Given that the primary motive for building power plants was electric light, and the mirrors don't work at night...

Any use of electricity or any other use of coal is what I am asking from powering a city to a solar cooker would be relevant. On the other hand I do get that the main use of electricity for the majority of that time period is electrical lighting. Not every area would be connected to water ways so while demand may not realistically exist in every city without the right political decisions some parts of the nation could still prefer a solar option.

Not just lights, things like pumps, which need to be run 24/7 don't work with solar either.

@John Depending what they're pumping they could find a way.

@cmaster efficiency would not be as big a problem as you think, steam engines would be more than 200 years old at this point.

@immibis for many pumps that steam engines were used for, not running at night would be a problem,but keep in mind hydroelectric was invented in the mid 1800's. The biggest loss is the lack of railroads and steam ships, improved transport was a major factor in improving infrastructure and standard of living. for the first time in history you did not have to live near a farm to get fresh produce.

@AlexP it still is. Roughly 19% of the world's electrical demand is for lighting.

The first electric locomotive was built in 1837 and used batteries.

you can get around the aiming problem by using concave mirrors to focus on pipes, as in solar water heater or solar oven concepts. They trade efficiency for simplicity.

@JoshVanderHook you don't need mirrors for heating water, just paint the pipes black. Very effective, even in temperate climates.

@Dan w. Strange false dichotomy. Absorbent materials plus local mirrors would get more heat, even.

@JoshVanderHook – Sorry, you're absolutely right, mirrors would help (and almost certainly boil water in the OP's hot desert environment), and local mirrors wouldn't need aiming. My comment was more because people don't realise how simple and effective solar hot water heating is even in temperate climates.

Check out en.wikipedia.org/wiki/… . Essentially a modern solution to long term solar power storage. Use mirrors to superheat salt, and then store it in giant thermoses until you need it to produce steam. The tech level should be just enough to make this feasible, with plenty of room for improvement

Archimedes used this concept well well before the 19th century so it is plausible.

Stop using water! Liquid sodium chloride works better for solar power here and could be used.

@DanW You absolutely need mirrors if you want to power a machine with the steam: There is a max temperature associated with the level of illumination, and for unconcentrated sunlight, that's somewhere around 109°C, if I remember correctly. If you want some decent, high-pressure, hot steam, you need temperatures more in the range of 500°C and upwards. That's what you use the mirrors for: They concentrate the sunlight, so the achievable temperature rises, so you get better steam. Black pipes are only good for heating a home (but for that, they are an excellent solution).

@Joshua As a storage medium, maybe. As a working medium for an engine, no way. You may heat the salt during day, and produce the steam at night with the stored heat, though. But, I guess, a big pile of sand would be the cheaper alternative.

@cmaster: Modern solar complexes (that aren't panels) use liquid sodium as an intermediate collector for efficiency reasons.

@Joshua Ah, I understand. I guess, the main reason is that the liquid sodium does not put pressure into the collector pipes, so the pipes can be cheaper. Still, after the heat is collected, and possibly stored, there's always a water evaporation stage before the steam engine/turbine.

@cmaster good point, I’d not realised you need it that hot.

@DanW You can build a steam machine that runs on 109°C steam, so you don't exactly need hotter steam. However, that machine would be horribly inefficient because the steam is not that much hotter than the surrounding air you use to cool your machine. That's why you want higher steam temperatures, to increase the efficiency of the machine. The hotter the steam, the more efficient the machine can be. If we could, we'd heat the steam to 5000°C to turn more energy into electricity. Sadly, we don't have the materials for that... (Pipes that hold the steam, also water dissociates at 1700°C.)

The 19th century was known as the "golden age of clockwork" for a reason. Keeping the mirrors aligned is trivial, given a power source for the mechanism.

@Joshua, molten salt is horribly corrosive. Liquid sodium is even more so. Modern alloys can deal with that, but 1800s steel wouldn't stand a chance.