Barnabas' inverness coat somehow made it to parallel time and 1897 though he was not wearing it at the time he sat down to do the I ching or when he entered the parallel time room. Julia when she came always seemed able to find her medical bag. The same is true for 1840.
Well, actually, his coat DIDN'T make it to 1897, he had a different Inverness. Remember, it had a different collar. But it DID somehow get to PT. I like to think that it got to PT this way--Julia, knowing he was in that time w/out his coat went and got it, presumably from the downstairs foyer coat rack, placed it into the room, the room changed and voila! The coat was there! Sorta like a transporter if you will. And who knows, maybe Stokes did the same for her medical bag!
when Barnabas becomes a bat and rematerializes as a man, he does so in his coat with his cane. How is it that he is able to carry these things when he is a bat?
There's a REALLY funny Sherlock cartoon out there where he's in bat form, has his coat, ring and cane as he's flying around and the bat says, "Figure it out!"