Pipe on (some) PRR steam locomotives

(I may post a related question to the PRR forum.)
A number of late PRR steam locomotives have a feature that I am curious about. A pipe -- diameter of, I guess, a few inches -- leaves the cab, near the front centre of the cab roof and slopes down and forward, entering the top of the boiler near the safety valves. I've seen this in the S2 turbine (the Lionel O-27 version is accurate at least in this!), and one of Stauffer's books has a photo of the boiler of the S1 "Big Engine" under construction: this photo is from before the boiler lagging was applied, and confirms that the pipe meets the boiler top near the safety valves. It was apparently something the PRR thought important: the C&O T1 2-10-4didn't have it, but when PRR modified that design for their own J1 2-10-4 they included it. But I haven't noticed it on any other railroad's steam power.
I assume it was a steam take-off for power to some cab (or otherwise rear end) equipment, but I don't have any clear idea what.
Does anybody here know?
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The Santa Fe also had a "proprietary" bit of boiler top tubing: several classes of big Santa Fe steam locomotives have a pair of pipes running from close to the mid-line of the front of the cab roof, parallel forward, looping around the safety valve turret, then ending a bit further forward. If anyone knows what they were, I'd love to hear THAT explanation as well.

If the pipe in question was "standard practice" for the Pennsylvania Railroad's steam designers in the final decade of steam construction, one would expect it on the T1... but no photo I have ever seen shows it. So maybe, I thought, it was missing because the T1 was a Baldwin design rather than Altoona one? But the design had to have been discussed and negotiated between BLW and the PRR before they were ordered, and surely Baldwin would have incorporated any details the PRR was really keen on...? (I have read, somewhere, that Baldwin would have preferred to build one of the T1 prototypes with piston valves -- for comparative purposes, at least -- but that the PRR, impressed by the performance of a K4 Pacific rebuilt with poppet valves, insisted that both be poppet equipped.) A puzzle...
BUT
when the T1 prototypes were new, "Railway Mechanical Engineer" published an article about them (February 1943), which was reprinted in fascicle #56 of the Newton K. Gregg "Train Shed Cyclopedia." The drawings (general and a more specific boiler drawing) have unexplained dotted lines and an unexplained apparent opening on the top of the boiler, tower the front of the combustion chamber. I SUSPECT that what they are meant to represent is that the T1 did have the cab-to-boiler pipe (the apparent opening in the boiler top being where the pipe inserted) but that it was hidden inside the skyline casing of the streamlining.

("Trains," a long time ago -- 1980s, maybe -- had a bunch of speculative drawings of what various streamlined steam locomotives would have looked like had they been built unstreamlines. The T1 was by far the weirdest. The shark nosed prow of the streamlining extends well forward of the smokebox: without it, the locomotive has an immense "front deck" in front of the boiler!)