If you believed in orbits, this meant that for a stone in a tilted orbit to return to its highest elevation was the fastest thing. For the Splinter to rotate around its axis took a little longer. And for a stone in an eccentric orbit to return to its greatest distance from the Hub took longer still.
Three phenomena, three different times.
«Where has all the simplicity gone?» Zak lamented.
Curiously, if he fed his original assumptions into the templates — if the shomal-junub weight was equal to the hidden rarb-sharq weight that was balanced by the spin, and if the garm-sard weight was, in total, three times as much — then all three periods would have been identical. The number three really would have made things very simple.
Roi took a break from the Null Chamber, and traveled a short way into the garmside to give herself some weight again, lest she lose too much strength. Even as she headed out of the Calm into the sights and sounds of ordinary life, she couldn't stop thinking about motion and orbits. At the end of each shift, when her mind had once filled with the images of weeds, now she saw stones, bouncing and looping and swerving in front of her. When she woke, her first thought was always of finding a new way to check Zak's conclusions. Their calculations deriving the Splinter's spin from the looping stones could be flawed. Or the weight measurements they had fed into the templates could be wrong.
Zak's simple experiment, when he'd launched a stone along the Null Line, had been compelling: it had made it obvious that the Splinter was turning while the stone was in flight. There had to be a way to measure the Splinter's rotation directly using that effect, without allowing the complications of the garm-sard weight to intrude. If you could keep the stone moving somehow — without ever letting it go too far from the Null Line — its path would act as a reference against which the turning of the Splinter could be judged.
How could you rein it in, though, without stopping it completely?
When Roi found the answer, she turned around and headed straight back to the Null Chamber. Zak wasn't there when she arrived, but she felt no hesitation about helping herself to his stores of material. They were a work team, now. These things were their common tools, not a lone eccentric's hoard.
Zak arrived just as she was putting the finishing touches to her apparatus, trial and error having led to some changes in the original design. Two equally heavy stones were glued firmly to the ends of a small bar. The bar was free to pivot around its center, where it was threaded by a stiff metal wire, which was bent around into a flat rectangular supporting frame large enough for the bar to turn continuously without obstruction. Another pivot, opposite the bar, attached the frame to the wire of the Null Line; this pivot left the frame free to rotate around the shomal-junub axis.
After they'd exchanged greetings, Zak watched in silence as Roi greased the pivots, marked the initial alignment of the frame on a card fixed to the wire above it, then gave the bar a flick to set it spinning.
An earlier version — with the bar spinning around one of its ends, and a single stone at the other — had been unbalanced, shuddering mercilessly, causing the frame to slip back and forth. This design seemed to have fixed that problem. All Roi could do now was wait.
Slowly but unmistakably, the plane of the spinning bar turned. Or, stayed fixed while everything in the chamber, everything in the Splinter, wheeled around it.
Zak said simply, «Who can doubt it now?»
There was no need to measure the speed of the stones. There were no elaborate calculations to perform. One rotation of the frame corresponded to one rotation of the Splinter, if they understood anything at all.
They set up a shomal-junub stone a short distance away, to compare the motions. After a while, no doubt remained that the period of this new phenomenon agreed with their earlier calculations, based on the more complex motion of the looping stones. The plane of the spinning bar took
Roi didn't know what to feel. She was relieved to see two lines of evidence converging on the same answer for a change, but she'd actually been hoping that this experiment might yield a different result, one that removed some of the complexity that had begun to infest the theory of orbits.
«Where did all the simplicity go?» she joked, echoing Zak's refrain.
«I think I know where some of it went,» he replied. «I didn't dare mention this before, because I wasn't confident in our results. But now that you've confirmed the period of the spin, it doesn't seem so foolish any more.»
Roi said, «Go on.»