Dome on top of bridge bubble (TOS/TAS era)

[Kamen Rider Blade]

Later on in the nebula both ships are so crippled they could of done more damage by having guys outside in space suits firing phaser rifles at each othe

I would love to see that just for the LOLS

 

[Admiral Archer]

Back to the subject of the dome on the top of the bridge, in TOS I always just assumed it was meant to be a transparent metal ceiling (as hinted at by "The Cage") with no specific purpose. Basically a giant sun/moon roof. Not everything on a starship has to have a specific function, sometimes just being able to look up and see the stars would be cool.

 

[Mytran]

That's a massive engineering undertaking for "sometimes" though!
Personally (and coupled with the inside view seen in WNMHGB of the opaque ceiling) I think that the camera trickery in The Cage is just that - a visual gag to convey to the viewers the location and size of the Bridge in relation to the rest of the ship. We've seen this plenty of times before in comics and film - a section of the wall of a house or vessel is rendered invisible to the audience, so we can see what's going on inside.
It doesn't need to mean that there are suddenly "holes" in the wall!

 

[Admiral Archer]

I guess the window in the Enterprise-D bridge ceiling was what inspired me to think that the TOS Enterprise Bridge had the same thing. And I'm not alone: I've seen model makers who build the 1:350 scale Enterprise put a little bridge set inside the dome, and put a clear plastic dome on top where you can see inside.

It's also possible that the dome has two settings similar to the viewscreen: opaque and transparent.