seat was quite empty. Peteleaned back, grinning to himself as the angry rumble rose around himlike a wave. He was a Public Relations man to the core--but right now hewas off duty. He chuckled to himself, and the passengers avoided himlike the plague all the way to New Philly. 

But as he walked down the gangway to hail a cab, he wasn't smiling somuch. He was wondering just how high Tommy was hanging him, this time. 

 * * * * *

The lobby of the Public Relations Bureau was swarming like an upturnedanthill when Pete disembarked from the taxi. He could almost smell thedesperate tension of the place. He fought his way past scurrying clerksand preoccupied poll-takers toward the executive elevators in the rear. 

On the newly finished seventeenth floor, he found Tommy Heinz pacing thecorridor like an expectant young father. Tommy had lost weight sincePete had last seen him. His ruddy face was paler, his hair thin andragged as though chunks had been torn out from time to time. He saw Petestep off the elevator, and ran forward with open arms. "I thought you'dnever get here!" he groaned. "When you didn't call, I was afraid you'dlet me down. "

"Me?" said Pete. "I'd never let down a pal. "

The sarcasm didn't dent Tommy. He led Pete through the ante-room intothe plush director's office, bouncing about excitedly, his wordstumbling out like a waterfall. He looked as though one gentle shovemight send him yodeling down Market Street in his underdrawers. "Holdit, " said Pete. "Relax, I'm not going to leave for a while yet. Yourgirl screamed something about a senator as we came in. Did you hearher?"

Tommy gave a violent start. "Senator! Oh, dear. " He flipped a deskswitch. "What senator is that?"

"Senator Stokes, " the girl said wearily. "He had an appointment. He'sready to have you fired. "

"All I need now is a senator, " Tommy said. "What does he want?"

"Guess, " said the girl. 

"Oh. That's what I was afraid of. Can you keep him there?"

"Don't worry about that, " said the girl. "He's growing roots. They sweptaround him last night, and dusted him off this morning. His appointmentwas for _yesterday_, remember?"

"Remember! Of course I remember. Senator Stokes--something about a riotin Boston. " He started to flip the switch, then added, "See if you canget Charlie down here with his giz. "

He turned back to Pete with a frantic light in his eye. "Good old Pete. Just in time. Just. Eleventh-hour reprieve. Have a drink, have acigar--do you want my job? It's yours. Just speak up. "

"I fail to see, " said Pete, "just why you had to drag me all the wayfrom L. A. To have a cigar. I've got work to do. "

"Selling movies, right?" said Tommy. 

"Check. "

"To people who don't want to buy them, right?"

"In a manner of speaking, " said Pete testily. 

"Exactly, " said Tommy. "Considering some of the movies you've beenselling, you should be able to sell anything to anybody, any time, atany price. "

"Please. Movies are getting Better by the Day. "

"Yes, I know. And the Grdznth are getting worse by the hour. They'recoming through in battalions--a thousand a day! The more Grdznth comethrough, the more they act as though they own the place. Not nasty oranything--it's that infernal politeness that people hate most, I think. Can't get them mad, can't get them into a fight, but they do anythingthey please, and go anywhere they please, and if the people don't likeit, the Grdznth just go right ahead anyway. "

Pete pulled at his lip. "Any violence?"

Tommy gave him a long look. "So far we've kept it out of the papers, butthere have been some incidents. Didn't hurt the Grdznth a bit--they havepersonal protective force fields around them, a little point they didn'tbother to tell us about. Anybody who tries anything fancy gets thrownlike a bolt of lightning hit him. Rumors are getting wild--people sayingthey can't be killed, that they're just moving in to stay. "

Pete nodded slowly. "Are they?"

"I wish I knew. I mean, for sure. The psych-docs say no. The Grdznthagreed to leave at a specified time, and something in their culturalbackground makes them stick strictly to their agreements. But that'sjust what the psych-docs think, and they've been known to be wrong. "

"And the appointed time?"

Tommy spread his hands helplessly. "If we knew, you'd still be in L. A. Roughly six months and four days, plus or minus a month for the timedifferential. That's strictly tentative, according to the math boys. It's a parallel universe, one of several thousand already explored, according to the Grdznth scientists working with Charlie Karns. Most ofthe parallels are analogous, and we happen to be analogous to theGrdznth, a point we've omitted from our PR-blasts. They have aneight-planet system around a hot sun, and it's going to get lots hotterany day now. "

Pete's eyes widened. "Nova?"

