help. Even if you could prove the sun was not rotating and you could see the other side half the time, there was no way of telling it was the other side! Consequently, there was no way to prove the Earth moved around the sun. Except that whoever or whatever it was that called herself Pallas Athene said that he would. Well, if it were that important, she could have left a clue! She had a reason for why she hadn't too: she had said whether the Earth moved was unimportant; what was important was the method by which he proved that it moved.
Then there was the engine. He recalled that his last problem had been to work out how steam could generate power. It was not that steam did not have power, for he had previously seen the results of water heated in an enclosed vessel: the subsequent explosion was quite horrifying. The problem was how to control it, and make it do something useful.
His first thought had been to reverse the principle of a small hand water pump that he had seen once before. Instead of a hand pulling the piston up and down, sucking and pushing water, the steam could come and go, pushing a piston up and down. Simple! Except that it was not that easy. Valves could easily be designed to open when they were pushed from one side, and close when pushed from the other, so the water did what was asked of it, and a hand can equally push or pull. Steam, however, would only push. The problem with the entry valve was that the steam was always pushing, so closing it to stop steam entering was difficult. Worse, if the steam closed the exit valve while it was entering, it would push even harder while it was supposed to be exiting! What could he do?
After speaking on this to Timothy, he received the laconic reply, "Use geometry."
Great! How?
"Quite simple, really," Timothy shrugged. "You need two paths, and a means of switching."
"Explain!" a frustrated Gaius muttered. But Timothy was not that interested in going further. Conceptually, the task was done.
He saluted another cohort, then glanced out at the marching legion. Not far away was a small crossroads, and a number of carts were waiting patiently. Then, as one cohort passed through, a Centurion stopped the next cohort, and waved the carts through. That, Gaius realized, could be the principle. He needed valves that could be opened and closed, and he could see how to achieve that: he needed some form of controller to switch paths at the right times. A rocker arm would do that. The valve could comprise a single path with, say, a right angle in it, and it could switch between two positions. In one configuration it would connect the steam generator with the cylinder, and in the other, achieved by turning it ninety degrees, it would connect the cylinder with the exit route. That should work. The valve would comprise a cylinder with the path through it that moved tightly inside another cylinder with connecting paths to the steam, the piston, and the exit. That would be easy until, he realized, someone had to make this contraption, and join it to the various pipes.
If the piston drove a wheel, that wheel could drive the rocker arm, as it had to be in phase. The problem now reduced itself to working out how he could make levers pull or push one or more valves into one or the other position. He quickly realized that simply fixing the valve to a lever would not do, because most of the time the valve would be closed to everything. It needed to be fully open to steam through almost all the power stroke, and fully open to the exit through the venting stroke. After some thought, he settled on a rocker arm plus a lever. The rocker arm would have a pin, and the lever would permit the pin to slide up and down a space. Accordingly, when the lever reached close to one extreme of its path, it would pull the rocker arm, which in turn would move the valve one way; when it reached the other extreme it would push the rocker arm, which would push the valve to the other position. All he had to
Sawyer Bennett, The 12 NAs of Christmas