Small photos c. 1919 1.75 X 2.75 prints

The format 1.75" x 2.75" sounds like the wallet print format. I believe it is still being used for small pictures in key rings etc.

I don't think that it is necessarily a format used by a camera. It is most likely a scaled down (or even cropped) print of a more common format like 2 x 3 or 3 x 4.

Most amateur and "consumer" photographs from the pre-1920 era were contact prints. The size you cite is what you'd expect (with allowance for a slight crop by the printing frame) for size 129 roll film (produced 1912-1951), which would have fit a Houghton Ensignette #E2. Like most of the "off size" roll film formats, this one didn't catch on the way 120 and 127 did.

It's also possible (if your measurement included a white print border) that it might originate from 121 film, 1902-1941, or 127, which originated in 1912 -- the "full frame" format of 127 is 4x6 cm, or about 1 5/8 x 2 3/8 inches (actual image area), while 121 appears to be the same width, but (like 120) may not have originally had framing numbers for multiple formats (127 had "full frame", square, and "half frame" just as 120 did). I don't have a reference to what cameras used 121, but it seems the difference from 127 may have been only the location of the ruby window. For 127, on the other hand, there were dozens of choices (some very good) early enough to travel with troops serving in the Great War (aka WWI).

Houghton made many very good cameras, ranging from view cameras starting in the 1890s through various folding roll film cameras (Ensign Commando, 1945-1951, was one of only two models ever offered, anywhere, of folding roll film cameras with film plane movement for focusing rather than lens movement or change in focal length of the lens).