Edwin and Inion passed through several smaller villages on their route, usually one just a bit over a days travel from the prior. None were that spectacular, though, consisting of a few buildings and a tavern or inn (what was the difference?), usually with a marginally higher concentration of hos in its vicinity.
There were also lots of Curicnan way-shrines, and they passed one or two each day. Edwin was content with his current sleeping arrangent atop his carriage, though, and so didnt bother using them. Sotis, Inion would join him atop the roof, and the two would stargaze for hours until Edwin fell asleep. About half the ti, she was still there when he woke up. It was it was nice, to have her by his side.
If only humans could get along with him. Or, he supposed hed accept other fey as friends, but there was no way hed find another Inion.
Edwin kept himself busy, mainly experinting with his Apparatus. Of all his new Skills, it was the one he was perhaps the most excited to really try out and experint with. Limits loosening as the level increased implied that hed get the most benefit of any of his Skills from leveling it, too. Maybe he could make the crystal flexible at so point.
For now, though, Edwin had a simple, if ambitious, goal, and one that could be fairly powerful if he could manage it. He wanted to get a comprehensive list of Sappers Apparatuss physical specifications. Refractive index for fun with light, density and tensile strength for building things, heat conductivity and capacity for fun with fire and insulation, electrical conductivity in case that ever ca up, and more. That would take him more ti than even he had right now, so he decided to focus his efforts on the more imdiately practical quantities.
Starting off with optics, Edwin quickly found that he only half-rembered the required equations that hed need to figure out the refractive index, so he had to re-derive most of them from scratch. In that whole process, Mathematics proved to be an utter lifesaver, and Nuracy helped a ton. Even still, he needed to use Almanac and mory to avoid getting lost in the numbers. Matrix translations were no joke, even if the derivations themselves werent too bad, though far, far from trivial.
His plan was to make a lens out of his apparatus crystal, figure out what its focal length was, run so calculations based on the shape of the lenses and using the refractive index as the unknown, and solve from there. Normally, you knew the refractive index- glass was 1.5, water was 1.33, air was basically 1- and were trying to find the focal length, but the nice thing about math was it didnt matter what your unknown was, so long as there was only one.
Edwin had at first tried to use the thin-lens optics equations, but his results were wildly inconsistent until he stumbled upon his problem- naly that his lenses werent infinitely thin. Trying to asure the refractive index by making a prism didnt work- the light just exited a uniform bluish color that matched his crystal. That implied things, but he held his excitent until he could asure it more precisely.
He couldnt calculate the refraction index just from the pyramids refraction either, sadly. The sorts of calculations needed required all sorts of tricky reference fra changes and angle calculations that Edwin wasnt sure he wanted to tangle with.
It was hard enough for him to rederive the thick-lens matrix equations, he didnt want to do any more work than he needed to.
So, Edwin now sat with an array of Apparatus crystal (he needed a better na for it than just that hed think of one eventually) rods, each as close to perfectly round and 1 centiter in diater as he could make them. Once he had numbers on the refractive index, he could do more work to figure out how precise he could make his Apparatus.
Thick-lens equations had been a colossal pain for Edwin once upon a ti, but considering these days he could multiply two nine-by-nine matricies in his head thanks to Mathematics it wasnt so bad. It just involved three basic components: a term to account for the initial refraction, when light passed from the air into the lens, a translation term for how thick the lens was, and a term to account for the refraction out of the lens and back into the air.
Things got more complicated when multiple lenses got involved, or when you started including reflection terms, but he was keeping things simple for now. And that ant figuring out the initial ray-matrix for his light source of the sun. If he assud it was infinitely far away, all of its light would be parallel, and by defining his axes properly he could
Anyway.
Basically, hed be running the calculation for a single ray of light with an angle of 0 radians at 0.5 centiters, asure where it crossed the y-axis- naly, where the focal point of the rod was- and from there he could back-calculate what the refractive index was.
He cracked his knuckles and pulled up Almanac. This would be a lot of numbers.
Even Edwins eyes were glazing over by the ti he finally got his equation in a half-readable state. He triumphantly looked over all he had accomplished as he did the final calculations
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L=2 cm, R = 1 cm, n = 1, n=?, q = 5.5 cm
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