Judging by the Honeywell R7184A Controller manual, you have one of these:
![illustration of R7184](https://i.stack.imgur.com/XSXvkm.png)
You described it as terminal 4 but the diagram just shows two terminals labelled "T", but that is fine:
![terminal connections of R7184](https://i.stack.imgur.com/P8htrl.png)
I found a manual for an EnviraCom device which shows terminals 2 and 3 are 24vac power:
![enter image description here](https://i.stack.imgur.com/mpouQ.png)
This means we have the right connections, and according to the R7184 manual:
EnviraCOM™ Current Available: 150 mA
So the liming factor here is simply the current available. I can't find any specs at all for the thermostat you posted, but so long as it needs 150 mA or less (at 24 Vac) then it should work. You would make the following connections:
Burner Thermostat Desc
Terminal 4 T W Heating call
Terminal 3 T R or Rh 24Vac
Terminal 2 C 24Vac "Common"
Note: your current wiring may not have W and R connected correctly, because with the two-wire system it doesn't matter. Now that you need a C wire, it is important to have R connected to constant power. If wrong, your thermostat simply won't get power.
If your thermostat draws more than 150 mA, you're going to run into various strange problems that may range from occasional glitches to your burner not working at all, and I'd highly advise against doing this.
If you do need more than 150mA, normally you could upgrade the transformer -- but in this case, it's all an integrated solid-state unit. I'm actually not sure you could wire this up without damaging the burner controller. The safest thing would be to use a separate circuit with a relay, but that is far beyond the original scope so I won't post how do to that unless necessary.
Since in your case, one side of the transformer is grounded. You can simply use a fork or ring terminal, to connect the C
wire to the chassis. Though it appears there's already a wire that's attached to ground, and comes right over near the thermostat wiring. I'd just put my C
wire in with the other two wires, in that twist-on wire connector near the bottom of the photo.
![enter image description here](https://i.stack.imgur.com/UZziE.jpg)
Best Answer
The blue wire coming off of the transformer is what you want, but there might be a better place to tie into that. Look for any wires that are simply screwed to the metal chassis of the air handler. You can check with a continuity tester, but those chassis grounds are usually a connection for that other side of the transformer (the blue wire).
Looking at that schematic, I can see a few places where a wire terminates to "ground", but I don't necessarily see any terminals where the "C wire" would be conveniently exposed. Also, when you find a ground screw use a volt meter to make sure you get a good 24v there between the ground point and the red wire from the thermostat and/or transformer.