Singer New Family 12 or 12k and Singer Improved Family 15.
Both of these machines are known as Fiddle base, as they have a curved base, unlike the later machines that have a rectangular base. The images below are of the machines as I found them “in the wild”. Slowly I am cleaning them and preserving their decals. Neither is perfect to look at, they both came in their original treadle tables. They both sew a straight stitch.
These are my oldest machines and more details can be found at ISMACS page The Singer Improved family.
2078448 377648 is 1875 , New Family 12
8193651 is 1888, Improved Family if15 (unlike most Singer machines, this serial number is found on the back of the machine.)
Side by side
The 12 series is much smaller than the IF 15.