"Apparently. Nobody knows how they predicted it, but they did. Spottedit coming several years ago, so they've been romping through parallelafter parallel trying to find one they can migrate to. They found one, sort of a desperation choice. It's cold and arid and full of impassablemountain chains. With an uphill fight they can make it support afraction of their population. "

Tommy shook his head helplessly. "They picked a very sensible system forgetting a good strong Grdznth population on the new parallel as fast aspossible. The males were picked for brains, education, ability andadaptability; the females were chosen largely according to how pregnantthey were. "

Pete grinned. "Grdznth in utero. There's something poetic about it. "

"Just one hitch, " said Tommy. "The girls can't gestate in that climate, at least not until they've been there long enough to get their glandsadjusted. Seems we have just the right climate here for gestatingGrdznth, even better than at home. So they came begging for permissionto stop here, on the way through, to rest and parturiate. "

"So Earth becomes a glorified incubator. " Pete got to his feetthoughtfully. "This is all very touching, " he said, "but it just doesn'twash. If the Grdznth are so unpopular with the masses, why did we letthem in here in the first place?" He looked narrowly at Tommy. "To bevery blunt, what's the parking fee?"

"Plenty, " said Tommy heavily. "That's the trouble, you see. The fee isso high, Earth just can't afford to lose it. Charlie Karns'll tell youwhy. "

 * * * * *

Charlie Karns from Math Section was an intense skeleton of a man with along jaw and a long white coat drooping over his shoulders like ashroud. In his arms he clutched a small black box. 

"It's the parallel universe business, of course, " he said to Pete, withTommy beaming over his shoulder. "The Grdznth can cross through. They'vebeen able to do it for a long time. According to our figuring, this mustinvolve complete control of mass, space and dimension, all three. Andtime comes into one of the three--we aren't sure which. "

The mathematician set the black box on the desk top and released thelid. Like a jack-in-the-box, two small white plastic spheres popped outand began chasing each other about in the air six inches above the box. Presently a third sphere rose up from the box and joined the fun. 

Pete watched it with his jaw sagging until his head began to spin. "Nowires?"

"_Strictly_ no wires, " said Charlie glumly. "No nothing. " He closed thebox with a click. "This is one of their children's toys, andtheoretically, it can't work. Among other things, it takes null-gravityto operate. "

Pete sat down, rubbing his chin. "Yes, " he said. "I'm beginning to see. They're teaching you this?"

Tommy said, "They're trying to. He's been working for weeks with theirtop mathematicians, him and a dozen others. How many computers have youburned out, Charlie?"

"Four. There's a differential factor, and we can't spot it. They havethe equations, all right. It's a matter of translating them intoconstants that make sense. But we haven't cracked the differential. "

"And if you do, then what?"

Charlie took a deep breath. "We'll have inter-dimensional control, apractical, utilizable transmatter. We'll have null-gravity, which meansthe greatest advance in power utilization since fire was discovered. Itmight give us the opening to a concept of time travel that makes somekind of sense. And power! If there's an energy differential of anymagnitude--" He shook his head sadly. 

"We'll also know the time-differential, " said Tommy hopefully, "and howlong the Grdznth gestation period will be. "

"It's a fair exchange, " said Charlie. "We keep them until the girls havetheir babies. They teach us the ABC's of space, mass and dimension. "

Pete nodded. "That is, if you can make the people put up with them foranother six months or so. "

Tommy sighed. "In a word--yes. So far we've gotten nowhere at a thousandmiles an hour. "

 * * * * *

"I can't do it!" the cosmetician wailed, hurling himself down on a chairand burying his face in his hands. "I've failed. Failed!"

The Grdznth sitting on the stool looked regretfully from the cosmeticianto the Public Relations men. "I say--I _am_ sorry. .. . " His coarse voicetrailed off as he peeled a long strip of cake makeup off his satinygreen face. 

Pete Greenwood stared at the cosmetician sobbing in the chair. "What'seating _him_?"

