It is always wise to keep ducts out of structural walls.

Renovator, I have absolutely no choice, as there is no continuous space through all three floors except the chimney flues--and the two ducts to the second floor are already IN the supporting wall in the center of the house. One of them branches off to supply the bath--that one would come up beneath the knee wall in the attic, which may have a joist under it.

"I'm assuming it is balloon-framed"

Do you you mean 1908?

"as there is no continuous space through all three floors except the chimney flues"

If the house is balloon framed the exterior walls will go from the top of the foundation to the roof with LONG studs all the way.
It is normally open all the way, and that is one of the fire risks of balloon framing. All those tall chimneys in the outside walls (and sometimes the inside bearing wall in the middle of the house).

"It is always wise to keep ducts out of structural walls."

It does not really make a lot of difference in residential framed houses, and ducts are routinely placed in bearing walls.
It is common in commercial, especially when the space will be finished out for a tenant anyway.

Brickeyee, on another page about permits. Perfect example, balloon framing. Fire stops, I doubt the diy's know anything about them or the difference in framing. The house I grew up in had 2 sets of duct work, one for heating and one for cooling. This house was built in 1905. Both systems were gravity fed, heat interior, cooling ex. Yes they were integrally fit into the structure. That was when people who knew what they were doing got paid to design a house. You know exactly what I mean.I am not an architect and I know you understand that.

I have some soffit like structures in various parts of the first and second floor of my 1837 post and beam house that were added to accomodate ductwork. If it weren't for the registers that appear here and there, I might not have noticed that they were functional, and not just an old-house quirk.