This pattern is from The Comprehensive Knitting Book by Esther Copley, published in 1849. This is #19, Travelling Gaiter for a Lady. They are done all in garter stitch except for a ribbed section just below the knee.

At this point, I’m nearly finished with the first gaiter and it’s been very easy, much easier than the fancy gaiters from the 1857 Godey’s Lady’s Book. I have found one error in the pattern: The instructions say to cast off 20 then knit 32, while running over the instep, but there are only 50 stitches on the needle. I chose to cast off 20 and knit 30, and it looks like it worked just fine. (ETA: It worked out fine.)

The pattern doesn’t actually specify that it’s knit flat then seamed up the back, but it seems to be clear from the instructions.