"Professional pride, " said Tommy. "He can take twenty years off the faceof any woman in Hollywood. But he's not getting to first base withGorgeous over there. This is only one thing we've tried, " he added asthey moved on down the corridor. "You should see the field reports. We've tried selling the advances Earth will have, the wealth, the power. No dice. The man on the street reads our PR-blasts, and then looks up tosee one of the nasty things staring over his shoulder at the newspaper. "

"So you can't make them beautiful, " said Pete. "Can't you make themcute?"

"With those teeth? Those eyes? Ugh. "

"How about the 'jolly company' approach?"

"Tried it. There's nothing jolly about them. They pop out of nowhere, anywhere. In church, in bedrooms, in rush-hour traffic through LincolnTunnel--look!"

Pete peered out the window at the traffic jam below. Cars were snarledup for blocks on either side of the intersection. A squad of trafficcops were converging angrily on the center of the mess, where a streamof green reptilian figures seemed to be popping out of the street andlumbering through the jammed autos like General Sherman tanks. 

"Ulcers, " said Tommy. "City traffic isn't enough of a mess as it is. Andthey don't _do_ anything about it. They apologize profusely, but theykeep coming through. " The two started on for the office. "Things aregetting to the breaking point. The people are wearing thin from sheerannoyance--to say nothing of the nightmares the kids are having, and thetrouble with women fainting. "

The signal light on Tommy's desk was flashing scarlet. He dropped into achair with a sigh and flipped a switch. "Okay, what is it now?"

"Just another senator, " said a furious male voice. "Mr. Heinz, myarthritis is beginning to win this fight. Are you going to see me now, or aren't you?"

"Yes, yes, come right in!" Tommy turned white. "Senator Stokes, " hemuttered. "I'd completely forgotten--"

The senator didn't seem to like being forgotten. He walked into theoffice, looked disdainfully at the PR-men, and sank to the edge of achair, leaning on his umbrella. 

"You have just lost your job, " he said to Tommy, with an icy edge to hisvoice. "You may not have heard about it yet, but you can take my wordfor it. I personally will be delighted to make the necessaryarrangements, but I doubt if I'll need to. There are at least a hundredsenators in Washington who are ready to press for your dismissal, Mr. Heinz--and there's been some off-the-record talk about a lynching. Nothing official, of course. "

"Senator--"

"Senator be hanged! We want somebody in this office who can manage to_do_ something. "

"Do something! You think I'm a magician? I can just make them vanish?What do you want me to do?"

The senator raised his eyebrows. "You needn't shout, Mr. Heinz. I'm notthe least interested in _what_ you do. My interest is focused completelyon a collection of five thousand letters, telegrams, and visiphone callsI've received in the past three days alone. My constituents, Mr. Heinz, are making themselves clear. If the Grdznth do not go, I go. "

"That would never do, of course, " murmured Pete. 

The senator gave Pete a cold, clinical look. "Who is this person?" heasked Tommy. 

"An assistant on the job, " Tommy said quickly. "A very excellentPR-man. "

The senator sniffed audibly. "Full of ideas, no doubt. "

"Brimming, " said Pete. "Enough ideas to get your constituents off yourneck for a while, at least. "

"Indeed. "

"Indeed, " said Pete. "Tommy, how fast can you get a PR-blast topenetrate? How much medium do you control?"

"Plenty, " Tommy gulped. 

"And how fast can you sample response and analyze it?"

"We can have prelims six hours after the PR-blast. Pete, if you have anidea, tell us!"

Pete stood up, facing the senator. "Everything else has been tried, butit seems to me one important factor has been missed. One that will takeyour constituents by the ears. " He looked at Tommy pityingly. "You'vetried to make them lovable, but they aren't lovable. They aren't evenpassably attractive. There's one thing they _are_ though, at least halfof them. "

Tommy's jaw sagged. "Pregnant, " he said. 

