Arden stood up, tossed Channing's napkin at him, and started toward the door. Channing watched her go, his hand making motions on the tablecloth. His eyes fell to the table and he took Franks' pencil and drew a long curve from a spot of gravy on one side of the table to a touch of coffee stain on the other. The curve went through a bit of grape jelly near the first stain. "Here goes the tablecloth strategist," said Franks. "What now, little man?" "That spot of gravy," explained Don, "is Mars. The jelly is the _Empress of Kolain_. Coffee stain is Venus, and up here by this cigarette burn is Venus Equilateral. Get me?" "Yop, that's clear enough." "Now it would be the job for seventeen astronomers for nine weeks to predict the movements of this jelly spot with respect to the usual astral standards. But, fellows, we know the acceleration of the _Empress of Kolain_, and we know her position with respect to Mars at the instant of take-off. We can correct for Mars' advance along her--or his--orbit. We can figure the position of the _Empress of Kolain_ from her angular distance from Mars! That's the only thing we need know. We don't give a ten-dollar damn about her true position." Channing began to write equations on the tablecloth. "You see, they aren't moving so fast in respect to us. The course is foreshortened as they are coming almost in line with Venus Equilateral, curving outward and away from the Sun. Her course, as we see it from the station here, will be a long radius-upward curve, slightly on the parabolic side. Like all long-range cruises the _Empress of Kolain_ will hoist herself slightly above the plane of the ecliptic to avoid the swarm of meteors that follow about the Sun in the same plane as the planets, lifting the highest at the point of greatest velocity. "I get it," said Franks. "We get the best beam controller we have to keep the planet on the cross hairs. We apply a spiral cam to advance the beam along the orbit. Right?" "Right." Don sketched a conical section on the tablecloth and added dimensions. He checked his dimensions against the long string of equations, and nodded. "We'll drive this cockeyed-looking cam with an isochronic clock, and then squirt a beam out there. Thank the Lord for the way our beam transmitters work." "You mean the effect of reflected waves?" asked Chuck. "Sure," grinned Don. "There's plenty of radar operating at our transmitting frequencies or near by. So far, no one has ever tried to radar anything as small as a spacecraft at that distance, though getting a radar signal from a planet is duck soup. Yet," he reflected cheerfully, "there are a couple of things we have handy out here, and one of them is a plethora of power output. We can soup up one of our beam transmitters and use it with a tightened beam to get a radar fix off of the _Empress of Kolain_." "And then?" asked Franks. "Then we will have left the small end, which I'll give to you, Walt, so that you can have part of the credit."