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So I've been working on restoring my grandpas 73 F100 for a couple years now. Anyways its been awhile since I took things apart and like a ******* I didn't take pictures, and now that I have the time to put it back together I'm struggling to remember just how it went. I need to re-install the rebuilt transmission (NP435), transfer case (Dana 21) and transfer case adaptor. My main problem is I dont remember how the seals went in the adaptor. I had a local shop rebuild the transmission for me and in there kit were the seals for the adaptor. I believe I'm correct in thinking there is a seal where it bolts to the transmission, and an inner seal that fits around the spud shaft. Is there a seal where it connects to the transfer case? I can upload pictures later.
If it were me, I'd take the parts to the shop that rebuilt the trans and ask them to show you how to install them.
You may not get the correct answer here.
Generally speaking when it comes to seals is that the side of the seal that has the compression spring to keep tension around whatever shaft it is sealing, will go to the inside to keep the gear oil or whatever fluid inside the "case" of whatever it is trying seal. I recently rebuilt my T18 and NP205 so I do not have pictures that will match your set up exactly. On the adapter housing the rear output seal for the transmission was installed "backwards" into the adapter housing that bolts to the back of the transmission. On the transfer case side there was a double lipped seal that could go in either direction. From factory on the transfer case side there were two single lipped seals that were stacked together. I'll post pictures below, I hope they help.
arrow pointing to the compression spring I am speaking of. This is the transmission side of the tail shaft housing What it looks like when bolted to transmission arrow pointing to "double lip" seal, from factory there were two seals, the first seal was installed with compression spring towards transfer case, and the outer seal was installed with compression spring facing towards transmission.