"Now see here, " said the senator. "If you're trying to make a fool outof me to my face--"

"Sit down and shut up, " said Pete. "If there's one thing the man in thestreet reveres, my friend, it's motherhood. We've got several hundredthousand pregnant Grdznth just waiting for all the little Grdznth toarrive, and nobody's given them a side glance. " He turned to Tommy. "Getsome copywriters down here. Get a Grdznth obstetrician or two. We'regoing to put together a PR-blast that will twang the people'sheart-strings like a billion harps. "

The color was back in Tommy's cheeks, and the senator was forgotten as adozen intercom switches began snapping. "We'll need TV hookups, andplenty of newscast space, " he said eagerly. "Maybe a few photographs--doyou suppose maybe _baby_ Grdznth are lovable?"

"They probably look like salamanders, " said Pete. "But tell the peopleanything you want. If we're going to get across the sanctity of Grdznthmotherhood, my friend, anything goes. "

"It's genius, " chortled Tommy. "Sheer genius. "

"If it sells, " the senator added, dubiously. 

"It'll sell, " Pete said. "The question is: for how long?"

 * * * * *

The planning revealed the mark of genius. Nothing sudden, harsh, orcrude--but slowly, in a radio comment here or a newspaper story there, the emphasis began to shift from Grdznth in general to Grdznth asmothers. A Rutgers professor found his TV discussion on "Motherhood asan Experience" suddenly shifted from 6:30 Monday evening to 10:30Saturday night. Copy rolled by the ream from Tommy's office, refinedcopy, hypersensitively edited copy, finding its way into the light ofday through devious channels. 

Three days later a Grdznth miscarriage threatened, and was averted. Itwas only a page 4 item, but it was a beginning. 

Determined movements to expel the Grdznth faltered, trembled withindecision. The Grdznth were ugly, they frightened little children, they_were_ a trifle overbearing in their insufferable stubbornpoliteness--but in a civilized world you just couldn't turn expectantmothers out in the rain. 

Not even expectant Grdznth mothers. 

By the second week the blast was going at full tilt. 

In the Public Relations Bureau building, machines worked on into thenight. As questionnaires came back, spot candid films and street-cornerinterview tapes ran through the projectors on a twenty-four-hourschedule. Tommy Heinz grew thinner and thinner, while Pete nursed sharppost-prandial stomach pains. 

"Why don't people _respond_?" Tommy asked plaintively on the morning thethird week started. "Haven't they got any feelings? The blast is washingover them like a wave and there they sit!" He punched the private wireto Analysis for the fourth time that morning. He got a man with ahag-ridden look in his eye. "How soon?"

"You want yesterday's rushes?"

"What do you think I want? Any sign of a lag?"

"Not a hint. Last night's panel drew like a magnet. The D-Date tag yousuggested has them by the nose. "

"How about the President's talk?"

The man from Analysis grinned. "He should be campaigning. "

Tommy mopped his forehead with his shirtsleeve. "Okay. Now listen: weneed a special run on all response data we have for tolerance levels. Got that? How soon can we have it?"

Analysis shook his head. "We could only make a guess with the data sofar. "

"Fine, " said Tommy. "Make a guess. "

"Give us three hours, " said Analysis. 

"You've got thirty minutes. Get going. "

Turning back to Pete, Tommy rubbed his hands eagerly. "It's starting tosell, boy. I don't know how strong or how good, but it's starting tosell! With the tolerance levels to tell us how long we can expect thisprogram to quiet things down, we can give Charlie a deadline to crackhis differential factor, or it's the ax for Charlie. " He chuckled tohimself, and paced the room in an overflow of nervous energy. "I can seeit now. Open shafts instead of elevators. A quick hop to Honolulu for anafternoon on the beach, and back in time for supper. A hundred miles tothe gallon for the Sunday driver. When people begin _seeing_ what theGrdznth are giving us, they'll welcome them with open arms. "

"Hmmm, " said Pete. 

"Well, why won't they? The people just didn't trust us, that was all. What does the man in the street know about transmatters? Nothing. Butgive him one, and then try to take it away. "

"Sure, sure, " said Pete. "It sounds great. Just a little bit _too_great. "

Tommy blinked at him. "Too great? Are you crazy?"

"Not crazy. Just getting nervous. " Pete jammed his hands into hispockets. "Do you realize where _we're_ standing in this thing? We're outon a limb--way out. We're fighting for time--time for Charlie and hisgang to crack the puzzle, time for the Grdznth girls to gestate. Butwhat are we hearing from Charlie?"

