I understand that ships used an Engine Order Telegraph to communicate between the bridge and the engine room - but all of the ones I have seen only have a few set speeds - "half ahead," "full ahead" and so on. When ships with various top speeds were traveling together (or when ships were traveling through speed-limited navigation channels), did they have to continually alter the EOT position? Or was there a way to set a certain speed? How did that work?
My next question - how did the ship engineer control the speed, himself? Did steamships have a steam throttle (like a steam car), or was speed increased simply by generating more steam? If there was a steam throttle, why didn't they just run the controls up to the bridge and give the helmsman direct control? If speed was increased just by increasing steam pressure, did the engineer have tabled that told him how much speed would increase at a given steam pressure, or did they just rely on gut knowledge?
Its all about RPM! And specifically RPM of the prop and prop shaft for actually controlling the speed of the vessel. The engine room would know how many RPM would be needed to make so many knots. And as prior to the development of the Reduction Gear or Steam Turbine or Turbo-Electric Drive, steam engines were usually direct engines, that meant that at whatever RPM the engine turned over at so too would the propeller shaft rotate. As the years came on newer technology allowed for more advanced steam turbine or Turbo-Electric designs, allowing even greater control over the RPM's transferred to the shaft, either through gears, or simply having the high rpm steam turbines run into a generator that would then power the low rpm propeller. Its sort of a tough thing to talk about "steamships" and for our purposes here I am trying to focus on older Triple Expansion and direct power designs. But we are in many ways still in the age of the steamship with modern nuclear subs and super carriers being powered by steam turbines.
For instance to reach her max speed of 21 knots, the last US Battleships with Triple Expansion Engines, USS Texas, had to get up to 125 RPM. As for why the bridge didn't and still today doesn't control it directly is a practical one. The amount of other things such as boiler temp, water levels, coal or oil levels, etc, that need to be monitored would be information overload to the bridge or CiC trying to fight the ship. And yes often fixed somewhere in the engine rooms themselves would be various quick reference tables for usage in how much steam was required for how many revolutions for how much speed, though it would be expected that at least the CHENG or Chief Engineer would know most of them by heart typically.
As for maintaining coherent squadrons with ships of different speeds, it was often a matter of conforming to established regulations. Often fleets would distribute standing orders for flag hoists that would correspond to a set speed. So "Cruising Speed 1" would be 10 Knots, "Battle Speed 1" 18 knots and so on. So that the Admiral could signal to his force the squadron speed. Then there were whole tomes of maneuver and signal books to rearrange or fight the squadron with either avoiding any ships having to change speed, or allow for semi independent maneuvering. So with that info the ships behind could adjust and set revolutions and power levels as needed. Otherwise voice tubes, runners, or other voice communications could allow for more exact orders about setting revolutions for X Knots. There is also the factor that conscious design decisions played into maintaining cohesive squadrons, especially by the later decades of the 1800's. In particular come the 1900's the USN for commissioned 12 battleships across 5 classes known as the "Standard Types" they were designed to all have similar and predictable characteristics even when operating in mixed company. Part of that then was all having a top speed of roughly 21 Knots.
From here /u/CiderDrinker gives an solid run down on how it works for the OotW in actually getting to the desired speed. More steam raised and more power would mean more speed but also a faster rate of fuel burn. And ships could have very complex powerplants and multiple types of engines all in the name of allowing for economical cruising and performance in battle.