Despite having the ability to produce fairly standardized components, I still didn't actually have the ability to put numbers to everything that I needed to. I have a decent idea about the relative ways that each component operates, whether it be inductors, transistors, capacitors, or antennas, but I don't actually have a formula to use. I already made a functional voltmeter, so the next important step was making an ammeter so that I could have a more complete picture of what I was doing while working in circuits.

For now, both the voltmeter and ammeter are simply numbered 1-20, with no units, but the idea moving forward is that I'll define the units as I work with standard sized equipment. For example, if I start by trying to define a capacitor's equation, I know that the area between the two terminal plates, the distance between the plates, voltage, and the material separating them influences the amount of charge they hold. From there, I can vary the physical dimensions of the capacitor to make measurements as I charge the capacitor at a known voltage until it stops charging. By adding together the amperage values multiplied by the time interval between each measurement, I get a decent approximation of the total capacitance for that capacitor.

I can then repeat that across different capacitor configurations to derive an empirical formula for capacitance. After I do that, I can repeat similar processes for the other components. After all the components have an arbitrary measurement system, I'll move on to the next step. The next step will be attempting to integrate them into a working radio circuit. I'll be attempting the much simpler amplitude modulation system to make things easier on myself.

If I can then derive a functional equation for determining frequencies based on the arbitrary component units, I can then take all that data and standardize my electrical units across the board. The main units that I'll have to standardize against are our units of length and time, since they are the main units involved in all the components. Whether in the wavelength to frequency conversion for the antenna, the distance between conductive plates or the area of their faces in capacitors, or the internal radius of an inductance coil, they all rely on length, which means standardizing the other units to all play nicely in the equations I'll define will save a lot of people a lot of headache down the road. Similarly, time is used in the calculations for the components, since I'll be measuring amps per unit time, and similarly calculating how long an induction circuit takes to reach near zero impedance.

Which makes me realize that we're actually starting to breach the precipice where a standardized system of measurements can actually be achieved and holds value. The main reason for a metric system is to make these conversions easy, after all. The hard part is actually having a reasonable standard that makes sense. the SI system of earth had 7 base units of meters, seconds, kilograms, moles, candelas, kelvins, and amperes. It's possible that this universe also has only 7 units, as I've been measuring mana density against mass based on fluorite crystals. Since the joule is defined via the kilogram, and I've seen magic have both energy and mass related effects, it's entirely possible that it too may be able to be defined via mass.

In any case, a true system like the metric system is just beyond our grasp currently, but after the academy is established, I'd expect we could develop it over the course of a few decades. The main holdup is essentially repeating the same process I'll be doing on the handful of electrical components I'm developing to define various equations that govern them, except over all the various measuring tools and components. From there, you need to start making definitional decisions on what values convert to other values reproducibly and effectively. The kilogram was defined by a physical object stored in a vault for almost the entirety of the existence of the unit, so defining things efficiently will be an important aspect of that academic endeavor.

Time really flew as I tried to derive empirical formulas for all the electromagnetic components I'd been working on. Since it takes time to create each component, set everything up, then run multiple tests to ensure data quality, I ended up taking 140 days deriving equations, developing radio circuits, testing them, then adjusting the unit definitions so that they all made sense. I had to define the value of second using a pendulum as part of that process. Again, these units aren't perfect, because there are variations in the way they're measured, but at least they convert fairly well now as a result.

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Until now, most of our time keeping was approximate, but after consulting the dwarves, they'd already created a time system for divvying up the day into equal time blocks, so I just had to use that to define a pendulum that could count that amount of time. In the time I took developing all these components and making a working small scale radio, the details of all the mainland trade deals and the cultural exchange cities treaties were settled.

For the next few years, it seems like we'll be providing the dwarves with more machine guns and bullets, though the amount of tanks is being reduced to only a few new units a year. There has been quite the reshuffling of population as well. Many dwarves that were on Kembora left for the mainland, but many new ones came to settle into the new city. They'll be under the same charter that Zeb and I defined in the past, where they'll have their own city government that is regulated under the national government, with their own minister representative. The city is in the process of being rebuilt, since so much of it was initially built as basic housing for the war.

We've set the date for the city elections and official recognition as the first of the year. Before then, they've been given certain executive liberties to rebuild and reshape the city. After that point, they'll have to follow the governmental charter. Not that there isn't any oversight in what they're doing, just that it's basically been given a pass to cut in line for all approvals, and is being given preferential access to extra construction resources until that time.

This was part of the negotiation terms that were agreed upon, so I'm not going to complain, especially given the initial incident that was waiting for us when we got back to the island. The central section of tunnel still hasn't made it to the top of the mountain either, and mining has slowed drastically while construction is going on. There are so many available construction materials piled around the island, and plenty of stockpiled ores and metals that the need to continue excavation is mostly gone.

I do hope I don't have to wait too long, as I've already replicated morse code wireless transmissions on the small scale. After I've figured out how to make a condenser microphone, there won't be much more that I can design before I want to put things into practice. I believe it should actually be a pretty straightforward application of two of the equations I've come up with for capacitors. By having one plate of a capacitor be made from a thin foil, I can have it act as a diaphragm and vibrate with sound waves. The variable distance between the places will cause the capacitance of the capacitor to change. By having it be supplied by a very low amperage voltage, the changes in capacitance will cause the voltage on the output to change slightly. That can then be used with a transistor vacuum tube to modulate the amplitude of the frequency signal from the radio.

After filtering the received signal and amplifying the small received voltage, I'll use a driven electromagnetic coil to pulse a diaphragm on the receiving end with the same pattern that the original signal was received. Based on everything I've done for testing and what I know about frequencies and wavelengths, I'm going to be aiming for a wavelength on the scale of hundreds to the one or two thousand feet range. That should allow sufficient groundwave propagation that a strong signal from the summit can probably reach all the other islands.

There is a lot of physical construction that will need to be completed for that to work, and I'll also need to do more frequency testing and calculations to ensure that we don't have to modify the tower when we put it up. For efficient transmission, we want the tower to be either 1/4 or 1/2 of the wavelength, which means a tower hundreds of feet tall. I have a lot of memories of what those towers look like, despite not having seen one in quite some time, so I think it should actually be easy to put into position using hoist cables and ties to keep it in place.

If we haven't reached the summit from inside the mountain by the time I've completed all the designs for the transmitters, I might work on a magnetic-based loop antenna to allow smaller local receiver units as well. As it currently stands, I already plan on using amplifier circuits after doing band filtering, so a mismatched receiver won't be the end of the world, but they will require a power source to actually hear anything.

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