"Pete, Charlie can't just--"

"That's right, " said Pete. "_Nothing_ is what we're hearing fromCharlie. We've got no transmatter, no null-G, no power, nothing except awhole lot of Grdznth and more coming through just as fast as they can. I'm beginning to wonder what the Grdznth _are_ giving us. "

"Well, they can't gestate forever. "

"Maybe not, but I still have a burning desire to talk to Charlie. Something tells me they're going to be gestating a little too long. "

They put through the call, but Charlie wasn't answering. "Sorry, " theoperator said. "Nobody's gotten through there for three days. "

"Three days?" cried Tommy. "What's wrong? Is he dead?"

"Couldn't be. They burned out two more machines yesterday, " said theoperator. "Killed the switchboard for twenty minutes. "

"Get him on the wire, " Tommy said. "That's orders. "

"Yes, sir. But first they want you in Analysis. "

Analysis was a shambles. Paper and tape piled knee-deep on the floor. The machines clattered wildly, coughing out reams of paper to be gulpedup by other machines. In a corner office they found the Analysis man, pale but jubilant. 

"The Program, " Tommy said. "How's it going?"

"You can count on the people staying happy for at least another fivemonths. " Analysis hesitated an instant. "If they see some baby Grdznthat the end of it all. "

There was dead silence in the room. "Baby Grdznth, " Tommy said finally. 

"That's what I said. That's what the people are buying. That's whatthey'd better get. "

Tommy swallowed hard. "And if it happens to be six months?"

Analysis drew a finger across his throat. 

Tommy and Pete looked at each other, and Tommy's hands were shaking. "Ithink, " he said, "we'd better find Charlie Karns right now. "

 * * * * *

Math Section was like a tomb. The machines were silent. In the office atthe end of the room they found an unshaven Charlie gulping a cup ofcoffee with a very smug-looking Grdznth. The coffee pot was floatinggently about six feet above the desk. So were the Grdznth and Charlie. 

"Charlie!" Tommy howled. "We've been trying to get you for hours! Theoperator--"

"I know, I know. " Charlie waved a hand disjointedly. "I told her to goaway. I told the rest of the crew to go away, too. "

"Then you cracked the differential?"

Charlie tipped an imaginary hat toward the Grdznth. "Spike cracked it, "he said. "Spike is a sort of Grdznth genius. " He tossed the coffee cupover his shoulder and it ricochetted in graceful slow motion against thefar wall. "Now why don't you go away, too?"

Tommy turned purple. "We've got five months, " he said hoarsely. "Do youhear me? If they aren't going to have their babies in five months, we'redead men. "

Charlie chuckled. "Five months, he says. We figured the babies to comein about three months--right, Spike? Not that it'll make much differenceto us. " Charlie sank slowly down to the desk. He wasn't laughing anymore. "We're never going to see any Grdznth babies. It's going to be alittle too cold for that. The energy factor, " he mumbled. "Nobodythought of that except in passing. Should have, though, long ago. Twocompletely independent universes, obviously two energy systems. Incompatible. We were dealing with mass, space and dimension--but theenergy differential was the important one. "

"What about the energy?"

"We're loaded with it. Super-charged. Packed to the breaking point andway beyond. " Charlie scribbled frantically on the desk pad. "Look, ittook energy for them to come through--immense quantities of energy. Every one that came through upset the balance, distorted our wholeenergy pattern. And they knew from the start that the differential wasall on their side--a million of them unbalances four billion of us. Allthey needed to overload us completely was time for enough crossings. "

"And we gave it to them. " Pete sat down slowly, his face green. "Like arubber ball with a dent in the side. Push in one side, the other sidepops out. And we're the other side. When?"

"Any day now. Maybe any minute. " Charlie spread his hands helplessly. "Oh, it won't be bad at all. Spike here was telling me. Mean temperaturein only 39 below zero, lots of good clean snow, thousands of nice jaggedmountain peaks. A lovely place, really. Just a little too cold forGrdznth. They thought Earth was much nicer. "

"For them, " whispered Tommy. 

"For them, " Charlie said. 

Transcriber's Note:

 This etext was produced from "Tiger by the Tail and Other Science Fiction Stories by Alan E. Nourse" and was first published in _Galaxy_ October 1956. 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.