My pet theory, touched on by Chuck (B/R) is that 26tpi is a Yankee-ization of what was probably a (nominal) 1mm pitch on the French arms, which we basically copied verbatim when setting up our "standards" in the late 1790s.

Wouldn't have taken much, given the non-interchangeable (pre-John Hall) standards, and measuring capabilities of the time to have either misread the dimension, or simply decided that an even 26 was "close enough" to 25.4 to work just fine for our new patterns.

Anyhow, that's my story (for which I charge nothing) and I'm sticken' to it until definite proof of another source is shown. :)