Sir Robert had returned from Scotland that morning and it was he who guessed it. “Jonnie, that group here didn't know who was attacking. Anyone in command here would have been tearing through those books. Have you looked on the corpses?”

That's where they were! In a shoulder bag on the body of the former mine manager up in the snow.

Not more than three hours later, comparing his own and Stormalong's pictures and the texts, he knew he was dealing with Tolneps, Hockners, Bolbods, and Hawvins. And he knew what they looked like and what their capabilities were– all dangerously nasty. There was no listing for the globe-shaped ship with the ring around it or any race of small gray men.

But the following day his luck ran out with Chirk. She had been doing very well. But he made a mistake.

She was sitting, all eight hundred pounds of her, at a desk in the library making some lists. Jonnie was looking at a sheet of figures he had drawn up.

The sheet concerned distances from Earth to various hostile bases nearest to it and the speeds of the types of alien ships. They had different types of drives. For the most part they ran on energy accumulated from suns, but they handled it differently. He was trying to calculate how many months those ships were from their relative bases. Terl's lists of inhabited planets had now been copied off in sheet form and it was evident they didn't include all systems or suns but only those in which Psychlo had an interest.

Jonnie had been amazed to find in other texts that there were four hundred billion suns in this galaxy alone and that this universe contained more than a hundred billion galaxies. And he had sixteen universes to look at.

The possible bases of hostile peoples were easier to mentally encompass. From Earth to this galaxy's center was about thirty thousand light-years. And one light-year was about six trillion miles. All these enemy ships exceeded the speed of light one way or another, but this still made it necessary to compute by how much they exceed it against what base where.

It was an awful lot of Psychlo arithmetic. He was not too patient doing it by hand. Thoughtlessly, he said to Chirk, “Could you help me add these figures up?”

She looked at him, totally blank for about a minute. Then she said, “I don't know how.”

Jonnie smiled. It s just arithmetic. Here, I’ll show you-'

Chirk's eyes glazed. She fell forward across the desk.

There was no response from her. She was totally unconscious. They had to get a forklift in and take her to her room and put her to bed.

Three days later, MacKendrick told Jonnie, “She's just lying there in a coma. Maybe in time she'll come out of it. She seems to have had a heavy shock.”

Although he felt bad about it, Jonnie had an idea now of what the silver capsule in the females was. They were not to be taught any Psychlo mathematics ever!

The key to the whole Psychlo empire must be mathematics. And aside from their arithmetic, he couldn't make head or tail of their equations. It seemed to be a dead end.

They had just completed the installation of a radio telescope when the courier came in.

Angus, his face red, first from sun at lake level and then from wind and snow up at the summit of nearby Mount Elgon, was very proud of himself. The German and Swedish pilots, with something to do besides train under the relentless Stormalong, had helped find and install the huge reflector bowls and relays from the peaks and down to the minesite.

Now that they had the frequencies, Angus was saying, they would soon be hearing everything those monkeys up there were saying to each other. He'd even have them on the screens!

Jonnie's ear caught the far-off approach of the plane above the overcast. He thanked Angus and the pilots and said they had done very well, and yes, now maybe they would know more about the intentions of their visitors.

Glencannon had taken over the ferrying of the vital discs from America. A copy was now going to Doctor MacDermott to bury in a deep underground vault and the originals were coming through to Jonnie in Africa.

Glencannon had lots of news. Pattie had been extremely ill for weeks but Chrissie was nursing her and there was hope. And Chrissie sent her love and said she'd found a lovely old house right near Castle Rock, and some of the Chiefs' wives were helping her find real furniture in old ruins, and she sent her love and when was he coming back?

Castle Rock was now so surrounded with antiaircraft blast cannon it made one fair nervous to fly near it.

Dunneldeen? Oh, he was flying the pants off new recruits but there weren't as many coming in now. Mostly machine operators were getting trained. Ker was fine and sent him some brand-new air masks he'd made that fit better and said not to turn him in for stealing company materials, ha, ha. And here were some personal letters for Sir Robert. And here was the latest set of you-know– whats.

Jonnie went deep underground and got the discs rolling. They had the place well set up now. Watching the female Psychlos, while not letting them handle anything vital, they had learned the use of some of the office machinery they had earlier ignored, and they could copy discs and make blowups of sections with a fine– line accuracy they had not thought possible. They had cabinets for files and all in all they could make the discs “talk” much better.

Terl! He was sitting there doing force equations, incomprehensible. The equations didn't balance and didn't make any sense. He was filling pages and pages with them. Still nothing to do with teleportation.

Jonnie almost skimmed by it. He backtracked. The pictures showed Terl getting up, going over to the cabinet, and opening up another false bottom. He took out a huge sheet of paper, so big it would take three scanners' views to encompass it. The paper was very old, creased until it nearly fell apart, stained brown and faded.

Terl spread it out, looked at it and then shook his head over it. He traced one claw along the north side of the big dam, way to the southwest of the American minesite. He nodded. Then he wadded the paper up and threw it at the shredder bin. He wrote down some footage figures and some voltage figures and then went back to his equations, and it was just equations for the next two days. And that was all there was in the discs.

It took an hour of patching from three different scanner channels to get it. But Jonnie recovered the huge piece of paper in its entirety and got a half-dozen huge copies of it.

It was entitled, “Defense Installations of Planet Number 203,534.” Jonnie knew already that was the Psychlo name for Earth.

It showed every minesite, every dam, every gun battery, and every ? A little symbol that trailed around each dam and below each power line from dams to minesites and branch minesites. Jonnie had no idea what that symbol was.

But there was a goody he had never, never dreamed of. Marked clearly was a firing, transshipment platform!

He compared the Psychlo mass of numbered locations with a man-map of ancient times. The second platform was alongside a dam which had once been named "Kariba" in a country which had once been called "Rhodesia" and then “Zimbabwe.”

The platform was marked

“Emergency Defense Armament Receipt Point.” Obviously, if the main minesite were ever knocked out, Psychlo could send in another force or the Psychlo command on the planet could demand troops or at least inform the home office.

Hopes soaring, but a little held down by the age of the map and Terl's treatment of it, Jonnie had a marine attack plane on the line and Scots piling into it. Robert the Fox boarded hastily. Just as they were about to close the door, MacKendrick piled in with a medical kit. Jonnie sent the plane racing to the south.